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We prove that several known upper bounds on the classical capacity of thermaland additive noise bosonic channels are actually strong converse rates. Ourresults strengthen the interpretation of these upper bounds, in the sense thatwe now know that the probability of correctly decoding a classical messagerapidly converges to zero in the limit of many channel uses if thecommunication rate exceeds these upper bounds. In order for these theorems tohold, we need to impose a maximum photon number constraint on the states inputto the channel (the strong converse property need not hold if there is only amean photon number constraint). Our first theorem demonstrates that Koenig andSmith's upper bound on the classical capacity of the thermal bosonic channel isa strong converse rate, and we prove this result by utilizing the structuraldecomposition of a thermal channel into a pure-loss channel followed by anamplifier channel. Our second theorem demonstrates that Giovannetti et al.'supper bound on the classical capacity of a thermal bosonic channel correspondsto a strong converse rate, and we prove this result by relating successprobability to rate, the effective dimension of the output space, and thepurity of the channel as measured by the Renyi collision entropy. Finally, weuse similar techniques to prove that similar previously known upper bounds onthe classical capacity of an additive noise bosonic channel correspond tostrong converse rates.

Strong converse rates for classical communication over thermal and additive noise bosonic channels