Measuring quantum state overlaps of traveling optical fields

Abstract 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 (and under realistic conditions small) number N of Fock states, |Ψ〉= ∑ n=0 N 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.