1305.0932 (Sina Salek et al.)

Negative Conditional Entropy of Post-Selected States    [PDF]

Sina Salek, Roman Schubert, Karoline Wiesner

Using Dirac complex distribution, and hence the statistics of weak measurements, we discuss a decomposition of "conditional state" of post-selected systems and introduce an entropic measure of information for them. In doing so we remark on the role of pre- and post- selection in the measurement of an ensemble. Conditional states are the quantum analogues of the conditional probabilities. We define them by selecting a particular condition in the measurement of a quantum system and studying a coarse grained set of events in the history of the state that ended in that particular condition. These states are different from what is known as conditional states in the literature [16, 6], in the sense that they are trace-1 operators and, by construction, they can be measured using weak measurements. We shall then define a conditional entropic measure based on these states, which as opposed to their classical counterparts, can have negative values. This is also the case even in the case of single state systems. This negative conditional entropy quantifies the amount of information in the post-selected ensembles, states which signify a non-separable class of histories of a quantum system.

View original: http://arxiv.org/abs/1305.0932