Bracket states for communication protocols with coherent states

We present the generation and characterization of the class of bracket states, namely phase-sensitive mixtures of coherent states exhibiting symmetry properties in the phase-space description. A bracket state can be seen as the statistical ensemble arriving at a receiver in a typical coherent-state-based communication channel. We show that when a bracket state is mixed at a beam splitter with a local oscillator, both the emerging beams exhibit a Fano factor larger than 1 and dependent on the relative phase between the input state and the local oscillator. We discuss the possibility to exploit this dependence to monitor the phase difference for the enhancement of the performances of a simple communication scheme based on direct detection. Our experimental setup involves linear optical elements and a pair of photon-number-resolving detectors operated in the mesoscopic photon-number domain.