QUANTUM PHASE MEASUREMENT - A SYSTEM-THEORY PERSPECTIVE

Phase measurements on a single-mode radiation field of annihilation operator a triple-overdot are examined from a system-theoretic viewpoint. Quantum estimation theory is used to establish the primacy of the Susskind-Glogower (SG) phase operator, exp triple-overdot(i-phi) = (a triple-overdot a triple-overdot dagger)-1/2 a triple overdot; its phase eigenkits generate the probability operator measure (POM) for maximum-likelihood phase estimation. When used with an optimum input state, the SG-POM produces a local phase accuracy delta-phi approximately 1/N2, where N is the average photon number of the state. This performance is far superior to the delta-phi approximately 1/square-root N and delta-phi approximately 1/N behaviors of coherent-state and optimized squeeze-state interferometers, respectively. A commuting-observables description for the SG-POM on an extended, signal x apparatus, state space is derived. It is analogous to the signal-band x image-band formulation for optical heterodyne detection. Because heterodyne detection realizes the a triple-overdot-POM, this analogy may help realize the SG-POM. Two new classes of nonclassical states are identified through study of the SG operator-the coherent phase states and the squeeze phase states. These are direct analogs of the familiar coherent and squeezed states associated with the annihilation operator. Linear system theory is used to elicit a broader class of states-the rational phase states-which includes the coherent and squeezed phase states as special cases, and affords a filter-theory derivation of the minimum average-energy quantum state with prescribed phase-measurement statistics. Fourier theory is also used to prove a number-phase uncertainty relation without recourse to the usual linearization procedures, and to show that the Pegg-Barnett phase operator has the same measurement statistics as the SG-POM for arbitrary quantum states.