Tootfinder

Pair state transfer in tensor product and double cover
Ming Jiang, Xiaogang Liu, Jing Wang
https://arxiv.org/abs/2509.18858 https://arxiv.org/pdf/2509.1885…

Non-negligible summands in tensor powers of some modular representations of finite $p$-groups
Kent B. Vashaw, Justin Zhang
https://arxiv.org/abs/2508.15730 https://

Non-negligible summands in tensor powers of some modular representations of finite $p$-groups
Let $p>0$ be a prime, $G$ be a finite $p$-group and $\Bbbk$ be an algebraically closed field of characteristic $p$. Dave Benson has conjectured that if $p=2$ and $V$ is an odd-dimensional indecomposable representation of $G$ then all summands of the tensor product $V \otimes V^*$ except for $\Bbbk$ have even dimension. It is known that the analogous result for general $p$ is false. In this paper, we investigate the class of graded representations $V$ which have dimension coprime to $p$ and for …

Matrix-Free Evaluation of High-Order Shifted Boundary Finite Element Operators
Micha{\l} Wichrowski
https://arxiv.org/abs/2507.17053 https://arxiv.org/pdf/…

Matrix-Free Evaluation of High-Order Shifted Boundary Finite Element Operators
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary conditions to nearby surrogate boundaries. We focus on the efficient evaluation of shifted boundary operators using precomputed data and tensor-product structures. The proposed method avoids the explicit assembly of global matrices, achieving a computational…

Strategies for Cantor games and Operator systems
Georgios Baziotis, Alexandros Chatzinikolaou, Ivan G. Todorov, Lyudmila Turowska
https://arxiv.org/abs/2509.18028 https://

Strategies for Cantor games and Operator systems
We study no-signalling correlations over Cantor spaces, placing the product of infinitely many copies of a finite non-local game in a unified general setup. We define the subclasses of local, quantum spatial, approximately quantum and quantum commuting Cantor correlations and describe them in terms of states on tensor products of inductive limits of operator systems. We provide a correspondence between no-signalling (resp. approximately quantum, quantum commuting) Cantor correlations and sequen…

Quantum-electrodynamical time-dependent density functional theory description of molecules in optical cavities
Yetmgeta Aklilu, Matthew Shepherd, Cody L. Covington, Kalman Varga
https://arxiv.org/abs/2509.19036

Had a great time presenting our paper “Domain-specific tensor languages” today at #ICFP2025 in Singapore 🇸🇬
The images attached are screenshots from the paper as teasers — diagrams for derivative rules, the Riemann curvature 4-tensor in Einstein’s index notation, and the same in diagram form.
📄 Slides:

Ideal Spaces of the Haagerup Tensor Product of Ternary Rings of Operators
Vandana Rajpal, Arpit Kansal
https://arxiv.org/abs/2508.12367 https://arxiv.org/p…

Ideal Spaces of the Haagerup Tensor Product of Ternary Rings of Operators
We characterize the primal, factorial, and Glimm ideals of the Haagerup tensor product $V\otimes^{h} B$ of a TRO $V$ and a $C^{\ast}$-algebra $B$.

Line Operators in 3d Holomorphic QFT: Meromorphic Tensor Categories and dg-Shifted Yangians
Tudor Dimofte, Wenjun Niu, Victor Py
https://arxiv.org/abs/2508.11749 https://…

Line Operators in 3d Holomorphic QFT: Meromorphic Tensor Categories and dg-Shifted Yangians
We study line operators and their OPE's in perturbative 3d holomorphic-topological QFT's, including holomorphic-topological twists (quarter-BPS sectors) of 3d $N=2$ theories. In particular, we develop the representation theory of the category $C$ of perturbative line operators and its chiral tensor product, by generalizing techniques introduced by Costello and collaborators. We argue that lines are equivalent to modules for an $A_\infty$ algebra $A^!$ that's Koszul-dual to bulk local operators.…

The tensor product of p-adic Hilbert spaces
Paolo Aniello, Lorenzo Guglielmi, Stefano Mancini, Vincenzo Parisi
https://arxiv.org/abs/2510.07504 https://arx…

The tensor product of p-adic Hilbert spaces
In the framework of quantum mechanics over a quadratic extension of the ultrametric field of p-adic numbers, we introduce a notion of tensor product of p-adic Hilbert spaces. To this end, following a standard approach, we first consider the algebraic tensor product of p-adic Hilbert spaces. We next define a suitable norm on this linear space. It turns out that, in the p-adic framework, this norm is the analogue of the projective norm associated with the tensor product of real or complex normed …

On definability of C*-tensor norms
Isaac Goldbring, Thomas Sinclair
https://arxiv.org/abs/2509.15086 https://arxiv.org/pdf/2509.15086

On definability of C*-tensor norms
We initiate the study of definability (in the model-theoretic sense) of C*-tensor norms. We show that neither the minimal nor maximal tensor norms are definable uniformly over all C*-algebras. The proof in the case of the minimal tensor product norm uses a deep theorem of Kirchberg characterizing exactness in terms of tensor products with matrix ultraproducts while the case of maximal tensor products uses Pisier's recent characterization of the lifting property in terms of maximal tensor produc…

Succinct Oblivious Tensor Evaluation and Applications: Adaptively-Secure Laconic Function Evaluation and Trapdoor Hashing for All Circuits
Damiano Abram, Giulio Malavolta, Lawrence Roy
https://arxiv.org/abs/2508.09673

Succinct Oblivious Tensor Evaluation and Applications: Adaptively-Secure Laconic Function Evaluation and Trapdoor Hashing for All Circuits
We propose the notion of succinct oblivious tensor evaluation (OTE), where two parties compute an additive secret sharing of a tensor product of two vectors $\mathbf{x} \otimes \mathbf{y}$, exchanging two simultaneous messages. Crucially, the size of both messages and of the CRS is independent of the dimension of $\mathbf{x}$. We present a construction of OTE with optimal complexity from the standard learning with errors (LWE) problem. Then we show how this new technical tool enables a host o…

Quantum Circuit Complexity of Matrix-Product Unitaries
Georgios Styliaris, Rahul Trivedi, J. Ignacio Cirac
https://arxiv.org/abs/2508.08160 https://arxiv.o…

Quantum Circuit Complexity of Matrix-Product Unitaries
Matrix-product unitaries (MPUs) are many-body unitary operators that, as a consequence of their tensor-network structure, preserve the entanglement area law in 1D systems. However, it is unknown how to implement an MPU as a quantum circuit since the individual tensors describing the MPU are not unitary. In this paper, we show that a large class of MPUs can be implemented with a polynomial-depth quantum circuit. For an $N$-site MPU built from a repeated bulk tensor with open boundary, we explici…

Cohomological Calibration and Curvature Constraints on Product Manifolds: A Topological Lower Bound
Alexander Pigazzini, Magdalena Toda
https://arxiv.org/abs/2509.11834 https://…

Cohomological Calibration and Curvature Constraints on Product Manifolds: A Topological Lower Bound
We establish a quantitative relationship between mixed cohomology classes and the geometric complexity of cohomologically calibrated metric connections with totally skew torsion on product manifolds. Extending the results of Pigazzini--Toda (2025), we show that the dimension of the off-diagonal curvature subspace of a connection $\nabla^C$ is bounded below by the sum of tensor ranks of the mixed Künneth components of its calibration class. The bound depends only on the mixed class $[ω]_{\math…

Computing Exchange Coupling constants in Transition metal complexes with Tensor Product Selected Configuration Interaction
Arnab Bachhar, Nicholas J. Mayhall
https://arxiv.org/abs/2508.13002

