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 Pr[F] to the conditional probability Pr[F|E].

For a discrete probability space, Pr[F|E] = Pr[F and E]/Pr[E], and thus we require that 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. doi:10.1098/rspa.2005.1546.. Preprint available at
  2. ↑ Aaronson, Scott (2004-01-11). "Complexity Class of the Week: PP". Computational Complexity Weblog. Retrieved 2008-05-02.
  3. ↑ Hensen; et al. "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres". Nature. 526: 682–686. doi:10.1038/nature15759.
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