Paweł Caban

Lorentz-covariant reduced spin density matrix and Einstein-Podolsky-Rosen–Bohm correlations

We show that it is possible to define a Lorentz-covariant reduced spin density matrix for massive particles. Such a matrix allows one to calculate the mean values of observables connected with spin measurements (average polarizations). Moreover, it contains not only information about polarization of the particle but also information about its average kinematical state. We also use our formalism to calculate the correlation function in the Einstein-Podolsky-Rosen-Bohm type experiment with massive relativistic particles.

An open quantum system approach to EPR correlations in K0K¯0 system

Abstract We find the time evolution of the system of two non-interacting unstable particles, distinguishable as well as identical ones, in arbitrary reference frame having only the Kraus operators governing the evolution of its components in the rest frame. We than calculate in the rigorous way Einstein–Podolsky–Rosen quantum correlation functions for K 0 K ¯ 0 system in the singlet state taking into account CP -violation and decoherence and show that the results are exactly the same despite the fact we treat kaons as distinguishable or identical particles which means that the statistics of the particles plays no role, at least in considered cases.

Unstable particles as open quantum systems

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 a 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.

Photon polarization and Wigner's little group

To discuss one-photon polarization states we find the explicit form of the Wigners little group element in the massless case for arbitrary Lorentz transformation. As is well known, when analyzing the transformation properties of the physical states, only the value of the phase factor is relevant. We show that this phase factor depends only on the direction of the momentum k/|k| and does not depend on the frequency k{sup 0}. Finally, we use this observation to discuss the transformation properties of the linearly polarized photons and the corresponding reduced density matrix. We find that they transform properly under Lorentz group.

Strange behavior of the relativistic Einstein-Podolsky-Rosen correlations

We show that configurations exist in which the correlation functions and the degree of violation of Bell-type inequalities in the relativistic Einstein-Podolsky-Rosen (EPR) experiment have local extrema for some values of the velocities of the EPR particles. Moreover, this strange behavior can be observed for both discussed relativistic spin operators and for spin-

Entanglement and tensor product decomposition for two fermions

1∕2

Spin operator in the Dirac theory

as well as spin-1 particles.

Einstein-Podolsky-Rosen correlations of vector bosons

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.

Einstein-Podolsky-Rosen correlations of Dirac particles: Quantum field theory approach

Department of Theoretical Physics, University of LodzPomorska 149/153, 90-236 L ´od´z, Poland(Dated: August 21, 2013)We find all spin operators for a Dirac particle satisfying the following very general conditions: (i)spin does not convert positive (negative) energy states into negative (positive) energy states, (ii)spin is a pseudo-vector, and (iii) eigenvalues of the projection of a spin operator on an arbitrarydirection are independent of this direction (isotropy condition). We show that there are four suchoperators and all of them fulfill the standard su(2) Lie algebra commutation relations. Nevertheless,only one of them has a proper non-relativistic limit and acts in the same way on negative andpositive energy states. We show also that this operator is equivalent to the Newton-Wigner spinoperator and Foldy-Wouthuysen mean-spin operator. We also discuss another operators proposedin the literature.

Destruction of states in quantum mechanics

We calculate the joint probabilities and the correlation function in Einstein-Podolsky-Rosen\char21{}type experiments with a massive vector boson in the framework of quantum field theory. We report on the strange behavior of the correlation function (and the probabilities)\char22{}the correlation function, which in the relativistic case still depends on the particle momenta, for some fixed configurations has local extrema. We also show that relativistic spin-1 particles violate some Bell inequalities more than nonrelativistic ones and that the degree of violation of the Bell inequality is momentum dependent.