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

The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz-covariant quantum mechanics formulated in the absolute synchronization framework. These results are the first exact Einstein-Podolsky-Rosen correlation functions obtained for Lorentz-covariant quantum-mechanical systems in moving frames under physically acceptable conditions, i.e., taking into account the localization of the particles during the detection and using the spin operator with proper transformation properties under the action of the Lorentz group. Some special cases and approximations of the calculated correlation function are given. The resulting correlation function can be used as a basis for a proposal of a decisive experiment for a possible existence of a quantum-mechanical preferred frame.

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].

We describe a q-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.

It is shown that the hypothesis of tachyonic neutrinos leads to the same oscillations effect as if they were usual massive particles. Therefore, the experimental evidence of neutrino oscillations does not distinguish between massive and tachyonic neutrinos.

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Abstract. -The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by such physicists as J. S. Bell and D. Bohm. The possibility of the existence of preferred frame was also seriously treated by P. A. M. Dirac. In this paper, we propose an Einstein-Podolsky-Rosen-type experiment for testing the possible existence of a quantum preferred frame. Our analysis suggests that to verify whether a preferred frame of reference in the quantum world exists it is enough to perform an EPR type experiment with pair of observers staying in the same inertial frame and with use of the massive EPR pair of spin one-half or spin one particles.Introduction. -Quantum mechanics (QM) is not a local realistic theory.It predicts a strange phenomenon, named by Einstein as "spooky action at a distance". It was confirmed in many experiments [1][2][3][4] which are Bohm's modifications of the Einstein-Podolsky-Rosen (EPR) famous thought experiment [5]. As a consequence of the ingenious paper by John S. Bell [6], we know that the Einstein's idea to find a local realistic theory describing quantum phenomena [7] was false: the nature of quantum world is non-local. This is related to the property of multiparticle states known as quantum entanglement. Although quantum non-locality is not in a conflict with the Galilean physics, it is rather baffling from the special relativity (SR) point of view. According to Shimony [8] quantum mechanics and special relativity might "peacefully coexist" if they attribute physical meaning to the final probabilities only. However, this "peaceful coexistence" relies on the ignoring some weak points of the relativistic QM, like lack of the covariant notion of localization or problem with spin observable [9][10][11][12]. It would be advisable for quantum mechanics if it admit the absolute simultaneity notion and consequently a preferred frame of reference [13,14] (which seems to be a natural framework for the non-locality) while preserving the (well established) Lorentz-covariance. In this paper we suggest how to verify whether a preferred frame of reference in the quantum

Verstraete, Dehaene and DeMoor showed that each of the two-qubit states can be generated from one of two canonical families of two-qubit states by means of transformations preserving the tensor structure of the state space. Precisely, each of such states can be generated from a three-parameter family of Bell-diagonal states or from three-parameter rank-deficient states. In this paper, we show that this classification of two-qubit states can be refined. In particular, we show that the latter canonical family of states can be reduced to three fixed states and a two-parameter family of two-qubit states. For this family of states, we provide a simple parametrization that guarantees positive semidefiniteness of the states and enables easier calculation of the Wootters concurrence and quantum discord. Moreover, we present a new general parametrization of all two-qubit states generated from the canonical families of states using sets of (pseudo)orthogonal four-vectors (frames). An advantage of the presented approach lies in the fact that the standard conditions for positive semidefiniteness of states are equivalent to (pseudo)orthogonality conditions for four-vectors serving as This work has been supported by the Polish National Science Centre under the contract 2014/15/B/ST2/00117 and by the University of Lodz.