Quantum logical entropy: Fundamentals and general properties

Boaz Tamir; Ismael Lucas Paiva; Zohar Schwartzman-Nowik; Eliahu Cohen

doi:10.1051/fopen/2021005

Quantum logical entropy: Fundamentals and general properties

Boaz Tamir
, Ismael Lucas Paiva
, Zohar Schwartzman-Nowik
, Eliahu Cohen^*

^*Corresponding author for this work

School of Physics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how this fundamental concept and other related definitions can be applied to the study of quantum systems with the use of quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.

Original language	English
Article number	2
Pages (from-to)	1-14
Number of pages	14
Journal	4open
Volume	5
DOIs	https://doi.org/10.1051/fopen/2021005
Publication status	Published - 25 Jan 2022

Bibliographical note

We thank D. Ellerman and Y. Neuman for many discussions on the topic as well as their helpful comments. We are also thankful to T. Landsberger and J. Kupferman for helpful feedback regarding a previous version of this manuscript. E.C. was supported by Grant No. FQXi-RFP-CPW-2006 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Valley Community Foundation, the Israel Innovation Authority under Projects No. 70002 and No. 73795, the Quantum Science and Technology Program of the Israeli Council of Higher Education, and the Pazy Foundation.

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title = "Quantum logical entropy: Fundamentals and general properties",

abstract = "Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how this fundamental concept and other related definitions can be applied to the study of quantum systems with the use of quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.",

author = "Boaz Tamir and Paiva, \{Ismael Lucas\} and Zohar Schwartzman-Nowik and Eliahu Cohen",

note = "We thank D. Ellerman and Y. Neuman for many discussions on the topic as well as their helpful comments. We are also thankful to T. Landsberger and J. Kupferman for helpful feedback regarding a previous version of this manuscript. E.C. was supported by Grant No. FQXi-RFP-CPW-2006 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Valley Community Foundation, the Israel Innovation Authority under Projects No. 70002 and No. 73795, the Quantum Science and Technology Program of the Israeli Council of Higher Education, and the Pazy Foundation.",

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AU - Cohen, Eliahu

N1 - We thank D. Ellerman and Y. Neuman for many discussions on the topic as well as their helpful comments. We are also thankful to T. Landsberger and J. Kupferman for helpful feedback regarding a previous version of this manuscript. E.C. was supported by Grant No. FQXi-RFP-CPW-2006 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Valley Community Foundation, the Israel Innovation Authority under Projects No. 70002 and No. 73795, the Quantum Science and Technology Program of the Israeli Council of Higher Education, and the Pazy Foundation.

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N2 - Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how this fundamental concept and other related definitions can be applied to the study of quantum systems with the use of quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.

AB - Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how this fundamental concept and other related definitions can be applied to the study of quantum systems with the use of quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.

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DO - 10.1051/fopen/2021005

M3 - Article (Academic Journal)

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VL - 5

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ER -

Quantum logical entropy: Fundamentals and general properties

Abstract

Bibliographical note

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