Entropic uncertainty relations via direct-sum majorization relation for generalized measurements

Kyunghyun Baek, Hyunchul Nha, Wonmin Son

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches (Friendland, S.; Gheorghiu, V.; Gour, G. Phys. Rev. Lett. 2013, 111, 230401; Rastegin, A.E.; Zyczkowski, K. J. Phys. A, 2016, 49, 355301), particularly by extending the direct-sum majorization relation first introduced in (Rudnicki, Ł.; Puchała, Z.; Zyczkowski, K. Phys. Rev. A 2014, 89, 052115). We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen-Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.

Original languageEnglish
Article number270
JournalEntropy
Volume21
Issue number3
DOIs
Publication statusPublished - 1 Mar 2019

Fingerprint

concavity
operators
Hilbert space

Keywords

  • Direct-sum majorization relation
  • Entropic uncertainty relations
  • Positive-operator-valued measure

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Entropic uncertainty relations via direct-sum majorization relation for generalized measurements. / Baek, Kyunghyun; Nha, Hyunchul; Son, Wonmin.

In: Entropy, Vol. 21, No. 3, 270, 01.03.2019.

Research output: Contribution to journalArticle

@article{6de8b34adbfe483695fe1b233e9f61c1,
title = "Entropic uncertainty relations via direct-sum majorization relation for generalized measurements",
abstract = "We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches (Friendland, S.; Gheorghiu, V.; Gour, G. Phys. Rev. Lett. 2013, 111, 230401; Rastegin, A.E.; Zyczkowski, K. J. Phys. A, 2016, 49, 355301), particularly by extending the direct-sum majorization relation first introduced in (Rudnicki, Ł.; Puchała, Z.; Zyczkowski, K. Phys. Rev. A 2014, 89, 052115). We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen-Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.",
keywords = "Direct-sum majorization relation, Entropic uncertainty relations, Positive-operator-valued measure",
author = "Kyunghyun Baek and Hyunchul Nha and Wonmin Son",
year = "2019",
month = "3",
day = "1",
doi = "10.3390/e21030270",
language = "English",
volume = "21",
journal = "Entropy",
issn = "1099-4300",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "3",

}

TY - JOUR

T1 - Entropic uncertainty relations via direct-sum majorization relation for generalized measurements

AU - Baek, Kyunghyun

AU - Nha, Hyunchul

AU - Son, Wonmin

PY - 2019/3/1

Y1 - 2019/3/1

N2 - We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches (Friendland, S.; Gheorghiu, V.; Gour, G. Phys. Rev. Lett. 2013, 111, 230401; Rastegin, A.E.; Zyczkowski, K. J. Phys. A, 2016, 49, 355301), particularly by extending the direct-sum majorization relation first introduced in (Rudnicki, Ł.; Puchała, Z.; Zyczkowski, K. Phys. Rev. A 2014, 89, 052115). We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen-Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.

AB - We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches (Friendland, S.; Gheorghiu, V.; Gour, G. Phys. Rev. Lett. 2013, 111, 230401; Rastegin, A.E.; Zyczkowski, K. J. Phys. A, 2016, 49, 355301), particularly by extending the direct-sum majorization relation first introduced in (Rudnicki, Ł.; Puchała, Z.; Zyczkowski, K. Phys. Rev. A 2014, 89, 052115). We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen-Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.

KW - Direct-sum majorization relation

KW - Entropic uncertainty relations

KW - Positive-operator-valued measure

UR - http://www.scopus.com/inward/record.url?scp=85063581152&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063581152&partnerID=8YFLogxK

U2 - 10.3390/e21030270

DO - 10.3390/e21030270

M3 - Article

VL - 21

JO - Entropy

JF - Entropy

SN - 1099-4300

IS - 3

M1 - 270

ER -