Computing Exchange Coupling constants in Transition metal complexes with Tensor Product Selected Configuration Interaction
Transition metal complexes present significant challenges for electronic structure theory due to strong electron correlation arising from partially filled $d$-orbitals. We compare our recently developed Tensor Product Selected Configuration Interaction (TPSCI) with Density Matrix Renormalization Group (DMRG) for computing exchange coupling constants in six transition metal systems, including dinuclear Cr, Fe, and Mn complexes and a tetranuclear Ni-cubane. TPSCI uses a locally correlated tensor …

The ideal structure of the minimal Tensor Product of Ternary Rings of Operators
Vandana Rajpal, Arpit Kansal
https://arxiv.org/abs/2508.12374 https://arxiv…

The ideal structure of the minimal Tensor Product of Ternary Rings of Operators
Let \( V \) be a ternary ring of operator and \( B \) a \( C^* \)-algebra. We study the structure of the ideal space of the operator space injective tensor product \( V \otimes^{\mathrm{tmin}} B \) via two maps: \[ Φ(I, J) = \ker(q_I \otimes^{\mathrm{tmin}} q_J) \quad \text{and} \quad Δ(I, J) = I \otimes^{\mathrm{tmin}} B + V \otimes^{\mathrm{tmin}} J. \] We show that \( Φ\) is continuous with respect to the hull-kernel topology, and that its restriction to primitive and prime ideals defines…

Sum-of-Gaussians tensor neural networks for high-dimensional Schr\"odinger equation
Qi Zhou, Teng Wu, Jianghao Liu, Qingyuan Sun, Hehu Xie, Zhenli Xu
https://arxiv.org/abs/2508.10454

Sum-of-Gaussians tensor neural networks for high-dimensional Schrödinger equation
We propose an accurate, efficient, and low-memory sum-of-Gaussians tensor neural network (SOG-TNN) algorithm for solving the high-dimensional Schrödinger equation. The SOG-TNN utilizes a low-rank tensor product representation of the solution to overcome the curse of dimensionality associated with high-dimensional integration. To handle the Coulomb interaction, we introduce an SOG decomposition to approximate the interaction kernel such that it is dimensionally separable, leading to a tensor re…

Completely Positive Biquadratic Tensors
Liqun Qi, Chunfeng Cui, Haibin Chen, Yi Xu
https://arxiv.org/abs/2510.10972 https://arxiv.org/pdf/2510.10972…

Completely Positive Biquadratic Tensors
In this paper, we systemically introduce completely positive biquadratic (CPB) tensors and copositive biquadratic tensors. We show that all weakly CPB tensors are sum of squares tensors, the CPB tensor cone and the copositive biquadratic tensor cone are dual cone to each other. We also show that the outer product of two completely positive matrices is a CPB tensor, and the outer product of two copositive matrices is a copositive biquadratic tensor. We then study two easily checkable subclasses …

Higher-Form Anomalies on Lattices
Yitao Feng, Ryohei Kobayashi, Yu-An Chen, Shinsei Ryu
https://arxiv.org/abs/2509.12304 https://arxiv.org/pdf/2509.12304…

Higher-Form Anomalies on Lattices
Higher-form symmetry in a tensor product Hilbert space is always emergent: the symmetry generators become genuinely topological only when the Gauss law is energetically enforced at low energies. In this paper, we present a general method for defining the 't Hooft anomaly of higher-form symmetries in lattice models built on a tensor product Hilbert space. In (2+1)D, for given Gauss law operators realized by finite-depth circuits that generate a finite 1-form $G$ symmetry, we construct an index r…

Category Theory for Supercomputing: The Tensor Product of Linear BSP Algorithms
Thomas Koopman, Rob H. Bisseling, Sven-Bodo Scholz
https://arxiv.org/abs/2510.00979 https://

Category Theory for Supercomputing: The Tensor Product of Linear BSP Algorithms
We show that a particular class of parallel algorithm for linear functions can be straightforwardly generalized to a parallel algorithm of their tensor product. The central idea is to take a model of parallel algorithms -- Bulk Synchronous Parallel (BSP) -- that decomposes parallel algorithms into so-called supersteps that are one of two types: a computation superstep that only does local computations, or a communication superstep that only communicates between processors. We connect each type …

Tensor Products with Verma Module and Restriction to Parabolic Subalgebra
Antoine Merceron
https://arxiv.org/abs/2509.14220 https://arxiv.org/pdf/2509.1422…

Tensor Products with Verma Module and Restriction to Parabolic Subalgebra
Using the tensor identity, we obtain decomposition results for the tensor product of a generalized Verma module with a module $M$ in the category $\mathcal{O}^{\mathfrak{p}}$, based on the decomposition of the restriction of $M$ to the parabolic subalgebra $\mathfrak{p}$. We show that this restriction admits an essentially unique decomposition into indecomposable $\mathfrak{p}$-modules and identify two particular types of direct summands: finite-dimensional quotients and tilting submodules. Fin…

Tensor Forms of Derivatives of Matrices and their applications in the Solutions to Differential Equations
Yiran Xu, Guangbin Wang, Changqing Xu
https://arxiv.org/abs/2509.08429 …

Tensor Forms of Derivatives of Matrices and their applications in the Solutions to Differential Equations
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of derivatives of a matrix w.r.t. another matrix. This tensor form makes possible for us to unify ordinary differential equations (ODEs) with partial differential equations (PDEs), and facilitates solution to them in some cases. For our purpose, we also extend the outer …

An Image Noise Level Estimation Based on Tensor T-Product
Hanxin Liu, Yisheng Song
https://arxiv.org/abs/2507.20515 https://arxiv.org/pdf/2507.20515…

An Image Noise Level Estimation Based on Tensor T-Product
Currently, the noise level of color images is estimated by many algorithms through separate selection of each page of the third-order tensor using sliding blocks of size ${M_1} \times {M_1}$. The data structure of the tensor is disrupted by this method, leading to errors in the estimation results. In order not to disrupt the data structure of the tensor, we directly select the tensor using a sliding block of size ${M_1} \times {M_1} \times 3$ and then re-arrange it. The newly obtained tensor is…

A tensor-based dynamic mode decomposition based on the $\star_{\boldsymbol{M}}$-product
Arvind K. Saibaba, Misha E. Kilmer, Khalil Hall-Hooper, Fan Tian, Alex Mize
https://arxiv.org/abs/2508.10126

A tensor-based dynamic mode decomposition based on the $\star_{\boldsymbol{M}}$-product
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors. Specifically, we use the $\star_{\boldsymbol{M}}$-product framework for tensor decompositions which we demonstrate offers excellent compression compared to matrix-based methods and can be implemented in a computationally efficient manner. We show how the proposed appr…

Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology
Diogo Andrade, Julia Bierent, Jennifer Brown, Tudor Caba, Matthew Cellot, Jonathan Davies, Adrien DeLazzer Meunier, Jannik Gr\"one, Benjamin Ha\"ioun, Alea Hofstetter, Theo Johnson-Freyd, David Jordan, Tessa Kammermeier, Patrick Kinnear, Cameron Krulewski, Theodoros Lagiotis, Leon Liu, Adri\`a Mar\'in Salvador, Nivedita, David Reutter, Lorenzo Riva, Iordanis Romaidis, Ja…

Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology
These lecture notes are the product of a week-long learning workshop on the work of Johnson-Freyd and Reutter on the problem of the existence of minimal nondegenerate extensions of braided fusion categories (arXiv:2105.15167). They recount the mathematical arguments of the original paper from an expository angle, with background material covering the algebra and homotopy theory required to understand the statement and follow the proof. The notes are aimed at newcomers to the field of (braided) …

Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture
Pan Yan
https://arxiv.org/abs/2508.09066 https://

Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture
We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,π\timesτ_1) L^S(s,π\timesτ_2)\cdots L^S(s,π\timesτ_r) \end{equation*} where $π$ is an irreducible cuspidal automorphic representation of a quasi-split $\mathrm{GSpin}$ group, and $τ_1, \cdots, τ_r$ are irreducible unitary cuspidal automorphic representations of $\mathrm{GL}_{k_1}, \cdots, \mathrm{GL}_{k_r}$ respectively. As an application, we prove one…

Light-induced nonlinear Edelstein effect under ferroaxial ordering
Akimitsu Kirikoshi, Satoru Hayami
https://arxiv.org/abs/2509.14241 https://arxiv.org/pdf…

Light-induced nonlinear Edelstein effect under ferroaxial ordering
Ferroaxial ordering, a spontaneous rotational distortion of the atomic arrangement, brings about a cross-product-type spin--orbit coupling (SOC) manifested as an electric toroidal dipole. We propose the light-induced nonlinear Edelstein effect (NLEE) -- a second-order optical response in which a static magnetization is induced by a time-dependent electric field -- as a promising probe of ferroaxial ordering. First, we elucidate the relationship between the NLEE tensor and the electric toroidal …

Geometric Construction of Quiver Tensor Products
Daigo Ito, John S. Nolan
https://arxiv.org/abs/2510.05277 https://arxiv.org/pdf/2510.05277

Geometric Construction of Quiver Tensor Products
By a classic theorem of Beilinson, the perfect derived category $\operatorname{Perf}(\mathbb{P}^n)$ of projective space is equivalent to the category of derived representations of a certain quiver with relations. The vertex-wise tensor product of quiver representations corresponds to a symmetric monoidal structure $\otimes_{\mathsf{Q}}$ on $\operatorname{Perf}(\mathbb{P}^n)$. We prove that, for a certain choice of equivalence, the symmetric monoidal structure $\otimes_{\mathsf{Q}}$ may be descr…

The logic of quantum mechanics
Eric Buffenoir
https://arxiv.org/abs/2510.12502 https://arxiv.org/pdf/2510.12502

The logic of quantum mechanics
The quantum logic program originated in a 1936 article by G. Birkhoff and J. von Neumann. This program is generally disregarded due to no-go theorems restricting the existence of the tensor product of elementary quantum logics and, above all, the impossibility of considering entangled states and Bell non-local states within the framework of these composite quantum logics. We revisit this study from the beginning and reverse the perspective. Here, the existence of a tensor product and a star inv…

Towards fairer public transit: Real-time tensor-based multimodal fare evasion and fraud detection
Peter Wauyo, Dalia Bwiza, Alain Murara, Edwin Mugume, Eric Umuhoza
https://arxiv.org/abs/2510.02165

Towards fairer public transit: Real-time tensor-based multimodal fare evasion and fraud detection
This research introduces a multimodal system designed to detect fraud and fare evasion in public transportation by analyzing closed circuit television (CCTV) and audio data. The proposed solution uses the Vision Transformer for Video (ViViT) model for video feature extraction and the Audio Spectrogram Transformer (AST) for audio analysis. The system implements a Tensor Fusion Network (TFN) architecture that explicitly models unimodal and bimodal interactions through a 2-fold Cartesian product. …

Oriented Category Theory
David Gepner, Hadrian Heine
https://arxiv.org/abs/2510.10504 https://arxiv.org/pdf/2510.10504

Oriented Category Theory
We develop foundations for oriented category theory, an extension of $(\infty,\infty)$-category theory obtained by systematic usage of the Gray tensor product, in order to study lax phenomena in higher category theory. As categorical dimension increases, classical category-theoretic concepts generally prove too rigid or fully break down and must be replaced by oriented versions, which allow more flexible notions of naturality and coherence. Oriented category theory provides a framework to addre…

Koszul dual $\mathcal{A}_{\infty}$-algebras from star-shaped diagrams -- part 2
Isabella Khan
https://arxiv.org/abs/2510.12575 https://arxiv.org/pdf/2510.1…

Koszul dual $\mathcal{A}_{\infty}$-algebras from star-shaped diagrams -- part 2
This paper proves a Koszul duality result between weighted $\mathcal{A}_{\infty}$-algebras constructed in the author's previous work. In the process, we construct a new box tensor product for weighted $\mathcal{A}_{\infty}$ bimodules, and verify a correspondence between weighted $\mathcal{A}_{\infty}$-algebra maps and a particular class of $\mathcal{A}_{\infty}$-bimodule. This paper is part 2 of arXiv:2408.01564.

Brushstrokes and Tensor Products: Painting with a Monoidal Category
Khyathi Komalan
https://arxiv.org/abs/2508.05482 https://arxiv.org/pdf/2508.05482

Brushstrokes and Tensor Products: Painting with a Monoidal Category
This article offers an intuitive introduction to monoidal categories through the lens of painting, presenting abstract mathematical concepts with visual and tactile analogies. Aimed at curious undergraduates and non-specialists, it seeks to demystify category theory by showing how ideas like the tensor product, associators, and braidings can be understood as compositional tools on a canvas.

Types of graded tensor products of graded von Neumann algebras
Jumpei Tanaka
https://arxiv.org/abs/2508.10084 https://arxiv.org/pdf/2508.10084

Types of graded tensor products of graded von Neumann algebras
There is a famous multiplication table of types of tensor product of two von Neumann algebras. We filled out the multiplication table of graded tensor product of two graded von Neumann algebras in special cases.

An $N$-independent tensor decomposition for SU($N$)
Stefan Keppeler, Malin Sjodahl, Bernanda Telalovic
https://arxiv.org/abs/2507.22981 https://arxiv.org/p…

An $N$-independent tensor decomposition for SU($N$)
To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an $N$-independent reduction of SU($N$) tensor products. To this end, we label each irreducible representation by a pair of Young diagrams, with parts acting on quarks and antiquarks. By combining this with a column-wise multiplication of Young diagrams, we generalize the Littlewood-Richardson rule for the product of two Young diagrams to the prod…

Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation
Qiaohua Liu, Jiehui Gu
https://arxiv.org/abs/2508.08557 https://arxiv…

Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation
Color images and video sequences can be modeled as three-way tensors, which admit low tubal-rank approximations via convex surrogate minimization. This optimization problem is efficiently addressed by tensor singular value thresholding (t-SVT). To mitigate the computational burden of tensor singular value decomposition (t-SVD) in each iteration, this paper introduces an adaptive randomized algorithm for tubal rank revelation in data tensors \(\mathcal{A}\). Our method selectively captures the p…

Forall-Exists Relational Verification by Filtering to Forall-Forall
Ramana Nagasamudram, Anindya Banerjee, David A. Naumann
https://arxiv.org/abs/2509.04777 https://

Forall-Exists Relational Verification by Filtering to Forall-Forall
Relational verification encompasses research directions such as reasoning about data abstraction, reasoning about security and privacy, secure compilation, and functional specificaton of tensor programs, among others. Several relational Hoare logics exist, with accompanying tool support for compositional reasoning of $\forall\forall$ (2-safety) properties and, generally, k-safety properties of product programs. In contrast, few logics and tools exist for reasoning about $\forall\exists$ propert…

Diagonalizing large-scale quantum many-body Hamiltonians using variational quantum circuit and tensor network
Peng-Fei Zhou, Shuang Qiao, An-Chun Ji, Shi-Ju Ran
https://arxiv.org/abs/2508.06159

Diagonalizing large-scale quantum many-body Hamiltonians using variational quantum circuit and tensor network
Exact diagonalization (ED) is an essential tool for exploring quantum many-body physics but is fundamentally limited by the exponentially-scaled computational complexity. Here, we propose tensor network variational diagonalization (TNVD), which encodes the full eigenenergy spectrum of a quantum many-body Hamiltonian into a matrix product state, and encodes the eigenstates as the evolutions of product states using variational quantum circuit (VQC). Thereby, TNVD reduces the computational complex…

Weak Centrality for Certain Tensor Products of $C^\ast$-algebras
Anmol Paliwal, Ranjana Jain
https://arxiv.org/abs/2508.08838 https://arxiv.org/pdf/2508.08…

Weak Centrality for Certain Tensor Products of $C^\ast$-algebras
In this article, we discuss the weak centrality of the tensor product $A\otimes_αB$ of $C^\ast$-algebras $A$ and $B$ in terms of the weak centrality of $A$ and $B$, where $α$ is either the Haagerup or the Banach space projective tensor product. In the due course, we also identify the largest weakly central ideal of $A\otimes_αB$ in certain cases. Centralilty and quasi-centrality of these tensor products are also discussed.

