Sharp Quantum Capacity Thresholds: Exponential Strong Converses for Degradable and Antidegradable Channels

Abstract:The quantum capacity of a noisy channel quantifies the maximum rate at which quantum information can be transmitted reliably. For general channels, its evaluation requires an optimization over arbitrarily many channel uses. Degradable channels form a central exception: their capacity is given by the single-letter coherent information, while antidegradable channels have zero capacity. Nevertheless, even for these fundamental classes, it has remained open whether communication above capacity becomes possible when a fixed non-maximal error is tolerated. Here we resolve this problem by proving an exponential strong converse for every finite-dimensional degradable and antidegradable channel: at any rate above capacity, the fidelity of every coding scheme decays exponentially with the number of channel uses. As an immediate consequence, we establish the first all-code exponential strong converse for the quantum erasure channel throughout its full parameter range, strengthening previous results that applied only to almost all codes. We also show that exponential strong-converse bounds are preserved under receiver post-processing. This yields efficiently computable semidefinite-programming bounds for arbitrary finite-dimensional channels, improved bounds for Pauli channels, and an exact exponential strong converse for a nondegradable multilevel amplitude-damping family.

arXiv:2608.01308 [quant-ph]

(or arXiv:2608.01308v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.01308 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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