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 Pr [ F ] {\textstyle \operatorname {Pr} [F]} to the conditional probability Pr [ F | E ] {\displaystyle \operatorname {Pr} [F\,|\,E]} . For a discrete probability space, Pr [ F | E ] = Pr [ F ∩ E ] Pr [ E ] {\textstyle \operatorname {Pr} [F\,|\,E]={\frac {\operatorname {Pr} [F\,\cap \,E]}{\operatorname {Pr} [E]}}} , and thus we require that Pr [ E ] {\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 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.
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