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Entropy 2019, 21(1), 49; https://doi.org/10.3390/e21010049

The von Neumann Entropy for Mixed States

1
Instituto Politécnico Nacional, ESFM Departamento de Física, Edificio 9 Unidad Profesional Adolfo López Mateos, 07738 México D.F., Mexico
2
Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro No. 1, 72840 Sta. María Tonantzintla, Pue., Mexico
*
Author to whom correspondence should be addressed.
Received: 27 November 2018 / Revised: 18 December 2018 / Accepted: 31 December 2018 / Published: 10 January 2019
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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. View Full-Text
Keywords: von Neumann entropy; mixed states; Araki–Lieb inequality; atom-field interaction von Neumann entropy; mixed states; Araki–Lieb inequality; atom-field interaction
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Anaya-Contreras, J.A.; Moya-Cessa, H.M.; Zúñiga-Segundo, A. The von Neumann Entropy for Mixed States. Entropy 2019, 21, 49.

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