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Bounds on general entropy measures

Dominic W Berry and Barry C Sanders1

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We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or quantum state) independent of the entropy measures, provided the entropy measures satisfy a concavity/convexity relation. These results may be applied to entropies for classical probability distributions, entropies of mixed quantum states and measures of entanglement for pure states.


PACS

03.67.Mn Entanglement measures, witnesses, and other characterizations

02.50.Cw Probability theory

03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)

MSC

94B65 Bounds on codes

94A17 Measures of information, entropy

94A24 Coding theorems (Shannon theory)

Subjects

Computational physics

Quantum information and quantum mechanics

Dates

Issue 49 (12 December 2003)

Received 23 May 2003

Published 25 November 2003



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