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 ${\displaystyle E}$, the probability of some other event ${\displaystyle F}$ changes from ${\textstyle \operatorname {Pr} [F]}$ to the conditional probability ${\displaystyle \operatorname {Pr} [F\,|\,E]}$.

For a discrete probability space, ${\textstyle \operatorname {Pr} [F\,|\,E]={\frac {\operatorname {Pr} [F\,\cap \,E]}{\operatorname {Pr} [E]}}}$, and thus we require that ${\textstyle \operatorname {Pr} [E]}$ 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 proved¹² PostBQP is equal to PP.

Some quantum experiments³ use post-selection after the experiment as a replacement for communication during the experiment, by post-selecting the communicated value into a constant.