Duality Structures in Unimodular Electrovacuum Gravity
Jack C. M. Hughes, Fedor V. Kusmartsev
https://arxiv.org/abs/2510.03048 https://arxiv.org/pdf/2510.0…

Duality Structures in Unimodular Electrovacuum Gravity
We show that the structure of the Lorentz group in four dimensions is such that unimodular (trace-free) gravity in electrovacuum can be consistently represented as an algebraic condition on the symmetric product space of 2-forms. This condition states that the commutator between the Riemann tensor and the Hodge dual must be equal to the commutator between Hodge dual and an operator constructed from the Maxwell tensor; symbolically, $[\text{Riem}, \star] = [\star, F \boxtimes F]$. We show that t…

Categorical Continuous Symmetry
Qiang Jia, Ran Luo, Jiahua Tian, Yi-Nan Wang, Yi Zhang
https://arxiv.org/abs/2509.13170 https://arxiv.org/pdf/2509.13170

Categorical Continuous Symmetry
We define the symmetry category in 1+1d for continuous 0-form $G$-symmetry to be $\textbf{Sky}^τ(G)$, the category of skyscraper sheaves of finite dimensional vector spaces with finite support on the group manifold of $G$, where $τ\in H^4(BG,\mathbb{Z})$ is the anomaly. We propose that the corresponding 2+1d SymTFT is described by the Drinfeld center of $\textbf{Sky}^τ(G)$. We show explicitly the way that $τ$ twists the convolution tensor product of the objects of $\textbf{Sky}^τ(G)$. As a…

Prime Factorization Equation from a Tensor Network Perspective
Alejandro Mata Ali, Jorge Mart\'inez Mart\'in, Sergio Mu\~niz Subi\~nas, Miguel Franco Hernando, Javier Sedano, \'Angel Miguel Garc\'ia-Vico
https://arxiv.org/abs/2508.00907

Prime Factorization Equation from a Tensor Network Perspective
This paper presents an exact and explicit equation for prime factorization, along with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which addresses combinatorial optimization problems through classical tensor networks. The presented tensor network performs the multiplication of every pair of possible input numbers and selects those whose product is the number to be factorized. Additionally, in order to make the algorithm more efficient, the number an…

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[4/5]:
- Tensor Product Neural Networks for Functional ANOVA Model
Seokhun Park, Insung Kong, Yongchan Choi, Chanmoo Park, Yongdai Kim

Efficient and accurate tensor network algorithm for Anderson impurity problems
Zhijie Sun, Zhenyu Li, Chu Guo
https://arxiv.org/abs/2510.11459 https://arxi…

Efficient and accurate tensor network algorithm for Anderson impurity problems
The Anderson impurity model (AIM) is of fundamental importance in condensed matter physics to study strongly correlated effects. However, accurately solving its long-time dynamics still remains a great numerical challenge. An emergent and rapidly developing numerical strategy to solve the AIM is to represent the Feynman-Vernon influence functional (IF), which encodes all the bath effects on the impurity dynamics, as a matrix product state (MPS) in the temporal domain. The computational cost of …

Transition Matrices between Plethystic Bases of Polysymmetric Functions via Bijective Methods
Aditya Khanna
https://arxiv.org/abs/2510.12723 https://arxiv.…

Transition Matrices between Plethystic Bases of Polysymmetric Functions via Bijective Methods
Many identities involving symmetric functions can be proved through bijective manipulations of tableaux. In this paper, we prove identities involving polysymmetric functions through bijections and sign-reversing involutions. In their paper titled "Polysymmetric functions and motivic measures of configuration spaces", Asvin G and Andrew O'Desky introduced the algebra of polysymmetric functions (PSym) which can be defined as the tensor product of copies of the symmetric functions algebra (Sym) wh…

Generalized quantum Chernoff bound
Kun Fang
https://arxiv.org/abs/2508.12889 https://arxiv.org/pdf/2508.12889

Generalized quantum Chernoff bound
We establish a generalized quantum Chernoff bound for the discrimination of multiple sets of quantum states, thereby extending the classical and quantum Chernoff bounds to the general setting of composite and correlated quantum hypotheses. Specifically, we consider the task of distinguishing whether a quantum system is prepared in a state from one of several convex, compact sets of quantum states, each of which may exhibit arbitrary correlations. Assuming their stability under tensor product, w…

Decomposition Theorem for Product of Fundamental Crystals in Monomial Realization of type $C_n$
Manal Alshuqayr, Toshiki Nakashima
https://arxiv.org/abs/2507.21444 https://

Decomposition Theorem for Product of Fundamental Crystals in Monomial Realization of type $C_n$
We consider a product of fundamental crystals of type $C_n$ in monomial realization, where the product means a natural product of Laurent monomials, not a tensor product. Then we shall show that the product still holds a crystal structure and describe how it is decomposed into irreducible crystals, which is, in general, different from the decomposition rule for the tensor product of the fundamental crystals.

Bayesian Neural Networks for Functional ANOVA model
Seokhun Park, Choeun Kim, Jihu Lee, Yunseop Shin, Insung Kong, Yongdai Kim
https://arxiv.org/abs/2510.00545 https://

Bayesian Neural Networks for Functional ANOVA model
With the increasing demand for interpretability in machine learning, functional ANOVA decomposition has gained renewed attention as a principled tool for breaking down high-dimensional function into low-dimensional components that reveal the contributions of different variable groups. Recently, Tensor Product Neural Network (TPNN) has been developed and applied as basis functions in the functional ANOVA model, referred to as ANOVA-TPNN. A disadvantage of ANOVA-TPNN, however, is that the compone…

A Low-Rank tensor framework for THB-Splines
Tom-Christian Riemer, Martin Stoll
https://arxiv.org/abs/2509.09434 https://arxiv.org/pdf/2509.09434

A Low-Rank tensor framework for THB-Splines
We introduce a low-rank framework for adaptive isogeometric analysis with truncated hierarchical B-splines (THB-splines) that targets the main bottleneck of local refinement: memory- and time-intensive matrix assembly once the global tensor-product structure is lost. The method interpolates geometry-induced weight and source terms in separable spline spaces and computes their tensor-train (TT) representations via the alternating minimal energy (AMEn) solver, enabling level-wise assembly of syst…

Way-below Relation and Tensor Products
Cristian Ivanescu, Hunter Labrecque
https://arxiv.org/abs/2510.11947 https://arxiv.org/pdf/2510.11947

Way-below Relation and Tensor Products
We establish the preservation of the way-below relation with respect to the tensor product.

