Phase distribution of a quantum state without using phase states

We use the field-strength eigenstates, that is, the quadrature eigenstates rotated by an angle ccphi, to define a phase distribution of a single mode of the radiation field. A measurement procedure lies at the heart of this operational phase distribution: A balanced homodyne-detection scheme measures, in principle, the field-strength probability curve in its dependence on ccphi. The probability of finding a zero electric field plotted versus ccphi constitutes the proposed distribution. For a wide class of quantum states, this curve is in good agreement with the abstract phase probability curve obtained from phase states, but it is free of the familiar problems accompanying the notion of a Hermitian phase operator. The phase distribution of a quantum state has been achieved without using phase states; this can be summarized as ‘‘phase without phase.’’