An objective theory of phase shift estimation is formulated within quantum mechanics and quantum estimation theory. The general validity of Bayesian analysis even in the limit of very low particle numbers is demonstrated using the information of measured phase-sensitive data. The formalism was applied to the estimation of an unknown phase in neutron interferometry operating near the quantum limit, when only a few particles are registered, and also in the regime of large particle numbers.
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Zawisky et al. (1998) studied this question.
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