Journal of Physics A Mathematical and General

Number-phase uncertainty relations

Tomáš Opatrný

Published Dec 7, 1995• 42 citations

Abstract

The minimization problem of finding the number-phase minimum uncertainty states (MUS) is considered and its solutions are found either numerically or, under some special conditions, analytically. The phase uncertainty measure is based on the Bandilla-Paul dispersion. The problem is treated (i) in a finite-dimensional Hilbert space and (ii) for a countably infinite-dimensional Hilbert space (i.e. the standard quantum harmonic oscillator), with the constraint of a given mean photon number. The MUS relations between the photon number uncertainty and phase uncertainty are presented. Connections to some other minimization problems are discussed.

DOI: 10.1088/0305-4470/28/23/034

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