Computable limits of optical multiple-access communications

Entanglement is a valuable quantum resource in quantum information processing. In classical communication over quantum channels, it is known to boost the communication rate drastically. To generalize such a boost to more general scenarios, we provide computable limits on the communication over optical multiple-access channels (MACs) for both the entanglement-assisted and unassisted communication. For the unassisted case, we generalize the coherent-state achievable rate region and outer bound known for the thermal-loss case [B. J. Yen and J. H. Shapiro, Phys. Rev. A 72, 062312 (2005)10.1103/PhysRevA.72.062312] to general bosonic Gaussian MACs. For the assisted case, we generalize the two-mode squeezed vacuum rate region and the outer bound for the thermal-loss case [H. Shi, npj Quantum Inf. 7, 74 (2021)10.1038/s41534-021-00412-3] to general bosonic MACs. In terms of the total communication rate of all senders, we prove additivity for general MACs, generalizing the two-sender version in M.-H. Hsieh, IEEE Trans. Inf. Theory 54, 3078 (2008)10.1109/TIT.2008.924726. Furthermore, for optical communication modeled as phase-insensitive bosonic Gaussian MACs, we prove that the optimal total rate is achieved by Gaussian entanglement and therefore can be efficiently evaluated. The computable limits confirm entanglement's boosts in optical multiple-access communications. Finally, we formulate an entanglement-assisted version of minimum entropy conjecture, which leads to the additivity of the capacity region of phase-insensitive bosonic Gaussian MACs if it is true.