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{{Short description|Measure of relative information in quantum information theory}}
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>{{Cite journal|last=Cerf|first=N. J.|last2=Adami|first2=C.|date=1997|title=Negative Entropy and Information in Quantum Mechanics|journal=[[Physical Review Letters]]|volume=79|issue=26|pages=5194–5197|doi=10.1103/physrevlett.79.5194|arxiv=quant-ph/9512022|bibcode=1997PhRvL..79.5194C}}</ref><ref>{{Cite journal|last=Cerf|first=N. J.|last2=Adami|first2=C.|date=1999-08-01|title=Quantum extension of conditional probability|journal=[[Physical Review A]]|volume=60|issue=2|pages=893–897|doi=10.1103/PhysRevA.60.893|arxiv=quant-ph/9710001|bibcode=1999PhRvA..60..893C}}</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]].
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