Postselection Explained

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 $\backslash operatorname[F]$ to the conditional probability \operatorname{Pr}[F | E] .

For a discrete probability space, $\backslash operatorname[F\backslash ,\; |\backslash ,\; E]\; =\; \backslash frac$, and thus we require that $\backslash operatorname[E]$ 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 . . 461 . 2063 . 3473–3482 . quant-ph/0412187 . 2005RSPSA.461.3473A . 10.1098/rspa.2005.1546.
2. Web site: Complexity Class of the Week: PP. Aaronson. Scott. 2004-01-11. Computational Complexity Weblog. 2008-05-02.
3. Hensen. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature. 526. 7575. 682–686. 10.1038/nature15759. etal. 26503041. 1508.05949. 2015Natur.526..682H. 2015.