Strong Converse for Quantum Capacity via a Fully Quantum Blowing-Up Lemma

• URL: http://arxiv.org/abs/2609.11771v1
• Date: Thu, 10 Sep 2026 16:25:56 GMT
• Title: Strong Converse for Quantum Capacity via a Fully Quantum Blowing-Up Lemma
• Abstract summary: We prove an exponential strong converse for quantum communication through every finite-dimensional memoryless channel.<n>First, a fully quantum blowing-up lemma converts a low-fidelity code into a high-fidelity code.<n>Second, a low-degree construction approximates the power of this projector with exponential accuracy while controlling its projective norm.
• Score: 14.896509623302839
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove an exponential strong converse for quantum communication through every finite-dimensional memoryless channel: at any fixed rate above the quantum capacity, the entanglement-transmission fidelity of every code decays exponentially with the number of channel uses. The proof has two main ingredients. First, a fully quantum blowing-up lemma converts a low-fidelity code into a high-fidelity code, with a loss in the number of transmitted qubits controlled by the projective tensor norm of the orthogonal projection on the image of the Stinespring dilation of the channel across the receiver--environment bipartition. Second, a low-degree polynomial construction approximates the tensor power of this projector with exponential accuracy while controlling its projective norm, providing the approximation needed for the blowing-up argument.

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