Discrete dynamics in the set of quantum measurements

2024
journal article
article
dc.abstract.enA quantum measurement, often referred to as positive operator-valued measurement, is a set of positive operators $P_{j} = P_{j}^{\dagger}\geqslant 0$ summing to identity, $\Sigma_{j}P_{j} = \mathbb{1}$. This can be seen as a generalization of a probability distribution of positive real numbers summing to unity, whose evolution is given by a stochastic matrix. We describe transformations in the set of quantum measurements by blockwise stochastic matrices, composed of positive blocks that sum columnwise to identity, and the notion of sequential product of matrices. We show that such transformations correspond to a sequence of quantum measurements. Imposing additionally the dual condition that the sum of blocks in each row is equal to identity we arrive at blockwise bistochastic matrices (also called quantum magic squares). Analyzing their dynamical properties, we formulate a quantum analog of the Ostrowski description of the classical Birkhoff polytope and introduce the notion of majorization between quantum measurements. Our framework provides a dynamical characterization of the set of blockwise bistochastic matrices and establishes a resource theory in the set of quantum measurements.
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki Teoretycznej
dc.contributor.authorRico, Albert - 444381
dc.contributor.authorŻyczkowski, Karol - 132981
dc.date.accessioned2025-03-25T17:49:08Z
dc.date.available2025-03-25T17:49:08Z
dc.date.createdat2025-03-25T15:03:10Zen
dc.date.issued2024
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number43
dc.description.versionostateczna wersja wydawcy
dc.description.volume57
dc.identifier.articleid435302
dc.identifier.doi10.1088/1751-8121/ad7dc2
dc.identifier.eissn1751-8121
dc.identifier.issn1751-8113
dc.identifier.urihttps://ruj.uj.edu.pl/handle/item/550677
dc.languageeng
dc.language.containereng
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.typeinne
dc.subject.enquantum measurement
dc.subject.enbistochastic
dc.subject.enstochastic
dc.subject.endynamics
dc.subject.enjoint measurability
dc.subject.enquantum magic square
dc.subject.enBirkhoff-von Neumann
dc.subtypeArticle
dc.titleDiscrete dynamics in the set of quantum measurements
dc.title.journalJournal of Physics A: Mathematical and Theoretical
dc.typeJournalArticle
dspace.entity.typePublicationen
dc.abstract.en
A quantum measurement, often referred to as positive operator-valued measurement, is a set of positive operators $P_{j} = P_{j}^{\dagger}\geqslant 0$ summing to identity, $\Sigma_{j}P_{j} = \mathbb{1}$. This can be seen as a generalization of a probability distribution of positive real numbers summing to unity, whose evolution is given by a stochastic matrix. We describe transformations in the set of quantum measurements by blockwise stochastic matrices, composed of positive blocks that sum columnwise to identity, and the notion of sequential product of matrices. We show that such transformations correspond to a sequence of quantum measurements. Imposing additionally the dual condition that the sum of blocks in each row is equal to identity we arrive at blockwise bistochastic matrices (also called quantum magic squares). Analyzing their dynamical properties, we formulate a quantum analog of the Ostrowski description of the classical Birkhoff polytope and introduce the notion of majorization between quantum measurements. Our framework provides a dynamical characterization of the set of blockwise bistochastic matrices and establishes a resource theory in the set of quantum measurements.
dc.affiliation
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki Teoretycznej
dc.contributor.author
Rico, Albert - 444381
dc.contributor.author
Życzkowski, Karol - 132981
dc.date.accessioned
2025-03-25T17:49:08Z
dc.date.available
2025-03-25T17:49:08Z
dc.date.createdaten
2025-03-25T15:03:10Z
dc.date.issued
2024
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.number
43
dc.description.version
ostateczna wersja wydawcy
dc.description.volume
57
dc.identifier.articleid
435302
dc.identifier.doi
10.1088/1751-8121/ad7dc2
dc.identifier.eissn
1751-8121
dc.identifier.issn
1751-8113
dc.identifier.uri
https://ruj.uj.edu.pl/handle/item/550677
dc.language
eng
dc.language.container
eng
dc.rights
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licence
CC-BY
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.type
inne
dc.subject.en
quantum measurement
dc.subject.en
bistochastic
dc.subject.en
stochastic
dc.subject.en
dynamics
dc.subject.en
joint measurability
dc.subject.en
quantum magic square
dc.subject.en
Birkhoff-von Neumann
dc.subtype
Article
dc.title
Discrete dynamics in the set of quantum measurements
dc.title.journal
Journal of Physics A: Mathematical and Theoretical
dc.type
JournalArticle
dspace.entity.typeen
Publication
Affiliations

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