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

Saldanha, Pablo L.; Vedral, Vlatko

doi:10.1088/1367-2630/14/2/023041

Cited by 51 publications

(83 citation statements)

References 42 publications

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“…However, it was shown that these violations critically depend on the type of spin operator involved [22,23] even when the finite wavepacket width effects [24,25] are not taken into account, since not all such operators [26] satisfy the necessary commutation relations [27]. In general, properties of relativistic spin are responsible for many features of relativistic quantum information theory that distinguish it from its nonrelativistic counterpart [11,28].…”

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confidence: 99%

Spin and localization of relativistic fermions and uncertainty relations

2016

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We discuss relations between several relativistic spin observables and derive a Lorentz-invariant characteristic of a reduced spin density matrix. A relativistic position operator that satisfies all the properties of its nonrelativistic analog does not exist. Instead we propose two causality-preserving positive operator-valued measures (POVM) that are based on projections onto one-particle and antiparticle spaces, and on the normalized energy density. They predict identical expectation values for position. The variances differ by less than a quarter of the squared de Broglie wavelength and coincide in the nonrelativistic limit. Since the resulting statistical moment operators are not canonical conjugates of momentum, the Heisenberg uncertainty relations need not hold. Indeed, the energy density POVM leads to a lower uncertainty. We reformulate the standard equations of the spin dynamics by explicitly considering the charge-independent acceleration, allowing a consistent treatment of backreaction and inclusion of a weak gravitational field.

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confidence: 99%

Spin and localization of relativistic fermions and uncertainty relations

2016

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“…But we do not know if such a coupling exists in nature. If spin couples to an electromagnetic field in the measuring apparatus, like in the Stern-Gerlach measurements, the spin operators must transform as part of a tensor under Lorentz transformations to guarantee the invariance of the outcomes probabilities, with different predictions in relation to the Pauli-Lubanski treatment [23].For the reasons described in the previous paragraphs, we believe that the analysis of spin quantum correlations of relativistic systems must be revisited. Here we apply our method to the case of two entangled spin-1/2 massive particles to show how the maximum amount of violation of the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequalities [3] depends on the velocity distribution of the particles.…”

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“…But in our recent work [23] we discussed that to use the Pauli-Lubanski (or similar) spin operators to describe spin measurements, spin must couple to a quantity that transforms as part of a 4-vector under Lorentz transformations in the measuring apparatus. But we do not know if such a coupling exists in nature.…”

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Spin quantum correlations of relativistic particles

Saldanha

Vedral

2012

Phys. Rev. A

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We show that a pair of massive relativistic spin-1/2 particles prepared in a maximally entangled spin state in general is not capable of maximally violating the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequalities without a post-selection of the particles momenta, representing a major difference in relation to non-relativistic systems. This occurs because the quantization axis of the measurements performed on each particle depends on the particle velocity, such that it is not possible to define a reduced density matrix for the particles spin. We also show that the amount of violation of the CHSH inequality depends on the reference frame, and that in some frames the inequality may not be violated.PACS numbers: 03.65. Ud, 03.65.Ta, 03.30.+p, Special relativity and quantum mechanics were two theories constructed in the last century that completely changed our way to see nature, being the foundations of present-day theoretical physics. One of the most striking features of quantum mechanics is entanglement, that leads to quantum correlations among parties of a system that are stronger than what is allowed by classical physics [1][2][3]. 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. One aspect extensively studied in the posterior works on relativistic quantum information was the influence of the Wigner rotations on the amount of entanglement of the reduced spin density matrix of a system with two ore more particles in different reference frames [8,10,[15][16][17]19]. However, in our recent work [23] we discussed that since it is not possible to measure the spin of a relativistic particle in a independent way from its momentum, the definition of a reduced density matrix for the particle spin is meaningless. The ideal apparatus which is not affected by the particle momentum conjectured by Peres et al. [5] does not exist, contradicting the assumptions (explicitly or implicitly) made by the cited works [5,6,8,10, 15- * Electronic address: saldanha@df.ufpe.br 17,19,20].A second aspect studied in many of the previous works on the subject is the influence of the dependence of the Pauli-Lubanski (or similar) spin operators with the particles momenta on the amo...

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“…The Gordon decomposition [19] may be useful in the analysis of electromagnetic interactions of charged particles. In this connection, the experimental review paper [22] which clearly distinguishes the spin angular momentum and the magnetic moment of the high-energy electron is valuable; this reference emphasizes the fact that a Stern-Gerlach apparatus, on which the argument of [35] is based, is useless for the electron we are interested in. The weak interaction we discussed can, in principle, measure the helicity of elementary particles directly.…”

Section: Discussionmentioning

confidence: 99%

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

Cited by 51 publications

References 42 publications

Spin and localization of relativistic fermions and uncertainty relations

Spin and localization of relativistic fermions and uncertainty relations

Spin quantum correlations of relativistic particles

Spin operator and entanglement in quantum field theory

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