  We define a quantum entropy conditioned on post-selection which has the von
Neumann entropy of pure states as a special case. This conditional entropy can
take negative values which is consistent with part of a quantum system
containing less information than the whole which can be in a pure state. The
definition is based on generalised density operators for postselected
ensembles. The corresponding density operators are consistent with the quantum
generalisation of classical conditional probabilities following Dirac s
formalism of quasiprobability distributions.
