Abstract

The Susskind-Glogower (SG) phase operator underlies quantum phase for a single-mode field—its phase eigenkets generate the probability operator measure (POM) for maximum-likelihood quantum phase estimation.¹ For an arbitrary state, the associated phase representation is the Fourier transform of the more familiar number representation. Thus, because the number representation is a one-sided sequence, the Paley-Wiener theorem constrains the possible phase measurement probability densities for finite-energy single-mode fields,² precluding error-free phase-modulated communication.³ The SG-POM is not an observable on the signal state space. However, by adjoining an unexcited apparatus mode, the SG-POM can be made as a pair of commuting observables on the extended, signal × apparatus, state space.² We show that a correlated signal × apparatus state—called a number-product vacuum state—leads to a two-sided Fourier relationship that thwarts the Paley-Wiener theorem. Using this arrangement, with a phase-conjugate modulator, we obtain error-free transmission of K phase shifts at a root-mean-squares photon number of K/2. Use of this construct in interferometric precision measurements is discussed.

© 1991 Optical Society of America