Crosslisted article(s) found for cs.CC. https://arxiv.org/list/cs.CC/new
[1/1]:
- Derandomised tensor product gap amplification for quantum Hamiltonians
Thiago Bergamaschi, Tony Metger, Thomas Vidick, Tina Zhang

Tomography-assisted noisy quantum circuit simulator using matrix product density operators
Wei-guo Ma, Yun-Hao Shi, Kai Xu, Heng Fan
https://arxiv.org/abs/2508.07610 https://

Tomography-assisted noisy quantum circuit simulator using matrix product density operators
In recent years, efficient quantum circuit simulations incorporating ideal noise assumptions have relied on tensor network simulators, particularly leveraging the matrix product density operator (MPDO) framework. However, experiments on real noisy intermediate-scale quantum (NISQ) devices often involve complex noise profiles, encompassing uncontrollable elements and instrument-specific effects such as crosstalk. To address these challenges, we employ quantum process tomography (QPT) techniques …

Rigged Hilbert Space Formulation of Quantum Thermo Field Dynamics and Mapping to Rigged Liouville Space
Junichi Takahashi, Shousuke Ohmori
https://arxiv.org/abs/2508.06923 https…

Rigged Hilbert Space Formulation of Quantum Thermo Field Dynamics and Mapping to Rigged Liouville Space
The rigged Hilbert space, a triplet extension of the Hilbert space, provides a mathematically rigorous foundation for quantum mechanics by extending the Hilbert space to accommodate generalized eigenstates. In this paper, we construct a triplet structure for the thermal space arising in Thermo Field Dynamics with the aid of the tensor product formulation of rigged Hilbert spaces, a formalism that reformulates thermal averages as pure-state expectation values in a doubled Hilbert space. We then …

General Learning of the Electric Response of Inorganic Materials
Bradley A. A. Martin, Alex M. Ganose, Venkat Kapil, Keith T. Butler
https://arxiv.org/abs/2508.17870 https://

General Learning of the Electric Response of Inorganic Materials
We present MACE-Field, a field-aware $O(3)$-equivariant interatomic potential that provides a compact, derivative-consistent route to dielectric properties (such as polarisation $\mathbf P$, Born effective charges $Z^*$ and polarisability $\boldsymbolα$) and finite-field simulations across chemistry for inorganic solids. A uniform electric field is injected within each message-passing layer via a Clebsch-Gordan tensor-product which couples the field to latent spherical-tensor features, and per…

On the spectrum of the symmetric tensor products of certain Hilbert-space operators
Yuchi Yang, Yuanhang Zhang
https://arxiv.org/abs/2509.07374 https://arx…

On the spectrum of the symmetric tensor products of certain Hilbert-space operators
This paper primarily investigates spectral properties of symmetric tensor products of Hilbert-space operators. For a unilateral weighted shift operator $S_w$, we present an algorithm to compute the point spectrum of its symmetric and antisymmetric tensor products with the adjoint $S_w^*$. Additionally, we analyze the symmetric tensor product of an injective unilateral weighted shift $S_α$ and a diagonal operator $M$ on $l^2$, demonstrating that its point spectrum must be contained in $\{0\}$.

Tensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting
Laura Estivalez, Adriano Moura
https://arxiv.org/abs/2510.04697 h…

Tensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting
We express the outer multiplicities in the tensor products of two fundamental simple modules for an affine Kac-Moody algebra of type $A$ in terms of counting certain sets of multipartitions by exploring the stabilizing limits of certain excellent filtrations. This extends for all ranks a previously obtained result by Jakelić and the second author for rank $1$. The same outer multiplicities were previously computed by Misra and Wilson in terms of counting certain sets of tableaux. By comparing …

Holographic Correlators from Thermal Bootstrap
Ilija Buri\'c, Ivan Gusev, Andrei Parnachev
https://arxiv.org/abs/2508.08373 https://arxiv.org/pdf/2508.…

Holographic Correlators from Thermal Bootstrap
Holographic thermal two-point functions can be analyzed using the operator product expansion which contains contributions from both multi-stress-tensor and double-trace operators. The former can be computed by analyzing the bulk equation of motion in a near-boundary expansion, but the latter has remained elusive-in practice, one resorts to solving a partial differential equation with limited accuracy. We show that imposing the Euclidean periodicity condition on the holographic correlator (also …

Multinode Shepard Functions and Tensor Product Polynomial Interpolation: Applications to Digital Elevation Models
Domingo Barrera, Francesco Dell'Accio, Filomena Di Tommaso, Salah Eddargani, Mar\'ia Jos\'e Ib\'a\~nez, Francesco Larosa, Federico Nudo, Juan F. Reinoso
https://arxiv.org/abs/2508.07764

Multinode Shepard Functions and Tensor Product Polynomial Interpolation: Applications to Digital Elevation Models
The paper presents an in-depth exploration of the multinode Shepard interpolant on a regular rectangular grid, demonstrating its efficacy in reconstructing surfaces from DEM data. Additionally, we study the approximation order associated to this interpolant and present a detailed algorithm for reconstructing surfaces. Numerical tests showcase the effectiveness of the proposed algorithm.

$C_{1}$-cofiniteness and vertex tensor categories
Yi-Zhi Huang
https://arxiv.org/abs/2509.20737 https://arxiv.org/pdf/2509.20737

$C_{1}$-cofiniteness and vertex tensor categories
We first generalize the logarithmic tensor category theory of Huang-Lepowsky-Zhang to the more general case that the module category for a vertex operator algebra $V$ (more generally a Möbius vertex algebra) might not be closed under the contragredient functor. Then by verifying the assumptions to use this generalization, we obtain that (logarithmic) intertwining operators among $C_{1}$-cofinite grading-restricted generalized $V$-modules satisfy the associativity property (operator product exp…

Projector Method for Nonlinear Light-Matter Interactions and Quantum Geometry
Zhichao Guo, Zhuocheng Lu, Hua Wang
https://arxiv.org/abs/2509.09216 https://…

Projector Method for Nonlinear Light-Matter Interactions and Quantum Geometry
We develop a systematic projector-based Feynman diagram framework that intrinsically encodes quantum geometry for nonlinear optical responses. By explicitly incorporating geometric quantities such as the quantum geometric tensor, quantum hermitian connection, and triple phase product, the method ensures component-wise gauge invariance and seamlessly extends to multiband systems, enabling accurate calculations of quantum geometry and nonlinear optical responses. We derive the projector formalism…

Steinberg skein identities at roots of unity
Vijay Higgins, Indraneel Tambe
https://arxiv.org/abs/2509.05502 https://arxiv.org/pdf/2509.05502

Steinberg skein identities at roots of unity
We obtain a family of skein identities in the Kauffman bracket skein module which relate Frobenius elements to Jones-Wenzl projectors at roots of unity. We view these skein identities as certain incarnations of Steinberg tensor product formulae from the theory of tilting modules of the quantum group $U_q(sl_2)$. We show that the simplest skein identities yield a short new proof of the existence of the Chebyshev-Frobenius homomorphism of Bonahon-Wong.

