Number-Phase Uncertainty Relation

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  • Kitajima Sachiko
    Graduate School of Humanities and Sciences and Department of Physics, Faculty of Science, Ochanomizu University
  • Shingu-Yano Mayumi
    Graduate School of Humanities and Sciences and Department of Physics, Faculty of Science, Ochanomizu University
  • Shibata Fumiaki
    Graduate School of Humanities and Sciences and Department of Physics, Faculty of Science, Ochanomizu University

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Abstract

Number-phase uncertainty relation is examined on the basis of an orthogonal phase state and a quasi-probability function. The measure of number fluctuation is not the usual standard deviation but a kind of Fisher information. This is a direct generalization to a discrete system of the corresponding quantity used recently by Hall in a theory of uncertainty for a coordinate-momentum system. It is essential to separate the “classical” part of a phase operator with the aid of the orthogonal phase state.

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