Wigner’s inequalities in quantum field theory

Nikitin, N.; Toms, K.

doi:10.1103/physreva.82.032109

Cited by 8 publications

(13 citation statements)

References 21 publications

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“…It is easy to show (see e.g. [12]), that the e + e − pair is in the state with zero momentum and spin. Let us suppose that at the time t 0 = 0, the spins of the electron and positron are fully anticorrelated along the axis z.…”

Section: Fieldmentioning

confidence: 99%

“…For an ideal (δ → 0) macro-device this inequality becomes inequality (12). If the time resolution of the device substantially exceeds the precession period (δ >> 1), then the inequality (13) turns into the trivial expression 0 ≤ 1/2.…”

Section: Fieldmentioning

confidence: 99%

“…An attempt at a relativistic generalization of the Bell inequalities in Wigner form may be found in [12], where various relativistic corrections were considered for decay of a pseudoscalar particle into a fermion-antifermion pair. Corrections due to non-parallel momenta of fermions (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…By changing the directions of the axes a and b to their opposite, as was done in [12], it is possible to obtain three more inequalities, analogous to (3): …”

Section: Introductionmentioning

confidence: 99%

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Time-dependent Bell inequalities in a Wigner form

2014

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Section: Fieldmentioning

confidence: 99%

Section: Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…By changing the directions of the axes a and b to their opposite, as was done in [12], it is possible to obtain three more inequalities, analogous to (3): …”

Section: Introductionmentioning

confidence: 99%

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Time-dependent Bell inequalities in a Wigner form

2014

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“…This paper is a continuation of series of papers studying time-dependent extensions of the Wigner inequalities [22,23,24,25]. This series was stimulated by a desire to generalize the Bell inequalities [10,11,12] and Wigner inequalities [9] for quantum field theory (QFT).…”

Section: Introductionmentioning

confidence: 99%

Wigner inequalities for testing the hypothesis of realism and concepts of macroscopic and local realism

Nikitin

Toms

2019

Phys. Rev. A

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We propose a new Wigner inequality suitable for test of the hypothesis of realism. We show that this inequality is not identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained inequality is suitable for test of realism not only in quantum mechanical systems, but also in quantum field systems.Also we propose a mathematically consistent derivation of the Leggett-Garg inequality in Wigner form, which was recently presented in the literature, for three and n distinct moments of time. Contrary to these works, our rigor derivation uses Kolmogorov axiomatics of probability theory. We pay special attention to the construction and studies of the spaces of elementary outcomes. Basing on the the Leggett-Garg inequality in Wigner form for n distinct moments of time we prove that any unitary evolution of a quantum system contradicts the concept of macroscopic realism. We show that application of the concept of macroscopic realism to any quantum system leads to "freezing" of the system in the initial state.It is shown that for a particle with an infinite number of observables the probability to find a pair of the observables in some defined state is zero, even if the operators of these observables commute. This fact might serve as an additional logical argument for the contradiction between quantum theory and classical realism.

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Test of a hypothesis of realism in quantum theory using a Bayesian approach

Nikitin

Toms

2017

Phys. Rev. A

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In this paper we propose a time-independent equality and time-dependent inequality, suitable for an experimental test of the hypothesis of realism. The derivation of these relations is based on the concept of conditional probability and on Bayes' theorem in the framework of Kolmogorov's axiomatics of probability theory. The equality obtained is intrinsically different from the well known GHZ-equality and its variants, because violation of the new equality might be tested in experiments with only two microsystems in a maximally entangled Bell state | Ψ − ⟩, while a test of the GHZ-equality requires at least three quantum systems in a special state | Ψ GHZ ⟩. The obtained inequality differs from Bell's, Wigner's, and Leggett-Garg inequalities, because it deals with spin = 1/2 projections onto only two non-parallel directions at two different moments of time, while a test of the Bell and Wigner inequalities requires at least three non-parallel directions, and a test of the Leggett-Garg inequalities -at least three distinct moments of time. Hence, the proposed inequality seems to allow one to avoid the "contextuality loophole". Violation of the proposed equality and inequality is illustrated with the behaviour of a pair of anti-correlated spins in an external magnetic field and also with the oscillations of flavour-entangled pairs of neutral pseudoscalar mesons.

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Wigner’s inequalities in quantum field theory

Cited by 8 publications

References 21 publications

Time-dependent Bell inequalities in a Wigner form

Time-dependent Bell inequalities in a Wigner form

Wigner inequalities for testing the hypothesis of realism and concepts of macroscopic and local realism

Test of a hypothesis of realism in quantum theory using a Bayesian approach

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