Degree of complementarity determines the nonlocality in quantum mechanics

Banik, Manik; Gazi, Md. Rajjak; Ghosh, Sibasish; Kar, Guruprasad

doi:10.1103/physreva.87.052125

Cited by 78 publications

(97 citation statements)

References 27 publications

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“…measured crosscorrelations are between compatible observables, and the cross-correlated observables have pairwise JD, the violation of a correlation inequality in this case arises from local incompatibility within A and/or within B. This explains the close connection between non-commutativity [29] or complementarity [30] or Heisenberg uncertainty [31] on the one hand and nonlocality on the other.…”

Section: P-2mentioning

confidence: 95%

Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: Hybrid spatio-temporal inequalities

Das¹,

Aravinda²,

Srikanth³

et al. 2013

EPL

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PACS 03.65.Ta -Foundations of quantum mechanics; measurement theory PACS 03.65.Ud -Entanglement and quantum nonlocality PACS 42.50.Xa -Optical tests of quantum theory Abstract -The Bell-type (spatial), Kochen-Specker (contextuality) or Leggett-Garg (temporal) inequalities are based on classically plausible but otherwise quite distinct assumptions. For any of these inequalities, satisfaction is equivalent to a joint probability distribution for all observables in the experiment. This implies a joint distribution for all pairs of observables, and is indifferent to whether or not they commute in the theory. This indifference underpins a unification of the above inequalities into a general framework of correlation inequalities. When the physical scenario is such that the correlated pairs are all compatible, the resulting correlation is non-signaling, which may be local or multi-particle, corresponding to contextuality or Bell-type inequalities. If the pairs are incompatible, the resulting correlation corresponds to Leggett-Garg (LG) inequalities. That quantum mechanics (QM) violates all these inequalities suggests a close connection between the local, spatial and temporal properties of the theory. As a concrete manifestation of the unification, we extend the method due to Roy and Singh (J. Phys. A, 11, L167 (1978)) to derive and study a new class of hybrid spatio-temporal inequalities, where the correlated pairs in the experiment are both compatible or incompatible. The implications for cryptography and monogamy inequalities of the unification are briefly touched upon.

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Section: P-2mentioning

confidence: 95%

Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: Hybrid spatio-temporal inequalities

Das¹,

Aravinda²,

Srikanth³

et al. 2013

EPL

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show abstract

“…In order to define an explicit quantification satisfying the above conditions, one can use [19] the general resource-theoretic notion of noise-robustness [2,[20][21][22][23][24]. Basically the idea is to use classical selection noise as a reference.…”

Section: Quantum Incompatibility a Definition Of Incompatibilitymentioning

confidence: 99%

Dynamics of incompatibility of quantum measurements in open systems

et al. 2016

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The non-classical nature of quantum states, often illustrated using entanglement measures or quantum discord, constitutes a resource for quantum information protocols. However, the nonclassicality of a quantum system cannot be seen as a property of the state alone, as the set of available measurements used to extract information on the system is typically restricted. In this work we study how the non-classicality of quantum measurements, quantified via their incompatibility, is influenced by quantum noise and how a non-Markovian environment can be useful for maintaining the measurement resources.

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“…Interestingly, in 2010, Oppenheim and Wehner related nonlocality with the uncertainty principle [7]. In another important piece of work, Banik et al connected nonlocality with the complementarity principle [8]. More explicitly, the results in [7,8] successfully explain a very peculiar feature of quantum nonlocality, namely its limited strength.…”

Section: Introductionmentioning

confidence: 99%

“…In another important piece of work, Banik et al connected nonlocality with the complementarity principle [8]. More explicitly, the results in [7,8] successfully explain a very peculiar feature of quantum nonlocality, namely its limited strength. The nonlocal strength of quantum correlations is restricted in comparison with other possible correlations compatible with the relativistic causality principle.…”

Section: Introductionmentioning

confidence: 99%

Role of Measurement Incompatibility and Uncertainty in Determining Nonlocality

et al. 2016

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Abstract:It has been recently shown that measurement incompatibility and fine grained uncertainty-a particular form of preparation uncertainty relation-are deeply related to the nonlocal feature of quantum mechanics. In particular, the degree of measurement incompatibility in a no-signaling theory determines the bound on the violation of Bell-CHSH inequality, and a similar role is also played by (fine-grained) uncertainty along with steering, a subtle non-local phenomenon. We review these connections, along with comments on the difference in the roles played by measurement incompatibility and uncertainty. We also discuss why the toy model of Spekkens (Phys. Rev. A 75, 032110 (2007)) shows no nonlocal feature even though steering is present in this theory.

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Degree of complementarity determines the nonlocality in quantum mechanics

Cited by 78 publications

References 27 publications

Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: Hybrid spatio-temporal inequalities

Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: Hybrid spatio-temporal inequalities

Dynamics of incompatibility of quantum measurements in open systems

Role of Measurement Incompatibility and Uncertainty in Determining Nonlocality

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