Comment on “Relativistic effects on the spin entanglement of two massive Dirac particles”

Caban, Paweł; Rembieliński, Jakub

doi:10.1103/physreva.86.066301

Cited by 3 publications

(1 citation statement)

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“…This simple fact has very important consequences: the same abstract operator can be represented by distinct matrices in Dirac theory (cf. [4] and [48]). We discuss this point in detail below.…”

Section: B Dirac Basismentioning

confidence: 98%

Spin operator in the Dirac theory

2013

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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 arbitrary direction are independent of this direction (isotropy condition). We show that there are four such operators 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 and positive energy states. We show also that this operator is equivalent to the Newton-Wigner spin operator and Foldy-Wouthuysen mean-spin operator. We also discuss another operators proposed in the literature.Comment: 9 page

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Section: B Dirac Basismentioning

confidence: 98%

Spin operator in the Dirac theory

2013

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Stability of flows with the BMP model in the yield stress limit

Frigaard

Renteria

2019

Korea-Aust. Rheol. J.

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Spin operator and entanglement in quantum field theory

Fujikawa

Zhang

2014

Phys. Rev. D

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Entanglement is studied in the framework of Dyson's S-matrix theory in relativistic quantum field theory, which leads to a natural definition of entangled states of a particle-antiparticle pair and the spin operator from a Noether current. As an explicit example, the decay of a massive pseudo-scalar particle into a pair of electron and positron is analyzed. Two spin operators are extracted from the Noether current. The Wigner spin operator characterizes spin states at the rest frame of each fermion and, although not measurable in the laboratory, gives rise to a straightforward generalization of low-energy analysis of entanglement to the ultrarelativistic domain. In contrast, if one adopts a (modified) Dirac spin operator, the entanglement measured by spin correlation becomes maximal near the threshold of the decay, while the entanglement is replaced by the classical correlation for the ultrarelativistic electron-positron pair by analogy to the case of neutrinos, for which a hidden-variables type of description is possible. Chiral symmetry differentiates the spin angular momentum and the magnetic moment. The use of weak interaction that can measure helicity is suggested in the analysis of entanglement at high energies instead of a Stern-Gerlach apparatus, which is useless for the electron. A difference between the electron spin at high energies and the photon linear polarization is also noted. The Standard Model can describe all of the observable properties of leptons.

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Comment on “Relativistic effects on the spin entanglement of two massive Dirac particles”

Abstract: The paper of Choi et al. [Phys. Rev. A 84, 012334 (2011)] discusses the use of the Foldy-Wouthuysen mean-spin operator in the theory of relativistic quantum information. However, the paper contains some incorrect statements and misunderstandings.

Cited by 3 publications

References 16 publications

Spin operator in the Dirac theory

Spin operator in the Dirac theory

Stability of flows with the BMP model in the yield stress limit

Spin operator and entanglement in quantum field theory

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