Related papers: Highly entangled, non-random subspaces of tensor p…
A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of…
We put forward a simple construction of genuinely entangled subspaces -- subspaces supporting only genuinely multipartite entangled states -- of any permissible dimensionality for any number of parties and local dimensions. The method uses…
Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models…
We describe the algebraic ingredients of a proof of the conjecture of Frenkel and Ip that the category of positive representations $\mathcal{P}_\lambda$ of the quantum group $U_q(\mathfrak{sl}_{n+1})$ is closed under tensor products. Our…
We consider the image of some classes of bipartite quantum states under a tensor product of random quantum channels. Depending on natural assumptions that we make on the states, the eigenvalues of their outputs have new properties which we…
It is shown that the algebraic structure of finite Heisenberg groups associated with the tensor product of two Hilbert spaces leads to a simple demonstration valid in all Hilbert space dimensions of the impossibility of non-contextual…
The entanglement production in bipartite quantum systems is studied for initially unentangled product eigenstates of the subsystems, which are assumed to be quantum chaotic. Based on a perturbative computation of the Schmidt eigenvalues of…
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and…
A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…
As a contribution to the field of quantum mereology, we study how a change of tensor product structure in a finite-dimensional Hilbert space affects its entanglement properties. In particular, we ask whether, given a time-evolving state,…
Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems…
Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
Mathematical foundation of the novel concept of quantum tensor product by Zanardi et al is rigorously established. The concept of relative quantum entanglement is naturally introduced and its meaning is made clear both mathematically and…
Entanglement is a well known fundamental resource in quantum information. Here the following question is addressed : which are the deeper roots of entanglement that may help in its better understanding and use ? The answer is that one can…
The rank of a tensor is analyzed in context of quantum entanglement. A pure quantum state $\bf v$ of a composite system consisting of $d$ subsystems with $n$ levels each is viewed as a vector in the $d$-fold tensor product of…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
Construction of genuinely entangled multipartite subspaces with certain characteristics has become a relevant task in various branches of quantum information. Here we show that such subspaces can be obtained from an arbitrary collection of…
We discuss the Kummer subspaces of tensor products of cyclic algebras, focusing mainly on the case of cyclic algebras of degree 3. We present a family of maximal spaces in the general case, classify all the monomial spaces in the case of…