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Some features of the conditional \({\mathsf q}\)-entropies of composite quantum systems

  • J. Batle
  • A. R. Plastino
  • M. Casas
  • A. PlastinoEmail author
OriginalPaper

Abstract.

The study of conditional q-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The q-entropies depend on the density matrix \(\rho\) through the quantity \(\omega_q = {\rm Tr}\rho^q\), and admit as a particular instance the standard von Neumann entropy in the limit case \(q\rightarrow 1\). A comprehensive numerical survey of the space of pure and mixed states of bipartite systems is here performed, in order to determine the volumes in state space occupied by those states exhibiting various special properties related to the signs of their conditional q-entropies and to their connections with other separability-related features, including the majorization condition. Different values of the entropic parameter q are considered, as well as different values of the dimensions N 1 and N 2 of the Hilbert spaces associated with the constituting subsystems. Special emphasis is paid to the analysis of the monotonicity properties, both as a function of q and as a function of N 1 and N 2, of the various entropic functionals considered.

Keywords

Entropy Hilbert Space State Space Density Matrix Quantum System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • J. Batle
    • 1
  • A. R. Plastino
    • 1
    • 2
    • 3
  • M. Casas
    • 1
  • A. Plastino
    • 2
    Email author
  1. 1.Departament de Fí sicaUniversitat de les Illes BalearsPalma de MallorcaSpain
  2. 2.Physics DepartmentUniversity of PretoriaPretoria 0002South Africa
  3. 3.National University La Plata and CONICETLa PlataArgentina

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