Experimental device-independent tests of classical and quantum entropy

Zhu, Fei; Zhang, Wei; Chen, Sijing; You, Lixing; Wang, Zhen

doi:10.1103/physreva.94.062340

Cited by 2 publications

(3 citation statements)

References 34 publications

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“…Hence, whichever probability structure  we choose (consistent with ), the observed marginal probabilities can always be interpreted as arising from a global probability distribution. Similarly, the choice of extended probability structure  including the switch variable Q in equation (34) implies also the existence of a global probability distribution…”

Section: Appendix C Relations Between Different Probability Structuresmentioning

confidence: 99%

“…Our goal in this paper is to introduce a new framework for the derivation of causal inequalities and the study of their potential violations: the entropic approach to causal correlations. The idea of using entropies to understand sets of correlations has its origins in the context of Bell inequalities [26][27][28][29] but since then has also found various other applications in quantum contextuality [30][31][32], device-independent applications [33,34], causal inference [9,35,36] and in the characterization of nonsignaling correlations [37]. As for these previous applications, the interest in characterizing the entropies compatible with causal correlations stems not only from practical and technical issues, but also from a more fundamental point.…”

Section: Introductionmentioning

confidence: 99%

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The entropic approach to causal correlations

et al. 2017

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The existence of a global causal order between events places constraints on the correlations that parties may share. Such 'causal correlations' have been the focus of recent attention, driven by the realization that some extensions of quantum mechanics may violate so-called causal inequalities. In this paper we study causal correlations from an entropic perspective, and we show how to use this framework to derive entropic causal inequalities. We consider two different ways to derive such inequalities. Firstly, we consider a method based on the causal Bayesian networks describing the causal relations between the parties. In contrast to the Bell-nonlocality scenario, where this method has previously been shown to be ineffective, we show that it leads to several interesting entropic causal inequalities. Secondly, we consider an alternative method based on counterfactual variables that has previously been used to derive entropic Bell inequalities. We compare the inequalities obtained via these two methods and discuss their violation by noncausal correlations. As an application of our approach, we derive bounds on the quantity of information-which is more naturally expressed in the entropic framework-that parties can communicate when operating in a definite causal order.

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Section: Appendix C Relations Between Different Probability Structuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The entropic approach to causal correlations

et al. 2017

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“…In a recent proposal, by employing binary-outcome measurements a certification of an arbitrary-dimensional quantum systems is proposed [20]. Experimental verifications of dimension witness including higher dimensional system has also been performed [25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Device-independent certification of the Hilbert-space dimension using a family of Bell expressions

Pan

Mahato

2020

Phys. Rev. A

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Dimension witness provides a device-independent certification of the minimal dimension required to reproduce the observed data without imposing assumptions on the functioning of the devices used to generate the experimental statistics. In this paper, we provide a family of Bell expressions where Alice and Bob perform 2 n−1 and n number of dichotomic measurements respectively which serve as the device-independent dimension witnesses of Hilbert space of 2 m dimensions with m = 1, 2..2 n/2. The family of Bell expressions considered here determines the success probability of a communication game known as n-bit parity-oblivious random access code. The parity obliviousness constraint is equivalent to preparation non-contextuality assumption in an ontological model of an operational theory. For any given n ≥ 3, if such a constraint is imposed on the encoding scheme of the random-access code, then the local bound of the Bell expression reduces to the preparation noncontextual bound. We provide explicit examples for n = 4, 5 case to demonstrate that the relevant Bell expressions certify the qubit and two-qubit system, and for n = 6 case, the relevant Bell expression certifies the qubit, two-qubit and three-qubit systems. We further demonstrate the sharing of quantum preparation contextuality by multiple Bobs sequentially to examine whether number of Bobs sharing the preparation contextuality is dependent on the dimension of the system. We provide explicit example of n = 5 and 6 to demonstrate that number of Bobs sequentially sharing the contextuality remains same for any of the 2 m dimensional systems.

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Experimental device-independent tests of classical and quantum entropy

Cited by 2 publications

References 34 publications

The entropic approach to causal correlations

The entropic approach to causal correlations

Device-independent certification of the Hilbert-space dimension using a family of Bell expressions

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