Postselection
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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 ${\textstyle Pr[F]}$ to the conditional probability ${\displaystyle Pr[F\,|\,E]}$.

For a discrete probability space, ${\textstyle Pr[F\,|\,E]={\frac {Pr[F\,\cap \,E]}{Pr[E]}}}$, and thus we require that ${\textstyle Pr[E]}$ 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[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

1. ^ 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.. Preprint available at [1]
2. ^ Aaronson, Scott (2004-01-11). "Complexity Class of the Week: PP". Computational Complexity Weblog. Retrieved .
3. ^ Hensen; et al. "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres". Nature. 526: 682-686. arXiv:1508.05949. Bibcode:2015Natur.526..682H. doi:10.1038/nature15759. PMID 26503041.

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