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The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular…

Operator Algebras · Mathematics 2011-02-25 Ali S. Kavruk , Vern I. Paulsen , Ivan G. Todorov , Mark Tomforde

This research introduces an improved framework for constructing matrix product operators (MPOs) and tree tensor network operators (TTNOs), crucial tools in quantum simulations. A given (Hamiltonian) operator typically has a known symbolic…

Quantum Physics · Physics 2025-07-04 Hazar Çakır , Richard M. Milbradt , Christian B. Mendl

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways. The first…

Operator Algebras · Mathematics 2024-06-25 Ralf Meyer , Sutanu Roy , Stanislaw Lech Woronowicz

In this paper, we introduce the $q$-Heisenberg algebra in the tensor product space $\otimes^2$. We establish its algebraic properties and provide applications to the theory of non-monogenic functions. Our results extend known constructions…

Mathematical Physics · Physics 2025-04-17 Julio César Jaramillo Quiceno

We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…

Quantum Physics · Physics 2026-04-22 Pia Siegl , Greta Sophie Reese , Tomohiro Hashizume , Nis-Luca van Hülst , Dieter Jaksch

The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a…

Statistical Mechanics · Physics 2020-03-30 Michal Daniška , Andrej Gendiar

We introduce the concept of quantum tensor product expanders. These are expanders that act on several copies of a given system, where the Kraus operators are tensor products of the Kraus operator on a single system. We begin with the…

Quantum Physics · Physics 2009-04-14 M. B. Hastings , A. W. Harrow

We introduce the main concepts and announce the main results in a theory of tensor products for module categories for a vertex operator algebra. This theory is being developed in a series of papers including hep-th 9309076 and hep-th…

High Energy Physics - Theory · Physics 2008-02-03 Yi-Zhi Huang , James Lepowsky

Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…

Numerical Analysis · Mathematics 2024-10-01 Katherine Keegan , Elizabeth Newman

The $\star_M$-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the…

Optimization and Control · Mathematics 2025-07-18 Alex Dunbar , Elizabeth Newman

This is the first part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…

High Energy Physics - Theory · Physics 2008-02-03 Yi-Zhi Huang , James Lepowsky

We study the concept of frame in tensor product of n-Hilbert spaces as tensor product of n-Hilbert spaces is again a n-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship…

Functional Analysis · Mathematics 2024-03-07 Prasenjit Ghosh , Tapas Kumar Samanta

In the quantum logic framework we show that the no-signaling box model is a particular type of tensor product of the logics of single boxes. Such notion of tensor product is too strong to apply in the category of logics of quantum…

Quantum Physics · Physics 2017-01-02 Tomasz I. Tylec , Marek Kuś

Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…

Quantum Physics · Physics 2013-11-13 Jacob Biamonte , Ville Bergholm , Marco Lanzagorta

We study idempotent analogs of topological tensor products in the sense of A. Grothendieck. The basic concepts and results are simulated on the algebraic level. This is one of a series of papers on idempotent functional analysis.

Functional Analysis · Mathematics 2007-05-23 Grigori Litvinov , Viktor Maslov , Grigori Shpiz

Estimation of a conditional mean (linking a set of features to an outcome of interest) is a fundamental statistical task. While there is an appeal to flexible nonparametric procedures, effective estimation in many classical nonparametric…

Methodology · Statistics 2022-06-08 Tianyu Zhang , Noah Simon

The problem of whether the cohomological support map of a finite dimensional Hopf algebra has the tensor product property has attracted a lot of attention following the earlier developments on representations of finite group schemes. Many…

Category Theory · Mathematics 2021-08-12 Daniel K. Nakano , Kent B. Vashaw , Milen T. Yakimov

Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…

Representation Theory · Mathematics 2023-12-05 Tim Seynnaeve

This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…

q-alg · Mathematics 2008-02-03 Yi-Zhi Huang , James Lepowsky

In this work we propose a generalization of the Hadamard product between two matrices to a tensor-valued, multi-linear product between k matrices for any $k \ge 1$. A multi-linear dual operator to the generalized Hadamard product is…

Number Theory · Mathematics 2007-05-23 Hristo S. Sendov