Marta Włodarczyk

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.

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-

Spin operator in the Dirac theory

1∕2

Einstein-Podolsky-Rosen correlations of vector bosons

as well as spin-1 particles.

Relativistic Einstein-Podolsky-Rosen correlations for vector and tensor states

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.

Covariant Abstract Description for a Dirac Particle

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.

Møller scattering and Einstein-Podolsky-Rosen spin correlations

Department of Theoretical Physics, University of LodzPomorska 149/153, 90-236 L ´od´z, Poland(ΩDated: November 30, 2010)We calculate and investigate the relativistic correlation function for bipartite systems of spin-1/2 invector and spin-1 particles in tensor states. We show that the relativistic correlation function, whichdepends on particles momenta, may have local extrema. What is more, the momentum dependanceof the correlation functions for two choices of relativistic spin operator may be significantly different.

Relativistic spin operator and Dirac equation

We give a direct link between covariant description of Dirac particles in the abstract framework of unitary representation of the Poincare group and description with the help of the Dirac equation. In this context we discuss the spin operator for a relativistic Dirac particle. We show also that the spin operator used in quantum field theory for spin s = 1/2 corresponds to the Foldy-Wouthuysen mean-spin operator. We hope that this formalism will be useful in the theory of relativistic quantum information.