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 , the conditional entropy is written , or , depending on the notation being used for the von Neumann entropy. The quantum conditional entropy was defined in terms of a conditional density operator by Nicolas Cerf and Chris Adami,[1][2] 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 non-separability.
In what follows, we use the notation for the von Neumann entropy, which will simply be called "entropy".
^Cerf, N. J.; Adami, C. (1997). "Negative Entropy and Information in Quantum Mechanics". Physical Review Letters. 79 (26): 5194–5197. arXiv:quant-ph/9512022. Bibcode:1997PhRvL..79.5194C. doi:10.1103/physrevlett.79.5194. S2CID 14834430.
^Cerf, N. J.; Adami, C. (1999-08-01). "Quantum extension of conditional probability". Physical Review A. 60 (2): 893–897. arXiv:quant-ph/9710001. Bibcode:1999PhRvA..60..893C. doi:10.1103/PhysRevA.60.893. S2CID 119451904.
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