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dc.contributor.authorHall, Michael
dc.contributor.authorPati, Arun Kumar
dc.contributor.authorWu, Junde
dc.date.accessioned2017-07-27T02:21:34Z
dc.date.available2017-07-27T02:21:34Z
dc.date.issued2016
dc.identifier.issn2469-9926
dc.identifier.doi10.1103/PhysRevA.93.052118
dc.identifier.urihttp://hdl.handle.net/10072/99566
dc.description.abstractThe products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a “product representation formula” allows the standard Heisenberg uncertainty relation to be derived from a classical uncertainty relation for complex random variables. We show this formula also leads to strong uncertainty relations for unitary operators and underlies an interpretation of weak values as optimal (complex) estimates of quantum observables. Furthermore, we show that two incompatible observables that are weakly and strongly measured in a weak measurement context obey a complementarity relation under the interchange of these observables, in the form of an upper bound on the product of the corresponding weak values. Moreover, general tradeoff relations between weak purity, quantum purity, and quantum incompatibility, and also between weak and strong joint probability distributions, are obtained based on products of real and imaginary components of weak values, where these relations quantify the degree to which weak probabilities can take anomalous values in a given context.
dc.description.peerreviewedYes
dc.languageEnglish
dc.language.isoeng
dc.publisherAmerican Physical Society
dc.relation.ispartofpagefrom052118-1
dc.relation.ispartofpageto052118-9
dc.relation.ispartofjournalPhysical Review A
dc.relation.ispartofvolume93
dc.subject.fieldofresearchQuantum Physics not elsewhere classified
dc.subject.fieldofresearchQuantum Optics
dc.subject.fieldofresearchcode020699
dc.subject.fieldofresearchcode020604
dc.titleProducts of weak values: Uncertainty relations, complementarity, and incompatibility
dc.typeJournal article
dc.type.descriptionC1 - Articles
dc.type.codeC - Journal Articles
dc.description.versionAccepted Manuscript (AM)
gro.rights.copyright© 2016 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
gro.hasfulltextFull Text
gro.griffith.authorHall, Michael J.


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