Time-dependent Bell inequalities in a Wigner form

Nikitin, N.; Sotnikov, Vasily; Toms, K.

doi:10.1103/physreva.90.042124

Cited by 7 publications

(27 citation statements)

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“…The complementarity principle is directly related to the concept of realism. We believe that the statement of "testing the concept of realism", most correctly reflects the gist and the results of [42][43][44]. Also the connection between the violation of Leggett-Garg inequalities and the complementarity principle does not appear to be that obvious.…”

Section: Introductionmentioning

confidence: 88%

“…The expression of the Leggett-Garg inequalities is similar to the Bell's inequalities in form [9]. Because of that the Leggett-Garg inequalities are sometimes called "temporal Bell Wigner's inequalities" were introduced [42]. References to all the key works related to…”

Section: Time-dependent Inequalities Were Proposed By a Leggett And mentioning

confidence: 99%

“…We now derive a time-dependent inequality which follows from the hypothesis of realism and Bayes' theorem. In [42][43][44] this inequality may be written as follows…”

Section: Testing the Realism Hypothesis Using Bayes' Theoremmentioning

confidence: 99%

“…The event 3 ( 0 ) remains the same. The explicit form of the functions F ( , , , ) is shown in Appendix D. The inequality (42) in systems of neutral -mesons is violated not only while choosing events to which the function F 1 , corresponds, but also for sets of events, to which correspond the functions F 2 and F 5 . The correspondence between sets of events and the functions is given in Table II. The behaviour of the function F 5 for -mesons is shown in Figure 1 In the case of entangled states of 0¯0 -mesons, the following functions lead to violation of inequality (42): F 3 , F 4 , and F 5 , which were already considered for entangled kaons.…”

Section: Corollaries Of Bayes' Theorem For Systems Of Neutral Psementioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 88%

Section: Time-dependent Inequalities Were Proposed By a Leggett And mentioning

confidence: 99%

“…We now derive a time-dependent inequality which follows from the hypothesis of realism and Bayes' theorem. In [42][43][44] this inequality may be written as follows…”

Section: Testing the Realism Hypothesis Using Bayes' Theoremmentioning

confidence: 99%

Section: Corollaries Of Bayes' Theorem For Systems Of Neutral Psementioning

confidence: 99%

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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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“…This is a temporal analogue of BI in terms of time-separated correlation functions corresponding to successive measurement outcomes for a temporally evolving system. While furnishing a signature of distinctly quantum behaviour, LGI complements BI in providing insight into physical reality manifested by non-classicality of quantum systems.LGI has been used for probing possible limits of quantum mechanics in the macroscopic regime in various scenarios [8][9][10][11][12][13][14][15][16][17][18][19][20]. For…”

mentioning

confidence: 99%

The Leggett-Garg inequality and Page-Wootters mechanism

Gangopadhyay

Roy

2016

EPL

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Violation of the Leggett-Garg inequality (LGI) implies quantum phenomena. In this light we establish that the Moreva et al. [21] experiment demonstrating the Page-Wootter's mechanism [3] falls in the quantum domain. An observer outside a 2-photons world does not detect any change in the 2−photons state,i.e. there is no time parameter for the outside observer. But an observer attached to one of the photons sees the other photon evolving and this means there is an "internal" time. The LGI is violated for the clock photon whose state evolves with the internal time as measured by the system photon. Conditional probabilities in this 2-photons system are computed for both sharp and unsharp measurements. The conditional probability increases for entangled states as obtained by Page and Wootters for both ideal and also unsharp measurements. We discuss how the conditional probabilities can be used to distinguish between massless and massive gravitons. This is important in the context of gravitational waves.1.Introduction-Field theories describing gauge particles are gauge theories and are invariant with respect to some local symmetry group transformations. In Yang-Mills theories these are the non-abelian gauge transformations corresponding to SU (N ) groups. For gravity these are space-time diffeomorphisms. The invariance corresponds to local Lorentz invariance. In gauge theories different solutions arising from same initial conditions become related by the local symmetry. So the general solution of the field equations is non-unique as it contains arbitrary time-dependent functions. So a subset of initial conditions needs to be chosen. This subset is defined by what are called the lagrangian constraints. In the hamiltonian formalism this implies conditions on the allowed initial positions and momenta. Time evolution must conserve these conditions. This can lead to further constraints. A first class constraint is a dynamical quantity in a constrained hamiltonian system whose Poisson bracket with all other constraints vanishes on the constraint surface in phase space. Any constraint which is not first class is a second class constraint. Local symmetry transformations are generated by the first class constraints. So gauge theories are systems with first class constraints.An early attempt to quantise gravity was through the Wheeler-DeWitt (WD) equation [1]. This results from the canonical quantisation of Einstein gravity using Dirac's constrained formalism [2]. An embodiment of the quantum version of the hamiltonian constraint using metric variables gives the WD equation. But this equation is time-independent. All observables are constant and the resulting universe is unchanging and boring.Page and Wootters [3] proposed that the static universe (as observed by an external observer) actually evolves with respect to time as seen by some internal observer within the universe. This is because of quantum correlations (entanglement ) between different con-stituents within the universe. Consider a direct product of two different sta...

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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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Time-dependent Bell inequalities in a Wigner form

Cited by 7 publications

References 49 publications

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

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

The Leggett-Garg inequality and Page-Wootters mechanism

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

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