Information-theoretic Bell inequalities based on Tsallis entropy

Wajs, Marek; Kurzyński, Paweł; Kaszlikowski, Dagomir

doi:10.1103/physreva.91.012114

Cited by 14 publications

(18 citation statements)

References 27 publications

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“…We refrain from presenting the details here, since similar conclusions were found in Ref. [26]. Instead, we will address the noisy trichotomic case in the Leggett-Garg scenario.…”

Section: Metric Inequalities For the Chsh Scenario In Dephasing mentioning

confidence: 92%

“…We can obtain (30) by taking the limit q → 1 in both the relations (25) and (26). We are now ready to prove that the conditional entropy (13) of degree q ≥ 1 obeys the triangle inequality.…”

Section: Propositionmentioning

confidence: 99%

“…In Ref. [26], the mentioned q-entropic metrics were used to study Bell inequalities for a pair of entangled qutrits. These metrics can all be represented in terms of the mutual q-information together with either…”

Section: Conditional Tsallis Entropies and Related Metricsmentioning

confidence: 99%

“…Some advantages of this approach were already examined [23,26,31]. We will mainly focus on entropic inequalities of the Bell type under decoherence.…”

Section: Introductionmentioning

confidence: 99%

“…Applications of this principle to qutrits with use of the Tsallis-type metrics were recently examined in Ref. [26].…”

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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“…We refrain from presenting the details here, since similar conclusions were found in Ref. [26]. Instead, we will address the noisy trichotomic case in the Leggett-Garg scenario.…”

Section: Metric Inequalities For the Chsh Scenario In Dephasing mentioning

confidence: 92%

Section: Propositionmentioning

confidence: 99%

Section: Conditional Tsallis Entropies and Related Metricsmentioning

confidence: 99%

“…Some advantages of this approach were already examined [23,26,31]. We will mainly focus on entropic inequalities of the Bell type under decoherence.…”

Section: Introductionmentioning

confidence: 99%

“…Applications of this principle to qutrits with use of the Tsallis-type metrics were recently examined in Ref. [26].…”

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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Quantum work fluctuations versus macrorealism in terms of non-extensive entropies

Rastegin

2018

Physica A: Statistical Mechanics and its Applications

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Fluctuations of the work performed on a driven quantum system can be characterized by the socalled fluctuation theorems. The Jarzynski relation and the Crooks theorem are famous examples of exact equalities characterizing non-equilibrium dynamics. Such statistical theorems are typically formulated in a similar manner in both classical and quantum physics. Leggett-Garg inequalities are inspired by the two assumptions referred to as the macroscopic realism and the non-invasive measurability. Together, these assumptions are known as the macrorealism in the broad sense. Quantum mechanics is provably incompatible with restrictions of the Leggett-Garg type. It turned out that Leggett-Garg inequalities can be used to distinguish quantum and classical work fluctuations. We develop this issue with the use of entropic functions of the Tsallis type. Varying the entropic parameter, we are often able to reach more robust detection of violations of the corresponding Leggett-Garg inequalities. In reality, all measurement devices suffer from losses. Within the entropic formulation, detection inefficiencies can naturally be incorporated into the consideration. This question also shows advantages that are provided due to the use of generalized entropies.

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Experimental investigation of the information entropic Bell inequality

Cao

Zhao

Liu

et al. 2016

Sci Rep

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Inequalities of information entropic play a fundamental role in information theory and have been employed effectively in finding bounds on optimal rates of various information-processing tasks. In this paper, we perform the first experimental demonstration of the information-theoretic spin-1/2 inequality using the high-fidelity entangled state. Furthermore, we study the evolution of information difference of entropy when photons passing through different noisy channels and give the experimental rules of the information difference degradation. Our work provides an new essential tool for quantum information processing and measurement, and offers new insights into the dynamics of quantum correlation in open systems.

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Information-theoretic Bell inequalities based on Tsallis entropy

Cited by 14 publications

References 27 publications

On generalized entropies and information-theoretic Bell inequalities under decoherence

On generalized entropies and information-theoretic Bell inequalities under decoherence

Quantum work fluctuations versus macrorealism in terms of non-extensive entropies

Experimental investigation of the information entropic Bell inequality

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