Replaced article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
- Quasilifting of hulls and depth of tensor product of modules
Sutapa Dey, Amit Tripathi

Fermion Discretization Effects in the Two-Flavor Lattice Schwinger Model: A Study with Matrix Product States
Tim Schw\"agerl, Karl Jansen, Stefan K\"uhn
https://arxiv.org/abs/2509.02329

Fermion Discretization Effects in the Two-Flavor Lattice Schwinger Model: A Study with Matrix Product States
We present a comprehensive tensor network study of staggered, Wilson, and twisted mass fermions in the Hamiltonian formulation, using the massive two-flavor Schwinger model as a benchmark. Particular emphasis is placed on twisted mass fermions, whose properties in this context have not been systematically explored before. We confirm the expected O(a) improvement in the free theory and observe that this improvement persists in the interacting case. By leveraging an electric-field-based method fo…

Crosslisted article(s) found for math.OA. https://arxiv.org/list/math.OA/new
[1/1]:
- Ideal Spaces of the Haagerup Tensor Product of Ternary Rings of Operators
Vandana Rajpal, Arpit Kansal

Eckmann-Hilton arguments in equivariant higher algebra
Natalie Stewart
https://arxiv.org/abs/2508.05556 https://arxiv.org/pdf/2508.05556

Eckmann-Hilton arguments in equivariant higher algebra
Let $\mathcal{O}^{\otimes}$ and $\mathcal{P}^{\otimes}$ be $k$- and $\ell$-connected unital $G$-operads subject to the condition for all $S$ that $\mathcal{O}(S) = \emptyset$ if and only if $\mathcal{P}(S) = \emptyset$. We show that the Boardman-Vogt tensor product $\mathcal{O}^{\otimes} \otimes \mathcal{P}^{\otimes}$ is $(k + \ell + 2)$-connected; equivalently, $\mathcal{O} \otimes \mathcal{P}$-monoids in any $(k + \ell + 3)$-category lift uniquely to incomplete semi-Mackey functors. As a cons…

TeMFpy: a Python library for converting fermionic mean-field states into tensor networks
Simon H. Hille, Attila Szab\'o
https://arxiv.org/abs/2510.05227 https://

TeMFpy: a Python library for converting fermionic mean-field states into tensor networks
We introduce TeMFpy, a Python library for converting fermionic mean-field states to finite or infinite matrix product state (MPS) form. TeMFpy includes new, efficient, and easy-to-understand algorithms for both Slater determinants and Pfaffian states. Together with Gutzwiller projection, these also allow the user to build variational wave functions for various strongly correlated electron systems, such as quantum spin liquids. We present all implemented algorithms in detail and describe how the…

Closed exact categories of modules over generalized adic rings. Part 1: The bounded case
Francesco Baldassarri
https://arxiv.org/abs/2510.00848 https://arx…

Closed exact categories of modules over generalized adic rings. Part 1: The bounded case
We develop general foundations of topological algebra over a linearly topologized ring k in a format applicable to both formal schemes and analytic adic spaces. We are especially interested in determining quasi-abelian categories of complete linearly topologized k-modules, which are also closed symmetric monoidal for a suitable choice of tensor product and internal Hom, and have enough projectives or injectives. For k a suitably generalized adic ring, we describe here a few examples of such cat…

Classical Neural Networks on Quantum Devices via Tensor Network Disentanglers: A Case Study in Image Classification
Borja Aizpurua, Sukhbinder Singh, Rom\'an Or\'us
https://arxiv.org/abs/2509.06653

Classical Neural Networks on Quantum Devices via Tensor Network Disentanglers: A Case Study in Image Classification
We address the problem of implementing bottleneck layers from classical pre-trained neural networks on a quantum computer, with the goal of achieving quantum advantage on near-term devices. Our approach begins with a compression step in which the target linear layer is represented as an effective matrix product operator (MPO) without degrading model performance. The MPO is then further disentangled into a more compact form. This enables a hybrid classical-quantum execution scheme, where the dis…

An Enriched Approach to the Strictification of $(\infty,1)$-Categories
Kimball Strong
https://arxiv.org/abs/2510.04254 https://arxiv.org/pdf/2510.04254

An Enriched Approach to the Strictification of $(\infty,1)$-Categories
We define a functor which takes in an $(\infty,1)$-category and outputs an $(ω,1)$-category, the natural maximally "strict" version of an $(\infty,1)$-category. We do this by modeling $(\infty,1)$-categories as categories enriched in $\infty$-groupoids, and then "locally strictifying" (applying the strictification of $\infty$-groupoids to each hom space) to obtain a category enriched in $ω$-groupoids with respect to the Gray tensor product, followed by "globally strictifying" (strictifying th…

On similarity to contraction semigroups and tensor products, I
J. Oliva-Maza, Y. Tomilov
https://arxiv.org/abs/2509.01005 https://arxiv.org/pdf/2509.01005

On similarity to contraction semigroups and tensor products, I
In the context of finite tensor products of Hilbert spaces, we prove that similarity of a tensor product of operator semigroups to a contraction semigroup is equivalent to the corresponding similarity for each factor, after an appropriate rescaling. A similar result holds with contractivity replaced by quasi-contractivity. This splitting phenomenon allows us to construct new and, in a sense, the strongest possible examples of $C_0$-semigroups not similar to contractions, thus completing an impo…

SymTFT Entanglement and Holographic (Non)-Factorization
Ethan Torres, Xingyang Yu
https://arxiv.org/abs/2510.06319 https://arxiv.org/pdf/2510.06319

SymTFT Entanglement and Holographic (Non)-Factorization
Given two otherwise decoupled $D$-dimensional CFTs which possess a common (finite) symmetry subcategory, one can consider entangled boundary states of their $(D+1)$-dimensional SymTFTs. This roughly corresponds to performing a gauging of the tensor product of two CFTs, and we call this phenomena ``SymTFT entanglement" (or ``S-entanglement" for short). In the case when these CFTs have semiclassical holographic duals, the S-entanglement relates the bulk gauge charges between two otherwise disconn…

Transfer entropy and O-information to detect grokking in tensor network multi-class classification problems
Domenico Pomarico, Roberto Cilli, Alfonso Monaco, Loredana Bellantuono, Marianna La Rocca, Tommaso Maggipinto, Giuseppe Magnifico, Marlis Ontivero Ortega, Ester Pantaleo, Sabina Tangaro, Sebastiano Stramaglia, Roberto Bellotti, Nicola Amoroso
https://

Transfer entropy and O-information to detect grokking in tensor network multi-class classification problems
Quantum-enhanced machine learning, encompassing both quantum algorithms and quantum-inspired classical methods such as tensor networks, offers promising tools for extracting structure from complex, high-dimensional data. In this work, we study the training dynamics of Matrix Product State (MPS) classifiers applied to three-class problems, using both fashion MNIST and hyper-spectral satellite imagery as representative datasets. We investigate the phenomenon of grokking, where generalization emer…

Applications of the factorization theorem of conformal blocks to vertex operator algebras
Xu Gao, Jianqi Liu
https://arxiv.org/abs/2508.01294 https://arxiv…

Applications of the factorization theorem of conformal blocks to vertex operator algebras
We apply the factorization and vector bundle propositionerty of the sheaves of conformal blocks on $\overline{\mathscr{M}}_{g,n}$. defined by vertex operator algebras (VOAs) and give geometric proofs of essential results in the representation theory of strongly rational VOAs. We first prove the associativity of the fusion tensor product by investigating four-point conformal blocks on genus zero curves. Then we give a formula to calculate the ranks of VOA-conformal block bundles. Finally, by inv…

Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
Stefan Rohshap, Jheng-Wei Li, Alena Lorenz, Serap Hasil, Karsten Held, Anna Kauch, Markus Wallerberger
https://arxiv.org/abs/2507.19069

Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information exchange between different length scales, has received far less attention. Here, we identify the quantics tensor train (QTT) technique, a matrix product state-inspired approach for overcoming computational bottlenecks in resource-intensive numerical calculations…

The standard construction for cocycle twisted and braided tensor product W$^*$-algebras
K. De Commer, J. Krajczok
https://arxiv.org/abs/2508.00595 https://…

