Measuring quantum state overlaps of traveling optical fields

We propose a detection scheme for measuring the overlap of the quantum state of a traveling-field mode with a reference quantum state that is an arbitrary superposition of a finite land under realistic conditions small) number N of Fock states, \Psi]= Sigma(n)(N)=(0)c(n)\ n]. In the scheme, an array of maximally N beam splitters is used in which the signal mode is successively mixed with modes prepared in coherent states and photon-number measurements are performed. To illustrate the method, we discuss the measurement of the quantum phase and the detection of Schrodinger-cat-like states. (C) 2000 Elsevier Science B.V. All rights reserved.