QUANTUM SUPERPOSITIONS, PHASE DISTRIBUTIONS AND QUASI-PROBABILITIES

The probability distribution for finding a quantum state of the light field with a particular phase can be described by a number of theoretical methods. One of the most frequently used in quantum optics is the Pegg-Barnett phase distribution which identifies the phase distribution as the (necessarily positive) modulus square of the overlap of the quantum state with the relevant phase state. Other phase distributions have been proposed which employ the phase-sensitivity of various quantum quasi-probabilities such as the Wigner function. In this paper we discuss the connections between these approaches and illustrate their similarities and important differences for a number of pertinent quantum states of light. For some of these states, quantum interference can generate significant regions of phase space for which the Wigner quasi-probability is negative, and as we show, this may render the quasi-probability phase distribution negative. We discuss the general significance of this phenomenon.