The von Neumann entropy for mixed states

Jorge A. Anaya-Contreras; Héctor M. Moya-Cessa; Arturo Zúñiga-Segundo

doi:10.3390/e21010049

The von Neumann entropy for mixed states

Jorge A. Anaya-Contreras, Héctor M. Moya-Cessa, Arturo Zúñiga-Segundo

Escuela Superior de Física y Matemáticas (ESFM)

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki-Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.

Translated title of the contribution	La entropía de von Neumann para estados mixtos
Original language	English
Article number	49
Journal	Entropy
Volume	21
Issue number	1
DOIs	https://doi.org/10.3390/e21010049
State	Published - 1 Jan 2019

Keywords

Araki-Lieb inequality
Atom-field interaction
Mixed states
Von Neumann entropy

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10.3390/e21010049

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abstract = "The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki-Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.",

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AU - Anaya-Contreras, Jorge A.

AU - Moya-Cessa, Héctor M.

AU - Zúñiga-Segundo, Arturo

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Y1 - 2019/1/1

N2 - The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki-Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.

AB - The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki-Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.

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The von Neumann entropy for mixed states

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