Entropic approach to local realism and noncontextuality

Chaves, Rafael; Fritz, Tobias

doi:10.1103/physreva.85.032113

Cited by 96 publications

(214 citation statements)

References 28 publications

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“…As was noted in Ref. [14], information-theoretic Bell inequalities for the n-cycle scenario can be represented in terms of the mutual information. Similarly to the standard case, the mutual q-information can be defined as [33] …”

Section: Conditional Tsallis Entropies and Related Metricsmentioning

confidence: 99%

“…[33] discussed three forms of an entropic distance based on the Tsallis entropies. First of these distances is defined similarly to (14):…”

Section: Conditional Tsallis Entropies and Related Metricsmentioning

confidence: 99%

“…Entropic inequalities of the Bell type are attractive due to their capabilities in studies of setting with arbitrary number of outcomes and inefficiencies of measurement devices. At the same time, entropic inequalities give only sufficient conditions of the non-locality or contextuality [14]. There are probability distributions that do violate Bell's inequality and do not its entropic counterpart.…”

Section: Introductionmentioning

confidence: 99%

“…Information-theoretic Bell inequalities for the KCBS scenario were examined in Refs. [14,22]. For both the CHSH and KCBS scenarios, inequalities in terms of Tsallis q-entropies were studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Formulations of Bell inequalities in terms of mean values typically assumes a fixed number of observable outcomes. Entropic treatment allows a unified expression irrespectively to a number of outcomes [14]. To test the local realism experimentally, several scenarios are known.…”

Section: Introductionmentioning

confidence: 99%

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On generalized entropies and information-theoretic Bell inequalities under decoherence

Rastegin

2015

Annals of Physics

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We consider information-theoretic inequalities of the Bell type in the presence of decoherence. It is natural that too strong coupling with the environment can prevent an observation of quantum correlations. In this regard, the use of various entropic functions may give additional capabilities to reveal desired correlations. It was already shown that the Bell and Leggett-Garg inequalities in terms conditional Tsallis entropies are more sensitive in the cases of detection inefficiencies. In this paper, we study capabilities of generalized conditional entropies of the Tsallis type in analyzing the Bell theorem in decoherence scenarios. Two forms of the conditional Tsallis q-entropy are known in the literature. We show that each of them can be used for defining a metric in the probability space of interest. Such metrics can be used in realizing the so-called triangle principle. The triangle principle has recently been proposed as a unifying approach to questions of local realism and noncontextuality. Applying the triangle principle leads to the two families of q-metric inequalities of the Bell type. Information-theoretic formulations in terms of the q-entropic metrics are first discussed for the CHSH scenario in dephasing environment. Then we also revisit q-entropic inequalities of the Leggett-Garg type. An environmental influence is modeled by the phase damping channel and by the depolarizing channel.

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Section: Conditional Tsallis Entropies and Related Metricsmentioning

confidence: 99%

“…[33] discussed three forms of an entropic distance based on the Tsallis entropies. First of these distances is defined similarly to (14):…”

Section: Conditional Tsallis Entropies and Related Metricsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On generalized entropies and information-theoretic Bell inequalities under decoherence

Rastegin

2015

Annals of Physics

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On Entropic Uncertainty Relations for Measurements of Energy and Its “Complement”

Rastegin

2019

Annalen der Physik

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Reformulation of Heisenberg's uncertainty principle in application to energy and time is a powerful heuristic principle. In a qualitative form, this statement plays the important role in foundations of quantum theory and statistical physics. A typical meaning of energy-time uncertainties is as follows. If some state exists for a finite interval of time, then it cannot have a completely definite value of energy. It is also well known that the case of energy and time principally differs from more familiar examples of two non-commuting observables. Since quantum theory was originating, many approaches to energy-time uncertainties have been proposed. Entropic approach to formulating the uncertainty principle is currently the subject of active researches. Using the Pegg concept of complementarity of the Hamiltonian, we obtain uncertainty relations of the "energy-time" type in terms of the Rényi and Tsallis entropies. Although this concept is somehow restricted in scope, derived relations can be applied to systems typically used in quantum information processing. Both the state-dependent and state-independent formulations are of interest. Some of the derived stateindependent bounds are similar to the results obtained within a more general approach on the base of sandwiched relative entropies. In this regard, our relations provide an alternative viewpoint on such bounds. The developed approach also allows us to address the case of detection inefficiencies. It is worth for several reasons including possible information-processing applications.

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Classical Invasive Description of Informationally‐Complete Quantum Processes

Richter,

Smirne,

Strunz

et al. 2023

Annalen der Physik

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In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic outcomes, these conditions reflect that the measurements do not alter the state of the underlying physical system. Prominently, this assumption has to be abandoned in the context of quantum mechanics, yet there are also classical processes in which measurements influence the measured system. Here, conditions that characterize uniquely classical processes that are probed by a reasonable class of such invasive measurements are derived. We then analyze under what circumstances such classical processes can simulate the statistics arising from quantum processes associated with informationally‐complete measurements. It is expected that this investigation will help build a bridge between two fundamental traits of non‐classicality, namely, coherence and contextuality.

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Entropic approach to local realism and noncontextuality

Cited by 96 publications

References 28 publications

On generalized entropies and information-theoretic Bell inequalities under decoherence

On generalized entropies and information-theoretic Bell inequalities under decoherence

On Entropic Uncertainty Relations for Measurements of Energy and Its “Complement”

Classical Invasive Description of Informationally‐Complete Quantum Processes

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