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 [math]\displaystyle{ E }[/math], the probability of some other event [math]\displaystyle{ F }[/math] changes from [math]\displaystyle{ \operatorname{Pr}[F] }[/math] to the conditional probability [math]\displaystyle{ \operatorname{Pr}[F\, |\, E] }[/math]. For a discrete probability space, [math]\displaystyle{ \operatorname{Pr}[F\, |\, E] = \frac{\operatorname{Pr}[F \, \cap \, E]}{\operatorname{Pr}[E]} }[/math], and thus we require that [math]\displaystyle{ \operatorname{Pr}[E] }[/math] 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[1][2] PostBQP is equal to PP.
Some quantum experiments[3] use post-selection after the experiment as a replacement for communication during the experiment, by post-selecting the communicated value into a constant.
References
- ↑ Aaronson, Scott (2005). "Quantum computing, postselection, and probabilistic polynomial-time". Proceedings of the Royal Society A 461 (2063): 3473–3482. doi:10.1098/rspa.2005.1546. Bibcode: 2005RSPSA.461.3473A.
- ↑ Aaronson, Scott (2004-01-11). "Complexity Class of the Week: PP". Computational Complexity Weblog. http://weblog.fortnow.com/2004/01/complexity-class-of-week-pp-by-guest.html. Retrieved 2008-05-02.
- ↑ Hensen (2015). "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres". Nature 526 (7575): 682–686. doi:10.1038/nature15759. PMID 26503041. Bibcode: 2015Natur.526..682H.
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