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 .

For a discrete probability space, , and thus we require that 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

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  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.
  2. ^ Aaronson, Scott (2004-01-11). "Complexity Class of the Week: PP". Computational Complexity Weblog. Retrieved 2008-05-02.
  3. ^ 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.


P ≟ NP 

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PostBQP

machine with postselection and bounded error (in the sense that the algorithm is correct at least 2/3 of the time on all inputs). Postselection is not considered

Weak value

shift of a measuring device's pointer when usually there is pre- and postselection. It should not be confused with a weak measurement, which is often defined

PP (complexity)

quantum Turing machine. By adding postselection, a larger class called PostBQP is obtained. Informally, postselection gives the computer the following

Scott Aaronson

University of California, Berkeley Known for Quantum Turing machine with postselection Algebrization Boson sampling Spouse Dana Moshkovitz Awards Alan T. Waterman

Quantum Turing machine

measurements without classical outcomes. A quantum Turing machine with postselection was defined by Scott Aaronson, who showed that the class of polynomial

BQP

power of quantum computing in relation to classical computing. Adding postselection to BQP results in the complexity class PostBQP which is equal to PP

Novikov self-consistency principle

Steinberg, Aephraim M. (27 January 2011). "Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency". Physical Review Letters

Boson sampling

measurements is universal for PostBQP, i.e. quantum polynomial-time class with postselection (a straightforward corollary of the KLM construction) The class PostBQP