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Article: Incompatibility of observables as state-independent bound of uncertainty relations

TitleIncompatibility of observables as state-independent bound of uncertainty relations
Authors
KeywordsUncertainty analysis
Bipartite state
Fundamental constraints
Intrinsic property
Measurement precision
Issue Date2019
PublisherAmerican Physical Society. The Journal's web site is located at http://journals.aps.org/pra/
Citation
Physical Review A: covering atomic, molecular, and optical physics and quantum information, 2019, v. 100 n. 3, article no. 032118 How to Cite?
AbstractFor a pair of observables, they are called “incompatible” if and only if their commutator does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the incompatibility among three or more observables? Here, we explore one possible route towards this goal through uncertainty relations, which impose fundamental constraints on the measurement precisions for incompatible observables. Specifically, we propose to measure the incompatibility by the optimal state-independent bounds of additive variance-based uncertainty relations. In this way, the degree of incompatibility becomes an intrinsic property among the operators, i.e., state independent. In particular, we focus on the incompatibility of spin-1/2 systems as an illustration. For an arbitrary, including nonorthogonal, setting of a finite number Pauli-spin operators, the incompatibility is analytically solved; the spins are maximally incompatible if and only if they are orthogonal to each other. On the other hand, our measure of incompatibility represents a versatile tool for applications such as testing the entanglement of bipartite states, and EPR-steering criteria.
Persistent Identifierhttp://hdl.handle.net/10722/278774
ISSN
2019 Impact Factor: 2.777

 

DC FieldValueLanguage
dc.contributor.authorXiao, Y-
dc.contributor.authorGuo, C-
dc.contributor.authorMENG, F-
dc.contributor.authorJing, N-
dc.contributor.authorYung, M-H-
dc.date.accessioned2019-10-21T02:13:49Z-
dc.date.available2019-10-21T02:13:49Z-
dc.date.issued2019-
dc.identifier.citationPhysical Review A: covering atomic, molecular, and optical physics and quantum information, 2019, v. 100 n. 3, article no. 032118-
dc.identifier.issn2469-9926-
dc.identifier.urihttp://hdl.handle.net/10722/278774-
dc.description.abstractFor a pair of observables, they are called “incompatible” if and only if their commutator does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the incompatibility among three or more observables? Here, we explore one possible route towards this goal through uncertainty relations, which impose fundamental constraints on the measurement precisions for incompatible observables. Specifically, we propose to measure the incompatibility by the optimal state-independent bounds of additive variance-based uncertainty relations. In this way, the degree of incompatibility becomes an intrinsic property among the operators, i.e., state independent. In particular, we focus on the incompatibility of spin-1/2 systems as an illustration. For an arbitrary, including nonorthogonal, setting of a finite number Pauli-spin operators, the incompatibility is analytically solved; the spins are maximally incompatible if and only if they are orthogonal to each other. On the other hand, our measure of incompatibility represents a versatile tool for applications such as testing the entanglement of bipartite states, and EPR-steering criteria.-
dc.languageeng-
dc.publisherAmerican Physical Society. The Journal's web site is located at http://journals.aps.org/pra/-
dc.relation.ispartofPhysical Review A: covering atomic, molecular, and optical physics and quantum information-
dc.rightsCopyright 2019 by The American Physical Society. This article is available online at https://doi.org/10.1103/PhysRevA.100.032118.-
dc.subjectUncertainty analysis-
dc.subjectBipartite state-
dc.subjectFundamental constraints-
dc.subjectIntrinsic property-
dc.subjectMeasurement precision-
dc.titleIncompatibility of observables as state-independent bound of uncertainty relations-
dc.typeArticle-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1103/PhysRevA.100.032118-
dc.identifier.scopuseid_2-s2.0-85072922316-
dc.identifier.hkuros307688-
dc.identifier.volume100-
dc.identifier.issue3-
dc.identifier.spagearticle no. 032118-
dc.identifier.epagearticle no. 032118-
dc.publisher.placeUnited States-

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