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

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.