Fundamental Limits of Thermal-noise Lossy Bosonic Multiple Access Channel

We develop the capacity region for the bosonic multiple access channel (MAC) in the presence of thermal-noise added by the environment. Bosonic channel describes quantum-mechanically many practical communication links such as optical, microwave, and radiofrequency. We find that the use of single-mode squeezed states can increase the capacity over that afforded by coherent state encoding when each transmitter is photon-number constrained individually. However, the benefit disappears in the asymptotic regimes of high and low signal-to-noise ratio. Additionally, under a combined total photon-number constraint at the transmitters, no benefit from squeezing is observed over the use of coherent states.