A Note on the Hierarchy of Quantum Measurement Incompatibilities

A Note on the Hierarchy of Quantum Measurement Incompatibilities

The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operat...

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Main Authors: Bao-Zhi Sun, Zhi-Xi Wang, Xianqing Li-Jost, Shao-Ming Fei
Format: Article
Language:English
Published: MDPI AG 2020-01-01
Series:Entropy
Subjects:
quntum measurements
hierarchy of incompatibilities
semidefinite program
Online Access:https://www.mdpi.com/1099-4300/22/2/161
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spelling doaj-09b592984e7044b9b1883a929288f1a02020-11-25T01:47:08ZengMDPI AGEntropy1099-43002020-01-0122216110.3390/e22020161e22020161A Note on the Hierarchy of Quantum Measurement IncompatibilitiesBao-Zhi Sun0Zhi-Xi Wang1Xianqing Li-Jost2Shao-Ming Fei3School of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaMax Planck Institute for Mathematics in the Sciences, 04103 Leipzig, GermanySchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaThe quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators, we present a complete classification of the incompatibility of a given measurement assemblage with <i>n</i> members. Detailed examples are given for the incompatibility of unbiased qubit measurements based on a semidefinite program.https://www.mdpi.com/1099-4300/22/2/161quntum measurementshierarchy of incompatibilitiessemidefinite program
collection DOAJ
language English
format Article
sources DOAJ
author Bao-Zhi Sun
Zhi-Xi Wang
Xianqing Li-Jost
Shao-Ming Fei
spellingShingle Bao-Zhi Sun
Zhi-Xi Wang
Xianqing Li-Jost
Shao-Ming Fei
A Note on the Hierarchy of Quantum Measurement Incompatibilities
Entropy
quntum measurements
hierarchy of incompatibilities
semidefinite program
author_facet Bao-Zhi Sun
Zhi-Xi Wang
Xianqing Li-Jost
Shao-Ming Fei
author_sort Bao-Zhi Sun
title A Note on the Hierarchy of Quantum Measurement Incompatibilities
title_short A Note on the Hierarchy of Quantum Measurement Incompatibilities
title_full A Note on the Hierarchy of Quantum Measurement Incompatibilities
title_fullStr A Note on the Hierarchy of Quantum Measurement Incompatibilities
title_full_unstemmed A Note on the Hierarchy of Quantum Measurement Incompatibilities
title_sort note on the hierarchy of quantum measurement incompatibilities
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2020-01-01
description The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators, we present a complete classification of the incompatibility of a given measurement assemblage with <i>n</i> members. Detailed examples are given for the incompatibility of unbiased qubit measurements based on a semidefinite program.
topic quntum measurements
hierarchy of incompatibilities
semidefinite program
url https://www.mdpi.com/1099-4300/22/2/161
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