Strong majorization entropic uncertainty relations

2014
journal article
article
119
dc.abstract.enWe analyze entropic uncertainty relations in a finite-dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the recent bounds by Coles and Piani [P. Coles and M. Piani, Phys. Rev. A 89, 022112 (2014)], which are known to be stronger than the well-known result of Maassen and Uffink [H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. 60, 1103 (1988)]. Furthermore, we find a bound based on majorization techniques, which also happens to be stronger than the recent results involving the largest singular values of submatrices of the unitary matrix connecting both bases. The first set of bounds gives better results for unitary matrices close to the Fourier matrix, while the second one provides a significant improvement in the opposite sectors. Some results derived admit generalization to arbitrary mixed states, so that corresponding bounds are increased by the von Neumann entropy of the measured state. The majorization approach is finally extended to the case of several measurements.pl
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiegopl
dc.contributor.authorRudnicki, Łukaszpl
dc.contributor.authorPuchała, Zbigniew - 228195 pl
dc.contributor.authorŻyczkowski, Karol - 132981 pl
dc.date.accessioned2015-02-09T13:46:31Z
dc.date.available2015-02-09T13:46:31Z
dc.date.issued2014pl
dc.description.number5pl
dc.description.publication1pl
dc.description.volume89pl
dc.identifier.articleid052115pl
dc.identifier.doi10.1103/PhysRevA.89.052115pl
dc.identifier.eissn1094-1622pl
dc.identifier.eissn1538-4446pl
dc.identifier.issn1050-2947pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/2932
dc.languageengpl
dc.language.containerengpl
dc.rightsDodaję tylko opis bibliograficzny*
dc.rights.licencebez licencji
dc.rights.uri*
dc.subtypeArticlepl
dc.titleStrong majorization entropic uncertainty relationspl
dc.title.journalPhysical Review. A, Atomic, Molecular, and Optical Physicspl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
We analyze entropic uncertainty relations in a finite-dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the recent bounds by Coles and Piani [P. Coles and M. Piani, Phys. Rev. A 89, 022112 (2014)], which are known to be stronger than the well-known result of Maassen and Uffink [H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. 60, 1103 (1988)]. Furthermore, we find a bound based on majorization techniques, which also happens to be stronger than the recent results involving the largest singular values of submatrices of the unitary matrix connecting both bases. The first set of bounds gives better results for unitary matrices close to the Fourier matrix, while the second one provides a significant improvement in the opposite sectors. Some results derived admit generalization to arbitrary mixed states, so that corresponding bounds are increased by the von Neumann entropy of the measured state. The majorization approach is finally extended to the case of several measurements.
dc.affiliationpl
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
dc.contributor.authorpl
Rudnicki, Łukasz
dc.contributor.authorpl
Puchała, Zbigniew - 228195
dc.contributor.authorpl
Życzkowski, Karol - 132981
dc.date.accessioned
2015-02-09T13:46:31Z
dc.date.available
2015-02-09T13:46:31Z
dc.date.issuedpl
2014
dc.description.numberpl
5
dc.description.publicationpl
1
dc.description.volumepl
89
dc.identifier.articleidpl
052115
dc.identifier.doipl
10.1103/PhysRevA.89.052115
dc.identifier.eissnpl
1094-1622
dc.identifier.eissnpl
1538-4446
dc.identifier.issnpl
1050-2947
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/2932
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Dodaję tylko opis bibliograficzny
dc.rights.licence
bez licencji
dc.rights.uri*
dc.subtypepl
Article
dc.titlepl
Strong majorization entropic uncertainty relations
dc.title.journalpl
Physical Review. A, Atomic, Molecular, and Optical Physics
dc.typepl
JournalArticle
dspace.entity.type
Publication
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