Hermitian Phase Operator and Approximate Quantum Measurement in Extended Number-State Space

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Considering an approximate quantum phase measurement, we show that the extended Pegg-Barnett formalism with dimension (2s + 1) is not plagued by Vorontsov and Rembovsky problem whereby unphysical states can appear after the phase measurement. The approximate phase measurement in this formalism gives, in the large s limit, the same result as that in the Susskind-Glogower formalism. The difficulty of defining a Hermitian phase operator, caused by the periodicity of the phase angle, is overcome by introducing an extended number-state space and by making use of periodic generalized functions (distributions) and their Fourier transforms. This space is the large s limiting case of the extended Pegg-Barnett formalism. Similarly, with the help of periodic generalized functions, Hermitian phase operators can be defined in other infinite-dimensional extended theories. It is also shown that approximate phase measurements give the same results in all these extended formalisms.
理論物理学刊行会の論文
2002-04-25