Quantum q-divergence

Sumiyoshi Abe

Physica A: Statistical Mechanics and its Applications, 2004, vol. 344, issue 3, 359-365

Abstract: The quantum q-divergence is the nonadditive relative entropy associated with the Tsallis entropy indexed by q. Here, its basic properties including the q-deformation and quantum-group structure, convexity and monotonicity are summarized. Then, it is applied to measuring the degree of state purification. It is shown that the quantum q-divergence is always well defined if the entropic index, q, is in the range (0,1), whereas the ordinary quantum relative entropy is singular when the reference state is a pure state. Thus, the additive limit, q→1−0, does not exist, in general.

Keywords: Quantum q-divergence; Nonadditive quantum information theory (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:344:y:2004:i:3:p:359-365

DOI: 10.1016/j.physa.2004.06.003

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