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 de- scription. 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 oscil- lator. 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.