Related papers: Bipartite matrix-valued tensor product correlation…

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…

Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any…

Determining the relationship between quantum correlation sets is a long-standing open problem. The most well-studied part of the hierarchy is captured by the chain of inclusions $\mathcal C_q \subseteq \mathcal C_{qs} \subsetneq \mathcal…

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…

We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…

We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.

Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…

Let K, K' be convex cones residing in finite-dimensional real vector spaces E, E'. An element in the tensor product E \otimes E' is K \otimes K'-separable if it can be represented as finite sum \sum_l x_l \otimes x'_l with x_l \in K and…

Based on the quantitative complementarity relations, we analyze thoroughly the properties of multipartite quantum correlations and entanglement in four-qubit pure states. We find that, unlike the three-qubit case, the single residual…

Tensor products of M random unitary matrices of size N from the circular unitary ensemble are investigated. We show that the spectral statistics of the tensor product of random matrices becomes Poissonian if M=2, N become large or M become…

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…

In this work we developed a general approach to the problem of detecting and quantifying different kind of correlations in bipartite quantum systems. Our method is based on the use of distances between quantum states and processes. We rely…

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…

In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…

Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state…

It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multi-partite tensor product structure of the state-space and the…

We demonstrate that the matrix quantum group $SL_q(2)$ gives rise to nontrivial matrix product operator representations of the Lie group $SL(2)$, providing an explicit characterization of the nontrivial global $SU(2)$ symmetry of the XXZ…

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…

The quantum process framework is devised as a generalization of quantum theory to incorporate indefinite causal structure. In this short paper we point out a restriction in forming products of processes: there exist both classical and…

Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify…