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arXiv:2610.08786

Energy-constrained two-way capacity bounds for noisy Gaussian channels

Stefano Pirandola

quant-phmath-phphysics.opticsSubmitted Oct 6, 2026• Announced Oct 7, 2026• 0 citations• Revised Oct 14, 2026 (v2)
v1 · Oct 6, 2026v2 · Oct 14, 2026
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Abstract

A gap between achievable rates and converse bounds persists for energy-constrained bosonic communication in the presence of excess noise. We derive a unified adaptive weak-converse bound for thermal attenuation, noisy amplification, and additive Gaussian noise under an unconditional mean transmitted-photon-number constraint. The bound applies to arbitrary adaptive protocols with quantum memories and constrains the two-way quantum, entanglement-distribution, private, and secret-key capacities. It vanishes throughout the entanglement-breaking region and approaches the corresponding PLOB bound at infinite energy. At finite energy, it improves the evaluated Gaussian squashed-entanglement and PLOB bounds in relevant parameter regimes, while comparison with hashing rates quantifies the remaining gap to achievability. The result provides a common energy-dependent benchmark for noisy bosonic Gaussian channels and extends finite-energy converse methods beyond the quantum-limited setting.

Comments
Presentation improved. REVTeX 28 pages. 2 figures

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Abstract: We determine the two-way quantum, entanglement-distribution, private, and secret-key capacities of the pure-loss bosonic channel under an unconditional mean transmitted-photon-number constraint. For transmissivity η\etaη and mean photon number NNN, all four capacities coincide and are given by g(N)−g((1−η)N)g(N)-g((1-\eta)N)g(N)−g((1−η)N),where ggg is the entropy of a thermal mode. This resolves the longstanding finite-energy capacity problem by establishing the optimality of the reverse-coherent-information rate introduced in 2009. Our central tool is sector teleportation simulation, which we develop specifically to transfer the input-energy constraint to the shared entanglement resource, thereby preserving the constraint throughout converse arguments for general adaptive protocols. For every N>0N>0N>0, we further show that the corresponding strong-converse thresholds coincide with the unconstrained value −log⁡2(1−η)-\log_2(1-\eta)−log2​(1−η). For parallel protocols with a hard total-photon-number cutoff, the same finite-energy capacity formula instead satisfies an exponential strong converse. Together, these results establish a unified finite-energy framework for adaptive bosonic communication and reveal how energy constraints fundamentally reshape both attainable rates and converse bounds.
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