Polarization correlations of Dirac particles

Abstract

We calculate the polarization correlation function in the Einstein-Podolsky-Rosen-type experiments with relativistic spin-1/2 particles. This function depends monotonically on the particle momenta. Moreover, we also show that the polarization correlation function violates the Clauser-Horn-Shimony-Holt inequality and the degree of this violation can depend on the particle momenta and the motion of observers.

Einstein-Podolsky-Rosen correlations in a hybrid system

“…2), and ς = ϕ = π/4, ψ = θ = π/3 (Fig. 3) The function (32) already been reported by us [22][23][24]26]. Moreover, it also influences the degree of violation of CHSH inequalities.…”

Physical interpretation of the Wigner rotations and its implications for relativistic quantum information

“…We are led to the conclusion that it is not possible to make a momentum-spin separation of the system and to define a reduced density matrix for spin, as was done in many previous papers on the subject [2, 4, 9, 10, 12, 15-21, 23, 24]. We also show that the use of the Pauli-Lubanski (or similar) spin operators to describe spin measurements, as in [1,5,8,11,13,14,16,22,23], depends on the coupling of the spin to a quantity that transforms as part of a four-vector under the Lorentz transformations in the measuring apparatus. However, we do not know if such a coupling exists in nature.…”

“…In the relativistic quantum information literature, many authors use the Pauli-Lubanski (or similar) spin operators to describe spin measurements on relativistic particles [1,5,8,11,13,14,16,22,23]. Their description is mathematically covariant, in the sense that the expectation values they obtain for the measurements are the same in all inertial reference frames [11], but none of the authors describe a physical system capable of making the measurements.…”

Spin quantum correlations of relativistic particles

“…Recently questions regarding the behaviour of the entropy and entanglement of quantum systems in different reference frames gave rise to the field of relativistic quantum information [4][5][6]. Since then, many studies of relativistic effects on spin quantum correlations of massive particles have appeared in the literature [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20].In the seminal work of Peres, Scudo and Terno [5], they showed that the reduced density matrix for the spin of a relativistic particle, that should give "the statistical predictions for the results of measurements of spin components by an ideal apparatus which is not affected by the momentum of the particle" [5], is not covariant under Lorentz transformations. This occurs because under a Lorentz boost the particle spin undergoes a Wigner rotation [21,22], which correspond to a momentumdependent change of the particle spin state.…”

“…Recently questions regarding the behaviour of the entropy and entanglement of quantum systems in different reference frames gave rise to the field of relativistic quantum information [4][5][6]. Since then, many studies of relativistic effects on spin quantum correlations of massive particles have appeared in the literature [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”