Capacities of Gaussian Quantum Channels With Passive Environment Assistance

Passive environment-assisted communication takes place via a quantum channel modeled as unitary interaction between the information carrying system and an environment, where latter is controlled by passive helper, who can set its initial state such to assist sender receiver, but not help actively adjusting her behaviour depending on message. Here we investigate transmission capabilities in this framework considering Gaussian unitaries acting Bosonic systems. We consider both classical with well free coordination helper (conferencing encoders). Concerning communication, prove general coding theorems without energy constraints, yielding multi-letter (regularized) expressions. In search for cases capacity formula computable, look that are universally degradable or anti-degradable. However, show no yields either anti-degradable all environment states. On other hand, restricting states, results unitaries, which thus give single-letter formulas. theorem under constraint, given expression. Furthermore, derive uncertainty-type relation capacities of helped respectively party, showing lower bound sum two capacities. Then, used rate scenario helper.