HOW "HOT" ARE MIXED QUANTUM STATES?

DOI10.1142/S0219749907002803zbMATH Open1129.81022arXivquant-ph/0606014OpenAlexW2044588447MaRDI QIDQ5292243

Publication date: 20 June 2007

Published in: International Journal of Quantum Information (Search for Journal in Brave)

Abstract: Given a mixed quantum state

h o

of a qudit, we consider any observable

M

as a kind of `thermometer' in the following sense. Given a source which emits pure states with these or those distributions, we select such distributions that the appropriate average value of the observable

M

is equal to the average Tr

M h o

of

M

in the stare

h o

. Among those distributions we find the most typical one, namely, having the highest differential entropy. We call this distribution conditional Gibbs ensemble as it turns out to be a Gibbs distribution characterized by a temperature-like parameter

. The expressions establishing the liaisons between the density operator

h o

and its temperature parameter

are provided. Within this approach, the uniform mixed state has the highest `temperature', which tends to zero as the state in question approaches to a pure state.

Full work available at URL: https://arxiv.org/abs/quant-ph/0606014

zbMATH Keywords

Gibbs distribution differential entropy quantum ensembles

Mathematics Subject Classification ID

Quantum computation (81P68) Measures of information, entropy (94A17)

Cites Work

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