The standard construction for cocycle twisted and braided tensor product W$^*$-algebras
Given a locally compact quantum group $\mathbb{G}$ and a (generalized) dual unitary $2$-cocycle $\hatΩ$, any W$^*$-algebra $A$ with a $\mathbb{G}$-action can be twisted into a new W$^*$-algebra $A_{\hatΩ}$ with an action by the cocycle twist $\mathbb{G}_{\hatΩ}$ of $\mathbb{G}$. We show how, in general, the standard space $L^2(A_{\hatΩ})$, with its standard $\mathbb{G}_{\hatΩ}$-representation, can be seen as a twist of $L^2(A)$ with its standard $\mathbb{G}$-representation. We then apply t…

Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems
Tianchu Li, Pranay Venkatesh, Nanako Shitara, Andr\'es Montoya-Castillo
https://arxiv.org/abs/2509.20604

Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems
Predicting the quantum dynamics of promising solid-state and molecular quantum technology candidates remains a formidable challenge. Yet, accessing these dynamics is key to understanding and controlling decoherence mechanisms -- a prerequisite for designing better qubits, sensors, and memories. We leverage a matrix product state representation to introduce a numerically exact and scalable method to achieve this goal. We demonstrate that our method accurately predicts coherence and population dy…

Energy minimisation using overlapping tensor-product free-knot B-splines
Alexandre Magueresse, Santiago Badia
https://arxiv.org/abs/2508.17705 https://arxi…

Energy minimisation using overlapping tensor-product free-knot B-splines
Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and often ineffective for such problems, as the mesh is not tailored to the solution. Adaptive strategies, such as $h$- and $p$-refinement, improve efficiency by sequentially refining the mesh based on a posteriori error estimates. However, these methods are geometrically rigid -- limited to specific refinement rules -- …

Yang-Mills kinematic algebra via homotopy transfer from a worldline operator algebra
Roberto Bonezzi, Christoph Chiaffrino, Olaf Hohm, Maria Foteini Kallimani
https://arxiv.org/abs/2508.17933

Yang-Mills kinematic algebra via homotopy transfer from a worldline operator algebra
The homotopy Lie or $L_{\infty}$ algebra encoding Yang-Mills theory is the tensor product of a color Lie algebra with the kinematic $C_{\infty}$ algebra. We derive this $C_{\infty}$ algebra, via homotopy transfer, from a strict operator algebra of a worldline theory, realized as an associative star product algebra. This gives a homotopy transfer interpretation to worldline vertex operators introduced in previous work.

MIPco=coRE
Junqiao Lin
https://arxiv.org/abs/2510.07162 https://arxiv.org/pdf/2510.07162

MIPco=coRE
In 2020, a landmark result by Ji, Natarajan, Vidick, Wright, and Yuen showed that MIP*, the class of languages that can be decided by a classical verifier interacting with multiple computationally unbounded provers sharing entanglement in the tensor product model, is equal to RE. We show that the class MIPco, a complexity class defined similarly to MIP* except with provers sharing the commuting operator model of entanglement, is equal to the class coRE. This shows that giving the provers two di…

The Morita $(\infty,2)$-category of a monoidal category as a $2$-complicial set
Arghan Dutta, Stefano Luneia, Martina Rovelli, Sam Silver
https://arxiv.org/abs/2509.21472 https:…

The Morita $(\infty,2)$-category of a monoidal category as a $2$-complicial set
We provide an explicit and elementary construction of the Morita $(\infty,2)$-category of a monoidal category which satisfies minimal conditions. We construct it as a $3$-coskeletal $2$-complicial set, in which the vertices encode the monoids, the edges encode the bimodules, the triangles encode the bimodule maps out of a balanced tensor product, and tetrahedra encode composition of bimodule maps. The marked edges encode invertible bimodules, and the marked triangles encode bimodule isomorphism…

Simple $\mathcal{W}\ltimes\widehat{H_4}$-modules from tensor products
Dashu Xu
https://arxiv.org/abs/2507.21927 https://arxiv.org/pdf/2507.21927

Simple $\mathcal{W}\ltimes\widehat{H_4}$-modules from tensor products
This paper investigates simple modules of the semi-direct product algebra $\mathcal{W}\ltimes\widehat{H_4}$, where $\mathcal{W}$ is the Witt algebra and $\widehat{H_4}$ is the loop Diamond algebra. We first use simple modules over the Weyl algebra to construct a family of simple $\mathcal{W}\ltimes\widehat{H_4}$-modules. Then, we classify simple $\mathcal{W}\ltimes\widehat{H_4}$-modules that are free $U(\mathbb{C}L_0\oplus\mathbb{C} a_0)$-modules of rank 1. Finally, we give a necessary and suff…

Replaced article(s) found for math.FA. https://arxiv.org/list/math.FA/new
[1/1]:
- On a variant of the Grothendieck inequality and estimates on tensor product norms
Rajeev Gupta, Gadadhar Misra, Samya Kumar Ray

Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups
Tattwamasi Amrutam, Yongle Jiang, Shuoxing Zhou
https://arxiv.org/abs/2508.18978 htt…

Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups
Let $G = G_{1} \times G_{2}$ be a product of two locally compact, second countable groups and $μ\in \mathrm{Prob}(G)$ be of the form $μ= μ_{1} \times μ_{2}$, where $μ_{i} \in \mathrm{Prob}(G_{i})$. Let $(B,ν_B)$ be the associated Poisson boundary. We show that every intermediate $G$-von Neumann algebra $\mathcal{M}$ with \[ \mathcal{N} \subseteq \mathcal{M} \subseteq \mathcal{N} \,\bar{\otimes}\, L^{\infty}(B,ν) \] splits as a tensor product of the form $\mathcal{N}\bar{\otimes}L^{\infty…

Kronecker Coefficients and Simultaneous Conjugacy Classes
Jyotirmoy Ganguly, Digjoy Paul, Amritanshu Prasad, K N Raghavan, Velmurugan S
https://arxiv.org/abs/2510.04497 https://…

Kronecker Coefficients and Simultaneous Conjugacy Classes
A Kronecker coefficient is the multiplicity of an irreducible representation of a finite group $G$ in a tensor product of irreducible representations. We define Kronecker Hecke algebras and use them as a tool to study Kronecker coefficients in finite groups. We show that the number of simultaneous conjugacy classes in a finite group $G$ is equal to the sum of squares of Kronecker coefficients, and the number of simultaneous conjugacy classes that are closed under elementwise inversion is the su…

Generalized Entanglement of Purification Criteria for 2-Producible States in Multipartite Systems
Tian-Ren Jin, Yu-Ran Zhang, Heng Fan
https://arxiv.org/abs/2510.04596 https://

Generalized Entanglement of Purification Criteria for 2-Producible States in Multipartite Systems
Multipartite entanglement has much more complex structures than bipartite entanglement, such as the semiseparable state. The multipartite state absent of multipartite entanglement is called a 2-producible state, which is a tensor product of at most 2-partite states. Recently, it is proved that a tripartite pure state is 2-producible if and only if the gap between entanglement of purification and its lower bound vanishes. Here, we show that the entanglement of purification gap is not sufficient …

Black Hole Entropy and Complexity Growth in Horndeski Gravity within the AdS/BCFT Framework
Fabiano F. Santos, Behnam Pourhassan, Emmanuel N. Saridakis
https://arxiv.org/abs/2509.23430

Black Hole Entropy and Complexity Growth in Horndeski Gravity within the AdS/BCFT Framework
This work investigates the connection between quantum complexity and gravitational dynamics within the framework of Horndeski gravity, extending the AdS/BCFT correspondence to include scalar-tensor interactions. By refining the ``\(complexity = action\)'' conjecture we investigate how Horndeski gravity modifies the Wheeler-DeWitt patch and the causal structure of the black hole. Our analysis reveals that the linear growth of complexity, proportional to the product of black hole entropy and temp…

Tensorial representations of positive weakly (q,r)-dominated multilinear operators
Abdelaziz Belaada, Adel Bounabab, Athmane Ferradi, Khalil Saadi
https://arxiv.org/abs/2509.08293

Tensorial representations of positive weakly (q,r)-dominated multilinear operators
We introduce and study the class of positive weakly (q,r)-dominated multilinear operators between Banach lattices. This notion extends classical domination and summability concepts to the positive multilinear setting and generates a new positive multi-ideal. A Pietsch domination theorem and a polynomial version are established. Finally, we provide a tensorial representation that yields an isometric identification with the dual of an appropriate completed tensor product.

