Optical state determination by operator synthesis

Paul G. Kwiat, Kevin McCusker, Radhika Rangarajan

L.S. Phillips, Stephen Mark Barnett, David Thomas Pegg

Lee S. Phillips, Stephen Mark Barnett, David Thomas Pegg

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.

Lee S. Phillips, Stephen Mark Barnett, David Thomas Pegg

We present an extension of the projection synthesis technique which allows us, at least in principle, to determine the probability distribution for any physical observable associated with a quantized optical field mode. This probability can be inferred from the photodetection statistics obtained by causing the field mode to be measured to interfere with a second mode prepared in a suitable reference state. We give an explicit expression for the required reference state. Weak-field homodyne detection using photon counting is, perhaps, the simplest system to which projection synthesis can be applied. We find the complete set of synthesized projectors for this system and show that they form a probability operator measure. We apply this set of projectors to study the discrimination between coherent states and to measure a quasiprobability distribution.

Jabez J. McClelland

Stephen Mark Barnett, David Thomas Pegg

Experimental determination of the canonical quantum optical phase probability distribution has, until now, required sufficient measurements to determine the complete state of the field. In this Letter we present a more direct means for measuring this distribution which involves synthesizing the projection onto a phase state. Projection synthesis may be applied more generally to measure the probability distribution associated with other observables.