We present the probability preserving description of the decaying particle within the framework of quantum mechanics of open systems taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In our approach the evolution of the system is given by a family of completely positive trace preserving maps forming one-parameter dynamical semigroup. We give the Kraus representation for the general evolution of such systems which allows one to write the evolution for systems with two or more particles. Moreover, we show that the decay of the particle can be regarded as a Markov process by finding explicitly the master equation in the Lindblad form. We also show that there are remarkable restrictions on the possible strength of decoherence.Comment: 11 pp, 2 figs (published version

Recently, it was realized that quantum discord can be seen as the minimal amount of correlations which are lost when some local quantum operations are performed. Based on this formulation of quantum discord, we provide a systematical analysis of quantum and classical correlations present in both bipartite and multipartite quantum systems. As a natural result of this analysis, we introduce a new measure of the overall quantum correlations which is lower bounded by quantum discord.

In this letter we demonstrate that there exists a remarkable class of quantum models admitting Z2 anti-isospectral transformations which change the form of the potential and invert the sign of a certain finite set of energy levels. These transformations help one to construct interesting classes of non-monic polynomials which are mutually orthogonal on two different intervals with two different weight functions.

Abstract. The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not the proper entanglement measure in this case. The explicit formula for the entanglement of formation is found. This formula shows that the entanglement of a given state depends on the tensor product decomposition of a Hilbert space. It is shown that the set of separable states is narrower than in the two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space.PACS numbers: 03.67. Mn, 03.65.Ud Entanglement is the key notion of quantum information theory and plays a significant role in most of its applications. The entanglement of a physical system is always relative to a particular set of experimental capabilities (see, e.g. [1, 2]), which is connected with decompositions of the system into subsystems. From the theoretical point of view this is closely related to possible choices of the tensor product decomposition (TPD) of the Hilbert space of the system. As a consequence the following question arises: How much entangled is a given state with respect to a particular TPD?In the present paper we discuss the problem of the choices of TPD in a system of two fermions, neglecting their spatial degrees of freedom and modifying tensor product in the rings of operators because of anticommuting canonical variables. We show that TPDs are connected with each other by Bogoliubov transformations of creation and annihilation operators. We also study the behavior of the entanglement of the system under these transformations. An importance of such investigation can be illustrated for example by the fact that the Bogoliubov transformations used in derivation of the Unruh effect also lead to the change of entanglement [3]. Different approach to the entanglement in the system of two identical fermions, based on the asymmetric decomposition of the algebra generated by a i , a † i (i = 1, 2) into tensor product of two subalgebras was taken up in [4]. Some aspects of the entanglement for two-fermion system were also discussed in [5].

A general theory of Bender–Dunne orthogonal polynomials is proposed. It is shown that these polynomials can easily be constructed for any explicitly tridiagonalizable Hamiltonians and are, in fact, the orthogonal polynomials in a discrete variable which takes its values in the set of energy levels of the corresponding quantum model. The weight functions for Bender–Dunne polynomials are explicitly constructed.