Postselection

In probability theory, to postselect is to condition a probability space upon the occurrence of a given event. In symbols, once we postselect for an event E {displaystyle E} , the probability of some other event F {displaystyle F} changes from P r [ F ] { extstyle Pr} to the conditional probability P r [ F | E ] {displaystyle Pr} . In probability theory, to postselect is to condition a probability space upon the occurrence of a given event. In symbols, once we postselect for an event E {displaystyle E} , the probability of some other event F {displaystyle F} changes from P r [ F ] { extstyle Pr} to the conditional probability P r [ F | E ] {displaystyle Pr} . For a discrete probability space, P r [ F | E ] = P r [ F ∩ E ] P r [ E ] { extstyle Pr={frac {Pr}{Pr}}} , and thus we require that P r [ E ] { extstyle Pr} be strictly positive in order for the postselection to be well-defined. See also PostBQP, a complexity class defined with postselection. Using postselection it seems quantum Turing machines are much more powerful: Scott Aaronson proved PostBQP is equal to PP. Some quantum experiments use post-selection after the experiment as a replacement for communication during the experiment, by post-selecting the communicated value into a constant.