Quantum capacity of thermal attenuator channels

For a thermal attenuator with environment photon number ν=1, can a non-Gaussian input have positive coherent information where every single-mode Gaussian input gives at most zero? The highlighted transmissivity range lies above the antidegradable threshold η=0.75.

Why it matters and what counts as progress

Why it matters: A positive certified value improves a one-use quantum-communication lower bound in a high-noise regime.

What counts as progress: A non-Gaussian input with a rigorously positive value at a smaller η, or a stronger capacity bound; a finite-input witness does not determine the full channel capacity.

How the problem developed

2001 · Lower bound [1][2]
Alexander S. Holevo and Reinhard F. Werner Derived the standard one-use coherent-information lower bound from thermal input states for bosonic Gaussian channels.
29 Jul 2026 · Capacity bound [2]
Francesco Anna Mele, Giuseppe Catalano, Marco Fanizza, Vittorio Giovannetti and Ludovico Lami Proved the thermal-state lower bound is optimal among single-mode Gaussian inputs and exhibited non-Gaussian inputs with strictly higher coherent information, including a certified positive witness at transmissivity 0.7841 with one thermal photon in the environment.

AI contribution

Bosonic quantum communication beyond the thermal threshold

Francesco Anna Mele, Giuseppe Catalano, Marco Fanizza, Vittorio Giovannetti, Ludovico Lami

For a thermal attenuator with environment photon number ν=1, a rank-two input on six Fock levels has certified coherent information at least 4.7×10⁻⁴ qubits per channel use at transmissivity η=0.8, while all single-mode Gaussian inputs have at most zero. A larger witness is certified positive at η=0.7841.

AI involvementAI-centered

ImportanceNotable

Technical verificationFormal (outward-rounded interval arithmetic and Gershgorin eigenvalue enclosures)

Human understandingFull