Mutating Species with Potentials and Cluster Tilting Objects
Christoffer S\"oderberg
https://arxiv.org/abs/2509.24707 https://arxiv.org/pdf/2509.24707…

Mutating Species with Potentials and Cluster Tilting Objects
Buan, Iyama, Reiten and Smith proved that cluster-tilting objects in triangulated 2-Calabi--Yau categories are closely connected with mutation of quivers with potentials over an algebraically closed field. We prove a more general statement where instead of working with quivers with potentials we consider species with potential over a perfect field. We describe the $3$-preprojective algebra of the tensor product of two tensor algebras of acyclic species using a species with potential. In the c…

The tetrahedral Horn problem and asymptotics of U(n) 6j symbols
Anton Alekseev, Matthias Christandl, Thomas C. Fraser
https://arxiv.org/abs/2510.04877 https://

The tetrahedral Horn problem and asymptotics of U(n) 6j symbols
Horn's problem is concerned with characterizing the eigenvalues $(a,b,c)$ of Hermitian matrices $(A,B,C)$ satisfying the constraint $A+B=C$ and forming the edges of a triangle in the space of Hermitian matrices. It has deep connections to tensor product invariants, Littlewood-Richardson coefficients, geometric invariant theory and the intersection theory of Schubert varieties. This paper concerns the tetrahedral Horn problem which aims to characterize the tuples of eigenvalues $(a,b,c,d,e,f)$ o…

Higher Order Unfitted Space-Time Methods for Transport Problems
Erik Burman, Fabian Heimann
https://arxiv.org/abs/2509.02253 https://arxiv.org/pdf/2509.022…

Higher Order Unfitted Space-Time Methods for Transport Problems
In this article, we present an Unfitted Space-Time Finite Element method for the scalar transport equation posed on moving domains. We consider the case of the domain boundary being transported by the same velocity field as the scalar concentration inside the physical domain. A standard continuous Galerkin Finite element space is considered on a fixed background mesh, as well as tensor product Space-Time elements, which can be discontinuous along time slice boundaries. For the computational geo…

Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits
Jef Pauwels, Cyril Branciard, Alejandro Pozas-Kerstjens, Nicolas Gisin
https://arxiv.org/abs/2509.01851

Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits
While the structure of entangled quantum states is relatively well understood, the characterization of entangled measurements, especially in multipartite and high-dimensional settings, remains far less developed. In this work, we introduce a general approach to construct highly symmetric, locally encodable orthonormal measurement bases, as orbits of a single fiducial state under tensor-product actions of Pauli subgroups. This framework recovers the Elegant Joint Measurement-a two-qubit measurem…

Anomaly-free symmetries with obstructions to gauging and onsiteability
Wilbur Shirley, Carolyn Zhang, Wenjie Ji, Michael Levin
https://arxiv.org/abs/2507.21267 https://

Anomaly-free symmetries with obstructions to gauging and onsiteability
We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently coupled to background or dynamical gauge fields or disentangled to a tensor product of on-site operators. These symmetries are nevertheless anomaly-free in the sense that they admit symmetric, gapped Hamiltonians with unique, invertible ground states. We show t…

Weak containment of representation on topological groupoids
K. N. Sridharan, N. Shravan Kumar
https://arxiv.org/abs/2510.05898 https://arxiv.org/pdf/2510.0…

Weak containment of representation on topological groupoids
Let $G$ be a second-countable, locally compact Hausdorff groupoid equipped with a Haar system. This paper investigates the weak containment of continuous unitary representations of groupoids. We show that both induction and inner tensor product of representations preserve weak containment. Additionally, we introduce the notion of a topological invariant mean on $G/H$ and explore its connection to amenability. With that, we establish a groupoid analogue of Greenleaf's theorem. Finally, we provid…

Node-Equivariant Message Passing for Efficient and Accurate Machine Learning Interatomic Potentials
Yaolong Zhang, Hua Guo
https://arxiv.org/abs/2508.16086 https://

Node-Equivariant Message Passing for Efficient and Accurate Machine Learning Interatomic Potentials
Machine learned interatomic potentials, particularly equivariant message-passing (MP) models, have demonstrated high fidelity in representing first-principles data, revolutionizing computational studies in materials science, biophysics, and catalysis. However, these equivariant MP models still incur substantial computational and memory needs due to their expensive tensor product operations over edge space, significantly limiting their applicability in large-scale or long-time simulations. In th…

Modular isomorphisms of $\mathrm{SL}_2(\mathbb{F})$-plethysms for Weyl modules labelled by hook partitions
\'Alvaro Guti\'errez, \'Alvaro L. Mart\'inez, Micha{\l} Szwej, Mark Wildon
https://arxiv.org/abs/2509.01490

Modular isomorphisms of $\mathrm{SL}_2(\mathbb{F})$-plethysms for Weyl modules labelled by hook partitions
Let $Δ^λ$ be the Weyl functor for the partition $λ$ and let $E$ be the natural $2$-dimensional representation of $\mathrm{SL}_2(\mathbb{F})$, where $\mathbb{F}$ is an arbitrary field. We give an explicit isomorphism showing that any $\mathrm{SL}_2(\mathbb{F})$-plethysm $Δ^{(M,1^N)}\mathrm{Sym}^d E$ factors as a tensor product of two simpler $\mathrm{SL}_2(\mathbb{F})$-plethysms, each defined using only symmetric powers. This result categorifies Stanley's Hook Content Formula for hook-shaped…

Quantum Hamming Metrics
Marc A. Rieffel
https://arxiv.org/abs/2507.23046 https://arxiv.org/pdf/2507.23046

Quantum Hamming Metrics
Given the set of words of a given length for a given alphabet, the Hamming metric between two such words is the number of positions where the two words differ. A quantum version of the corresponding Kantorovich-Wasserstein metric on states was introduced in 2021 by De Palma, Marvian, Trevisan and Lloyd. For the quantum version the alphabet is replaced by a full matrix algebra, and the set of words is replaced by the tensor product of a corresponding number of copies of that full matrix algebra.…

Resource-Efficient Simulations of Particle Scattering on a Digital Quantum Computer
Yahui Chai, Joe Gibbs, Vincent R. Pascuzzi, Zo\"e Holmes, Stefan K\"uhn, Francesco Tacchino, Ivano Tavernelli
https://arxiv.org/abs/2507.17832

Resource-Efficient Simulations of Particle Scattering on a Digital Quantum Computer
We develop and demonstrate methods for simulating the scattering of particle wave packets in the interacting Thirring model on digital quantum computers, with hardware implementations on up to 80 qubits. We identify low-entanglement time slices of the scattering dynamics and exploit their efficient representation by tensor networks. Circuit compression based on matrix product state techniques yields on average a reduction by a factor of 3.2 in circuit depth compared to conventional approaches, …