Optimal detection with squeezed state for quantum communication in thermal noise channel

Pulse position modulation (PPM) is widely adopted in free space optical transmission, and is a candidate for deep space transmission, also in quantum form. The change of signal photon number probability distribution is caused by thermal noise in quantum PPM format. We prove that squeezing improves state discrimination at fixed channel energy, and also in the presence of thermal noise. Then we compare the difference between coherent state and squeezed state in thermal noise and reveal that the squeezed state has better robustness. It is shown that for the fixed channel energy, the larger the squeezed parameter is not the better. For some given total channel energies, we further study and get the optimal squeezed parameter. Finally, combined with the actual situation, the simulation results show that, as a resource for noisy quantum communication channels, the squeezing operation can improve the quality of deep space quantum communication system with PPM.