Connection between measurement disturbance relation and multipartite quantum correlation

Li, Junli; Du, Kun; Qiao, C. F.

doi:10.1103/physreva.91.012110

Cited by 5 publications

(6 citation statements)

References 27 publications

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“…Explicit functional relations between variance and entropy are constructed for higher spin system. While interest in their own right, these results may also have direct applications in the study of quantum nonlocality, as the uncertainty relations are employed to determine the strength of quantum correlations [4,5]. Another important impact of the equivalence theorem is on the structure of the uncertainty relation in the presence of quantum memory [37], which is crucial for the security of quantum key distribution.…”

Section: Discussionmentioning

confidence: 99%

Equivalence theorem of uncertainty relations

Qiao

2016

J. Phys. A: Math. Theor.

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We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators. That means an uncertainty relation in the language of entropy may be mapped onto a variance-based one, and vice versa. Employing the equivalence theorem, alternative formulations of entropic uncertainty relations stronger than existing ones in the literature are obtained for qubit system, and variance based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations.

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Section: Discussionmentioning

confidence: 99%

Equivalence theorem of uncertainty relations

Qiao

2016

J. Phys. A: Math. Theor.

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“…While the uncertainty relation involves the ensemble properties of variances, the MDR relates the measurement precision to its back actions, which is currently a hot topic [20]. Though being fundamentally different, the uncertainty relation and the MDR are both shown to be correlated with the quantum nonlocality [8,21]. Therefore, it is expected that every new forms of uncertainty relations may shed some light on the study of the connection between uncertainty principle and quantum nonlocality.…”

Section: Discussionmentioning

confidence: 99%

“…. For completely mixed state where | p | = 0, we have x = y = 0 from equation (21), and the variances reduce to ∆A 2 = Tr[A 2 ]/N and ∆B 2 = Tr[B 2 ]/N.…”

Section: An Example Of N -Dimensional Systemmentioning

confidence: 99%

Reformulating the Quantum Uncertainty Relation

Qiao

2015

Sci Rep

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Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic quantities. Both these forms are inequalities involving pairwise observables, and are found to be nontrivial to incorporate multiple observables. In this work we introduce a new form of uncertainty relation which may give out complete trade-off relations for variances of observables in pure and mixed quantum systems. Unlike the prevailing uncertainty relations, which are either quantum state dependent or not directly measurable, our bounds for variances of observables are quantum state independent and immune from the “triviality” problem of having zero expectation values. Furthermore, the new uncertainty relation may provide a geometric explanation for the reason why there are limitations on the simultaneous determination of different observables in N-dimensional Hilbert space.

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“…Optical quantum systems [19][20][21][22][23][24][25][26] are prominent candidates for testing nonlocal quantum correlations, since multiphoton entanglement, interferometry and measurement are relatively easy to perform in experiments, as long as the number of photons is not very large. In 2001, Weinfurter and Żukowski [27] proposed a scheme to produce a superposition of four-photon GHZ state with a product state of two Bell states and investigated the features of this state by constructing a Bell-type inequality.…”

Section: Introductionmentioning

confidence: 99%

Violation of generalized Bell inequality and its optimal measurement settings

Ding,

He,

Yan

et al. 2018

Preprint

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We provide a method to describe quantum nonlocality for n-qubit systems. By treating the correlation function as an n-index tensor, we derive a generalized Bell inequality. Taking generalized Greenberger-Horne-Zeilinger (GHZ) state for example, we calculate quantum prediction under a series of measurement settings involving various angle parameters. We reveal the exact relationship between quantum prediction and the angle parameters. We show that there exists a set of optimal measurement settings and find the corresponding maximal quantum prediction for n-qubit generalized GHZ states. As an example, we consider an interesting situation involving only two angle parameters. Finally, we obtain a criterion for the violation of the generalized Bell inequality.

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Connection between measurement disturbance relation and multipartite quantum correlation

Cited by 5 publications

References 27 publications

Equivalence theorem of uncertainty relations

Equivalence theorem of uncertainty relations

Reformulating the Quantum Uncertainty Relation

Violation of generalized Bell inequality and its optimal measurement settings

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