Content deleted Content added
Bibcode Bot (talk | contribs) m Adding 2 arxiv eprint(s), 3 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot |
|||
Line 1:
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|url=https://link.aps.org/doi/10.1103/PhysRevLett.79.5194|journal=[[Physical Review Letters]]|volume=79|issue=26|pages=5194–5197|doi=10.1103/physrevlett.79.5194|via=|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|url=https://link.aps.org/doi/10.1103/PhysRevA.60.893|journal=[[Physical Review A]]|volume=60|issue=2|pages=893–897|doi=10.1103/PhysRevA.60.893|via=|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]].
In what follows, we use the notation <math>S(\cdot)</math> for the [[von Neumann entropy]], which will simply be called "entropy".
Line 10:
By analogy with the classical conditional entropy, one defines the conditional quantum entropy as <math>S(A|B)_\rho \ \stackrel{\mathrm{def}}{=}\ S(AB)_\rho - S(B)_\rho</math>.
An equivalent operational definition of the quantum conditional entropy (as a measure of the [[quantum communication]] cost or surplus when performing [[quantum state]] merging) was given by [[Michał Horodecki]], [[Jonathan Oppenheim]], and [[Andreas Winter]].<ref>{{Cite journal|last=Horodecki|first=Michał|last2=Oppenheim|first2=Jonathan|last3=Winter|first3=Andreas|date=|title=Partial quantum information|url=http://www.nature.com/doifinder/10.1038/nature03909|journal=Nature|volume=436|issue=7051|pages=673–676|arxiv=quant-ph/0505062|doi=10.1038/nature03909|via=|bibcode=2005Natur.436..673H}}</ref>
==Properties==
| |||