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arXiv · 2608.01308

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

Tulja Varun Kondra·Raphael Brinster·Hermann Kampermann·Dagmar Bruß·Nikolai Wyderka
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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.

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Tulja Varun Kondra, Raphael Brinster, Hermann Kampermann, Dagmar Bruß, Nikolai Wyderka. 2026-08-02. Sharp Quantum Capacity Thresholds: Exponential Strong Converses for Degradable and Antidegradable Channels. https://arxiv.org/abs/2608.01308

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