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 , the probability of some other event changes from to the conditional probability .
![{\textstyle \operatorname {Pr} [F]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e0de6b26fd6267317c401229f254b6c89d66278)
![{\displaystyle \operatorname {Pr} [F\,|\,E]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b22ed8aff3c909e40b92b4ac14de7ddc269c8abc)
For a discrete probability space, , and thus we require that be strictly positive in order for the postselection to be well-defined.
![{\textstyle \operatorname {Pr} [F\,|\,E]={\frac {\operatorname {Pr} [F\,\cap \,E]}{\operatorname {Pr} [E]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cefb4f6c5d2bf963f709c8b1c333bb42760fb68c)
![{\textstyle \operatorname {Pr} [E]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d3524bb493868a439651569e9a732371699d9fd8)
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.
- ^ Aaronson, Scott (2005). "Quantum computing, postselection, and probabilistic polynomial-time". Proceedings of the Royal Society A. 461 (2063): 3473–3482. arXiv:quant-ph/0412187. Bibcode:2005RSPSA.461.3473A. doi:10.1098/rspa.2005.1546.
- ^ Aaronson, Scott (2004-01-11). "Complexity Class of the Week: PP". Computational Complexity Weblog. Retrieved 2008-05-02.
- ^ Hensen; et al. (2015). "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres". Nature. 526 (7575): 682–686. arXiv:1508.05949. Bibcode:2015Natur.526..682H. doi:10.1038/nature15759. PMID 26503041.