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arXiv:quant-ph/0507056 · Physical Review A

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

Paweł Caban, Jakub Rembieliński

Published Jul 5, 2005• 76 citations
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Abstract

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.

DOI
10.1103/physreva.72.012103

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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.
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We calculate correlation functions for a relativistic Einstein-Podolsky-Rosen--type experiment with massive Dirac particles. We take into account the influence of the Newton-Wigner localization and perform the calculations for a couple of physically interesting states. In particular, we show that localization inside detectors does not significantly affect correlation functions in the case when localization regions are macroscopic or in the case when Einstein-Podolsky-Rosen particles are in a definite momentum state (irrespectively of the size of localization regions).
We calculate the joint probabilities and the correlation function in Einstein-Podolsky-Rosen--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)---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.
We have shown that the covariant relativistic spin operator is equivalent to the spin operator commuting with the free Dirac Hamiltonian. This implies that the covariant relativistic spin operator is a good quantum observable. The covariant relativistic spin operator has a pure quantum contribution that does not exist in the classical covariant spin operator. Based on this equivalence, reduced spin states can be clearly defined. We have shown that depending on the relative motion of an observer, the change in the entropy of a reduced spin density matrix sweeps through the whole range.