J Batle et al 2002 J. Phys. A: Math. Gen. 35 10311 doi:10.1088/0305-4470/35/48/307
J Batle1, A R Plastino1,2, M Casas1 and A Plastino2
Show affiliationsWe revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues pi through the quantity ωq = ∑ipqi. Rényi's and Tsallis' measures constitute particular instances of these entropies. We perform a systematic numerical survey of the space of mixed states of two-qubit systems in order to determine, as a function of the degree of mixture, and for different values of the entropic parameter q, the volume in state space occupied by those states characterized by positive values of the relative entropy. Similar calculations are performed for qubit–qutrit systems and for composite systems described by Hilbert spaces of larger dimensionality. We pay particular attention to the limit case q → ∞. Our numerical results indicate that, as the dimensionalities of both subsystems increase, typical mixed states of composite quantum systems tend, as far as their relative q-entropies are concerned, to behave in a classical way.
03.67.Lx Quantum computation architectures and implementations
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
Issue 48 (6 December 2002)
Received 1 August 2002, in final form 2 October 2002
Published 19 November 2002
J Batle et al 2002 J. Phys. A: Math. Gen. 35 10311
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