Eur. Phys. J. B 35, 391-398 (2003)
https://doi.org/10.1140/epjb/e2003-00291-3

Some features of the conditional q-entropies of composite quantum systems

¹ Departament de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
² Physics Department, University of Pretoria, Pretoria 0002, South Africa
³ National University La Plata and CONICET, C.C. 727, 1900 La Plata, Argentina

Corresponding author: ^a plastino@sinectis.com.ar

Received: 30 May 2003
Published online: 15 October 2003

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 ρ through the quantity , and admit as a particular instance the standard von Neumann entropy in the limit case . 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 N₁ and N₂ 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 N₁ and N₂, of the various entropic functionals considered.