A strong converse for stabilizer codes over Pauli channels via the blowing-up lemma

• URL: http://arxiv.org/abs/2607.23450v1
• Date: Sun, 26 Jul 2026 04:29:18 GMT
• Title: A strong converse for stabilizer codes over Pauli channels via the blowing-up lemma
• Abstract summary: We prove a strong converse for quantum communication over Pauli channels within the class of stabilizer codes.<n>For memoryless channels this determines the $varepsilon$-quantum capacity of the class for every $varepsilon 1$.
• Score: 13.537117504260623
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove a strong converse for quantum communication over Pauli channels within the class of stabilizer codes. If a code whose code space is a full joint eigenspace of a stabilizer group transmits above the coherent information of its own input state, its entanglement fidelity decays exponentially in the block length; the encoder may be any isometry onto that space and the decoder any channel. For memoryless channels this determines the $\varepsilon$-quantum capacity of the class for every $\varepsilon < 1$, so that tolerating a constant error buys no rate; for antidegradable channels, such as the depolarizing channel with error probability $p \in [1/4, 3/4]$, that capacity is zero, while for $p \in [1/4,1/2)$ partial-transposition bounds provably cannot certify a strong converse. The proof uses neither additivity assumptions nor semidefinite relaxations: optimal decoding succeeds precisely on an event in a product probability space, so the blowing-up lemma of Ahlswede, Gács and Körner applies, and the side information it produces is charged against the coherent information. The argument also constrains near-deterministic decoding for codes of any kind, and we isolate the encoder-side statement that would extend it to all of them.

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