Measurement incompatibility and Schrödinger-Einstein-Podolsky-Rosen steering in a class of probabilistic theories

Banik, Manik

doi:10.1063/1.4919546

Cited by 33 publications

(32 citation statements)

References 42 publications

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“…Recently, postquantum nonlocality has been discussed in discrete [48] and continuous variable scenarios [49,50]. The postquantum steering has been studied in a discrete scenario [51,52]. However, the postquantum steering for a continuous variable system has not been discussed, which remains an open question.…”

Section: Discussionmentioning

confidence: 99%

Einstein-Podolsky-Rosen steering in Gaussian weighted graph states

et al. 2019

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Einstein-Podolsky-Rosen (EPR) steering, as one of the most intriguing phenomenon of quantum mechanics, is a useful quantum resource for quantum communication. Understanding the type of EPR steering in a graph state is the basis for application of it in a quantum network. In this paper, we present EPR steering in a Gaussian weighted graph state, including a linear tripartite and a four-mode square weighted graph state. The dependence of EPR steering on weight factor in the weighted graph state is analyzed. Gaussian EPR steering between two modes of a weighted graph state is presented, which does not exist in the Gaussian cluster state (where the weight factor is unit). For the four-mode square Gaussian weighted graph state, EPR steering between one and its two nearest modes is also presented, which is absent in the four-mode square Gaussian cluster state. We also show that Gaussian EPR steering in a weighted graph state is also bounded by the Coffman-Kundu-Wootters monogamy relation. The presented results are useful for exploiting EPR steering in a Gaussian weighted graph state as a valuable resource in multiparty quantum communication tasks.I.

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Section: Discussionmentioning

confidence: 99%

Einstein-Podolsky-Rosen steering in Gaussian weighted graph states

et al. 2019

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“…For the specific case of our protocol where Alice uses mutually unbiased Pauli bases for a single qubit, we have v = 2. Substituting (13) in (12), we get,…”

Section: Quantum Key Authentication Protocolmentioning

confidence: 99%

Authentication protocol based on collective quantum steering

et al. 2019

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It is well known that certain quantum correlations like quantum steering exhibit a monogamous relationship. In this paper, we exploit the asymmetric nature of quantum steering and show that there exist states which exhibit a polygamous correlation, known as collective correlation [He and Reid, Phys. Rev. Lett. 111, 250403 (2013)], where the state of one party, Alice, can be steered only by the joint effort of the other two parties, Bob and Charlie. As an example, we explicitly single out a particular set of 3 qubit states which exhibit this polygamous relationship, known as collective steerability. We provide a recipe to identify the complete set of such states. We also provide a possible application of such states to an information theoretic task, termed as quantum key authentication (QKA) protocol. QKA can also be used in conjunction with other well known cryptography protocols to improve their security and we provide one such example with quantum private comparison (QPC).he sent indeed belongs to an entangled state and it is possible for him to steer her state.

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“…It has been recently established that in quantum mechanics a set of observables does not admit joint measurement if and only if it can be used to demonstrate steering [30][31][32][33]. From the spirit of the proof, it is obvious that if there is steering in any no signaling theory, then there must be incompatible measurements.…”

Section: Spekkens' Toy Theory: Steerable But Localmentioning

confidence: 99%

“…However, it has been shown very recently that in this generalized scenario, measurement incompatibility does not always imply Bell nonlocality, but implies a weaker form of nonlocality-namely, steering [30][31][32][33].…”

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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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Measurement incompatibility and Schrödinger-Einstein-Podolsky-Rosen steering in a class of probabilistic theories

Cited by 33 publications

References 42 publications

Einstein-Podolsky-Rosen steering in Gaussian weighted graph states

Einstein-Podolsky-Rosen steering in Gaussian weighted graph states

Authentication protocol based on collective quantum steering

Role of Measurement Incompatibility and Uncertainty in Determining Nonlocality

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