Related papers: Quantum marginal problem and representations of th…

In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…

The problem of the relationship between entanglement and two-qubit systems in which it is embedded is central to the quantum information theory. This paper suggests that the concurrence hierarchy as an entanglement measure provides an…

It is possible to understand whether a given BPS spectrum is generated by a relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from the periodicity properties of the corresponding quantum monodromy. With the aim of…

Many problems of quantum information theory rely on the set of quantum marginals. A precise knowledge of the faces of this convex set is necessary, for example, in the reconstruction of states from their marginals or in the evaluation of…

We consider density matrices which are sums of projectors on states spanning irreducible representations of the permutation group of L sites (eigenstates of permutational invariant quantum system with L sites) and construct the reduced…

One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even…

This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.

The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states {\rho} with the property that U^*{\rho}U is separable for all unitary matrices U. This problem has been solved when the…

We give a criterion of classicality for mixed states in terms of expectation values of a quantum observable. Using group representation theory we identify all cases when the criterion can be computed exactly in terms of the spectrum of a…

We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…

In this paper, we consider the local unitary classification of the class of qudit bipartite mixed states for which no information can be obtained locally. These states are represented by symmetrical density matrices in which both tracial…

We provide a rate distortion interpretation of the problem of quantum data compression of ensembles of mixed states with commuting density operators. There are two versions of this problem. In the visible case the sequence of states is…

We discuss complementarity relations in a bipartite continuous variable system. Building up from the work done on discrete d-dimensional systems, we prove that for symmetric two-mode states, quantum complementarity relations can be put in a…

It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…

We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…

The equivalence of multidimensional systems is closely related to the reduction of multivariate polynomial matrices, with the Smith normal form of matrices playing a key role. So far, the problem of reducing multivariate polynomial matrices…

The problems of the luminescent enhancement and life time shortening for the inverted quantum system (QS) are analysed. The commonly accepted in publications approach appears to be questionable from the point of view of basic principles. An…

The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…

We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally…

This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…