Bounds on general entropy measures

Dominic W. Berry; Barry C. Sanders

doi:10.1088/0305-4470/36/49/008

Bounds on general entropy measures

Dominic W. Berry^*, Barry C. Sanders

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

39 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	12255-12265
Number of pages	11
Journal	Journal of Physics A: Mathematical and General
Volume	36
Issue number	49
DOIs	https://doi.org/10.1088/0305-4470/36/49/008
Publication status	Published - 12 Dec 2003

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title = "Bounds on general entropy measures",

abstract = "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.",

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AU - Sanders, Barry C.

PY - 2003/12/12

Y1 - 2003/12/12

N2 - 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.

AB - 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.

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U2 - 10.1088/0305-4470/36/49/008

DO - 10.1088/0305-4470/36/49/008

M3 - Article

AN - SCOPUS:0348252356

SN - 0305-4470

VL - 36

SP - 12255

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 49

ER -

Bounds on general entropy measures

Abstract

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