Optical measurements using projection synthesis
Lee S. Phillips, Stephen Mark Barnett, David Thomas Pegg · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
We present an extension of the projection synthesis technique which allows, at least in principle, the determination of the probability distribution of any physical observable of a quantized optical field mode. This involves directly measuring a quantity proportional to the squared modulus of the projection of an input pure state onto the eigenstate associated with the observable to be measured. It is found that we need to synthesize a specific reference state conditioned upon the property under investigation. A general expression for these reference states is given. We provide the specific reference states needed to synthesize a measurement of canonical phase. A variant on homodyne detection is investigated using projection synthesis and we form the probability operator measure (POM) required to characterize the measurement. The POM is not that which is formed in conventional balanced homodyne detection. As an application, we utilize these results to form the POM and a quasi probability distribution function associated with a measurement scheme used to distinguish between nonorthogonal coherent states.