Transition probabilities and measurement statistics of postselected ensembles

Details Transition probabilities and measurement statistics of postselected ensembles Transition probabilities and measurement statistics of postselected ensembles

2010-03-23

arxiv.org/abs/1003.4437v3

J. Math. Phys 51, 082105 (2010)

Physics

Quantum Physics

23 pages, 5 figures, minor update

Scientific paper

10.1063/1.3479748

It is well-known that a quantum measurement can enhance the transition probability between two quantum states. Such a measurement operates after preparation of the initial state and before postselecting for the final state. Here we analyze this kind of scenario in detail and determine which probability distributions on a finite number of outcomes can occur for an intermediate measurement with postselection, for given values of the following two quantities: (i) the transition probability without measurement, (ii) the transition probability with measurement. This is done for both the cases of projective measurements and of generalized measurements. Among other constraints, this quantifies a trade-off between high randomness in a projective measurement and high measurement-modified transition probability. An intermediate projective measurement can enhance a transition probability such that the failure probability decreases by a factor of up to 2, but not by more.

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