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Entropy Production in Quantum is Different

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Jülich-Aachen Research Alliance Institute (JARA) and Peter Grünberg Institute (PGI-2), Forschungszentrum Jülich, D-52425 Jülich, Germany
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Department of Quantum Nanoscience, Kavli Institute of Nanoscience, TU Delft, Lorentzweg 1, 2628CJ Delft, The Netherlands
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(9), 854; https://doi.org/10.3390/e21090854
Received: 30 June 2019 / Revised: 6 August 2019 / Accepted: 28 August 2019 / Published: 31 August 2019
(This article belongs to the Special Issue Quantum Transport in Mesoscopic Systems)
Currently, ‘time’ does not play any essential role in quantum information theory. In this sense, quantum information theory is underdeveloped similarly to how quantum physics was underdeveloped before Erwin Schrödinger introduced his famous equation for the evolution of a quantum wave function. In this review article, we cope with the problem of time for one of the central quantities in quantum information theory: entropy. Recently, a replica trick formalism, the so-called ‘multiple parallel world’ formalism, has been proposed that revolutionizes entropy evaluation for quantum systems. This formalism is one of the first attempts to introduce ‘time’ in quantum information theory. With the total entropy being conserved in a closed system, entropy can flow internally between subsystems; however, we show that this flow is not limited only to physical correlations as the literature suggest. The nonlinear dependence of entropy on the density matrix introduces new types of correlations with no analogue in physical quantities. Evolving a number of replicas simultaneously makes it possible for them to exchange particles between different replicas. We will summarize some of the recent news about entropy in some example quantum devices. Moreover, we take a quick look at a new correspondence that was recently proposed that provides an interesting link between quantum information theory and quantum physics. The mere existence of such a correspondence allows for exploring new physical phenomena as the result of controlling entanglement in a quantum device. View Full-Text
Keywords: time evolution; quantum information; entropy production; Renyi entropy; quantum thermodynamics time evolution; quantum information; entropy production; Renyi entropy; quantum thermodynamics
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Ansari, M.H.; van Steensel, A.; Nazarov, Y.V. Entropy Production in Quantum is Different. Entropy 2019, 21, 854.

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