Quantum entanglement and entropy

Filippo Giraldi and Paolo Grigolini
Phys. Rev. A 64, 032310 – Published 20 August 2001
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Abstract

Entanglement is the fundamental quantum property behind the now popular field of quantum transport of information. This quantum property is incompatible with the separation of a single system into two uncorrelated subsystems. Consequently, it does not require the use of an additive form of entropy. We discuss the problem of the choice of the most convenient entropy indicator, focusing our attention on a system of two qubits, and on a special set, denoted by I. This set contains both the maximally and partially entangled states that are described by density matrices diagonal in the Bell basis set. We select this set for the main purpose of making our work of analysis more straightforward. As a matter of fact, we find that in general the conventional von Neumann entropy is not a monotonic function of the entanglement strength. This means that the von Neumann entropy is not a reliable indicator of the departure from the condition of maximum entanglement. We study the behavior of a form of nonadditive entropy, made popular by the 1988 work by Tsallis [J. Stat. Phys. 52, 479 (1988)]. We show that in the set I, implying the key condition of nonvanishing entanglement, this nonadditive entropy indicator turns out to be a strictly monotonic function of the strength of the entanglement, if entropy indexes q larger than a critical value Q are adopted. We argue that this might be a consequence of the nonadditive nature of the Tsallis entropy, implying that the world is quantum and that uncorrelated subsystems do not exist.

  • Received 30 January 2001

DOI:https://doi.org/10.1103/PhysRevA.64.032310

©2001 American Physical Society

Authors & Affiliations

Filippo Giraldi and Paolo Grigolini

  • Dipartimento di Fisica dell’Università di Pisa and INFM, Piazza Torricelli 2, 56127 Pisa, Italy
  • Istituto di Biofisica CNR, Area della Ricerca di Pisa, Via Alfieri 1, San Cataldo 56010 Ghezzano-Pisa, Italy
  • Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 203-1427

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Issue

Vol. 64, Iss. 3 — September 2001

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