Conditional quantum entropy: Difference between revisions

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The '''conditional quantum entropy''' is an [[entropy measure]] used in [[quantum information theory]]. It is a generalization of the [[conditional entropy]] of [[classical information theory]]. For a bipartite state <math>\rho^{AB}</math>, the conditional entropy is written <math>S(A|B)_\rho</math>, or <math>H(A|B)_\rho</math>, depending on the notation being used for the [[von Neumann entropy]]. The quantum conditional entropy was defined in terms of a conditional density operator <math> \rho_{A|B} </math> by [[Nicolas Cerf]] and [[Chris Adami]],<ref name="negent">{{cite journal|url=http://prl.aps.org/abstract/PRL/v79/i26/p5194_1 |archive-url=https://archive.is/20130223112832/http://prl.aps.org/abstract/PRL/v79/i26/p5194_1 |dead-url=yes |archive-date=2013-02-23 |title=Negative entropy and information in quantum mechanics |publisher=[[Physical Review Letters]] |year=1997 }}{{dead link|date=November 2016 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{cite journal|url=http://pra.aps.org/abstract/PRA/v60/i2/p893_1 |title=Quantum extension of conditional probability |publisher=[[Physical Review]] |year=1999 }}{{dead link|date=November 2016 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> who showed that quantum conditional entropies can be negative, something that is forbidden in classical physics. The negativity of quantum conditional entropy is a sufficient criterion for quantum [[Separable state|non-separability]].

In what follows, we use the notation <math>S(\cdot)</math> for the [[von Neumann entropy]], which will simply be called "entropy".