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probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
, to postselect is to condition a
probability space In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models t ...
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 \operatorname /math> to the
conditional probability In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occur ...
\operatorname \, E/math>. For a discrete probability space, \operatorname \, E= \frac, and thus we require that \operatorname /math> be strictly positive in order for the postselection to be well-defined. See also
PostBQP In computational complexity theory, PostBQP is a complexity class consisting of all of the computational problems solvable in polynomial time on a quantum Turing machine with postselection and bounded error (in the sense that the algorithm is corr ...
, a complexity class defined with postselection. Using postselection it seems
quantum Turing machine A quantum Turing machine (QTM) or universal quantum computer is an abstract machine used to model the effects of a quantum computer. It provides a simple model that captures all of the power of quantum computation—that is, any quantum algori ...
s are much more powerful:
Scott Aaronson Scott Joel Aaronson (born May 21, 1981) is an American theoretical computer scientist and David J. Bruton Jr. Centennial Professor of Computer Science at the University of Texas at Austin. His primary areas of research are quantum computing an ...
proved PostBQP is equal to PP. Some quantum experiments use post-selection after the experiment as a replacement for communication during the experiment, by post-selecting the communicated value into a constant.


References

Conditional probability Theoretical computer science Quantum complexity theory {{Probability-stub