A preprint posted to arXiv — not yet peer-reviewed — reports exact, absolutely convergent series expressions for three fundamental capacities of the qubit amplitude damping channel: its quantum capacity, unassisted classical capacity, and entanglement-assisted classical capacity. The amplitude damping channel models energy dissipation in two-level quantum systems, making it one of the most physically relevant noise models in quantum information theory, yet closed-form capacity expressions have remained elusive.
The authors claim their formulas eliminate the residual numerical optimizations and implicit root-finding steps that have previously complicated capacity calculations. They additionally derive analytical upper and lower bounds on two-way assisted quantum and private communication capacities by evaluating a balanced-squashing bound and optimizing the reverse coherent information. The work also characterizes optimal input state populations and establishes convergence and truncation error properties for the series.
If the results withstand peer review, they would provide analytically tractable benchmarks for assessing quantum and classical communication protocols over dissipative channels — a class of practical importance for superconducting qubits and optical systems. Independent verification of the convergence claims and the tightness of the two-way capacity bounds will be key questions for the community to address.