Negative conditional entropy of postselected states

We define a quantum entropy conditioned on postselection 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 generalized density operators for postselected ensembles. The corresponding density operators are consistent with the quantum generalization of classical conditional probabilities following Dirac's formalism of quasiprobability distributions.