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.
^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.
in order for the postselection to be well-defined. See also PostBQP, a complexity class defined with postselection. Using postselection it seems quantum...
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...
measurements without classical outcomes. A quantum Turing machine with postselection was defined by Scott Aaronson, who showed that the class of polynomial...
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...
University of California, Berkeley Known for Quantum Turing machine with postselection Algebrization Boson sampling Spouse Dana Moshkovitz Awards Alan T. Waterman...
power of quantum computing in relation to classical computing. Adding postselection to BQP results in the complexity class PostBQP which is equal to PP...
neutrons had a magnetic moment oriented in to the right. By means of this postselection, it can be confidently stated that the neutron that reached the detector...
Lynden K.; Steinberg, Aephraim M. (2011). "Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency". Phys. Rev. Lett. 106...
Hall problem Pairwise independent distribution Posterior probability Postselection Regular conditional probability Gut, Allan (2013). Probability: A Graduate...
Steinberg, Aephraim M. (27 January 2011). "Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency". Physical Review Letters...
measurements is universal for PostBQP, i.e. quantum polynomial-time class with postselection (a straightforward corollary of the KLM construction) The class PostBQP...
allows heralded production of the N = 4 NOON state without the need for postselection or zero photon detections, and has the same success probability of 3/64...
S2CID 4411647. Knill, E. (2002-11-14). "Quantum gates using linear optics and postselection". Physical Review A. 66 (5): 052306. arXiv:quant-ph/0110144. Bibcode:2002PhRvA...