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

For a discrete probability space, $\backslash operatorname\{Pr\}[F\backslash ,\; |\backslash ,\; E]\; =\; \backslash frac\{\backslash operatorname\{Pr\}[F\; \backslash ,\; \backslash cap\; \backslash ,\; E]\}\{\backslash operatorname\{Pr\}[E]\}$, and thus we require that $\backslash operatorname\{Pr\}[E]$ 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{{cite journal |last=Aaronson |first=Scott |year=2005 |title=Quantum computing, postselection, and probabilistic polynomial-time |journal=Proceedings of the Royal Society A |volume=461 |issue=2063 |pages=3473–3482 |arxiv=quant-ph/0412187 |bibcode=2005RSPSA.461.3473A |doi=10.1098/rspa.2005.1546}}{{cite web|url=http://weblog.fortnow.com/2004/01/complexity-class-of-week-pp-by-guest.html|title=Complexity Class of the Week: PP|last=Aaronson|first=Scott|date=2004-01-11|work=Computational Complexity Weblog|accessdate=2008-05-02}} PostBQP is equal to PP.

Some quantum experiments{{cite journal|last1=Hensen|title=Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres|journal=Nature|volume=526|issue=7575|pages=682–686|doi=10.1038/nature15759|display-authors=etal|pmid=26503041|arxiv=1508.05949|bibcode=2015Natur.526..682H|year=2015}} use post-selection after the experiment as a replacement for communication during the experiment, by post-selecting the communicated value into a constant.