Related papers: Local operator system structures and their tensor …
We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of…
We conduct the first detailed analysis in quantum information of recently derived operator relations from the study of quantum one-way local operations and classical communications (LOCC). We show how operator structures such as operator…
In this paper we study, in the relaxed context of locally convex spaces, intrinsic properties of monotone operators needed for the sum conjecture for maximal monotone operators to hold under classical interiority-type domain constraints.
This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. This theory generalizes the tensor category theory for…
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…
We develop a systematic study of the schur tensor product both in the category of operator spaces and in that of $C^*$-algebras.
Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dimensional problems in scientific computing. In this work, we…
This is the fourth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part IV), we give constructions of the…
We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their…
Concept of a family of local atoms in n-Hilbert space is being studied. K-frame in tensor product of n-Hilbert spaces is described and a characterization is given. Atomic system in tensor product of n-Hilbert spaces is presented and…
We investigate a general structure theory for a vertex operator algebra. We discuss the center and blocks, the Jacobson radical and solvable radical and local vertex operator algebras. The main consequence of our structure theory is that if…
Given a Banach space $X$, there are many operator space structures possible on $X$, which all have $X$ as their first matrix level. Blecher and Paulsen identified two extreme operator space structures on $X$, namely $Min(X)$ and $Max(X)$…
We present the explicit expressions for the matrix product operator (MPO) representation for the local conserved quantities of the Heisenberg chain. The bond dimension of the MPO grows linearly with the locality of the charges. The MPO has…
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…
Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation,…
In this paper we study invariant local operations that can performed on a Fedosov manifold, with a particular emphasis on tensor-valued operations (also known as natural tensors). Our main result describes the spaces of homogeneous natural…
We demonstrate how a simple linear-algebraic technique used earlier to compute low-degree cohomology of current Lie algebras, can be utilized to compute other kinds of structures on such Lie algebras, and discuss further generalizations,…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…
We show how to exploit excitable regimes mediated by localized structures (LS) to perform AND, OR, and NOT logical operations providing full logical functionality. Our scheme is general and can be implemented in any physical system…
In this paper we show that the theory of Hankel operators in the torus $\T^d$, for $d > 1$, presents striking differences with that on the circle $\T$, starting with bounded Hankel operators with no bounded symbols. Such differences are…