"Pretty strong" converse for the quantum capacity of degradable channels

Abstract

We exhibit a possible road towards a strong converse for the quantum capacity of degradable channels. In particular, we show that all degradable channels obey what we call a "pretty strong" converse: When the code rate increases above the quantum capacity, the fidelity makes a discontinuous jump from 1 to at most 0.707, asymptotically. A similar result can be shown for the private (classical) capacity. Furthermore, we can show that if the strong converse holds for symmetric channels (which have quantum capacity zero), then degradable channels obey the strong converse: The above-mentioned asymptotic jump of the fidelity at the quantum capacity is then from 1 down to 0.

17 pages, requires IEEEtran.cls. v2 has new title and updated references; several small errors are corrected and some explanations expanded. v3 is final version accepted by journal; improved presentation, more references and a few more typos corrected

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• Coding Theorem and Strong Converse for Quantum Channels
• Post-selection technique for quantum channels with applications to quantum cryptography
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• The structure of degradable quantum channels
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• Multiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity
• Quantum Coding with Finite Resources
• Application of the Resource Theory of Channels to Communication Scenarios
• Strong converse rates for quantum communication
• Thermodynamic Capacity of Quantum Processes
• No second law of entanglement manipulation after all
• Positivity of linear maps under tensor powers
• Extendibility limits the performance of quantum processors
• Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
• Decoding quantum information via the Petz recovery map
• Amortization does not enhance the max-Rains information of a quantum channel
• Entanglement-assisted private communication over quantum broadcast channels
• Capacity estimation and verification of quantum channels with arbitrarily correlated errors
• Resource theory of unextendibility and non-asymptotic quantum capacity
• Reversibility of quantum resources through probabilistic protocols
• Thermodynamic Implementations of Quantum Processes
• Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels
• Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
• Detecting Quantum Capacities of Continuous-Variable Quantum Channels
• An upper bound on quantum capacity of unital channels