The Signal
Peixue Wu Finds No Entanglement Advantage for Phase-Covariant Channels
A paper posted by Peixue Wu on October 29, 2026, proves that entangling codewords does not increase classical communication rates for phase-covariant channels in any dimension. It also establishes strong additivity for qubit-to-qubit channe
Quantum.world Team · Written with AI · fact-checked ·
Wu’s result covers phase-covariant channels in any dimension
For every phase-covariant quantum channel, entangling codewords across separate channel uses does not increase the rate of classical information transmission, according to a paper Peixue Wu posted on arXiv on October 29, 2026. The result applies in any dimension to channels whose action remains covariant under arbitrary diagonal unitaries in a fixed basis. Wu says that class includes multi-level amplitude-damping, generalized dephasing, and damping-dephasing channels.
The paper also establishes strong additivity for all qubit-to-qubit channels.
“As a by-product, we also recover the recently established result that there is no entanglement advantage for all qubit channels,” writes Peixue Wu, the paper’s author.
Why additivity answers a rate question
A sender can encode classical messages in quantum states sent through a noisy channel. With product-state codewords, the highest achievable rate is described by the channel’s maximum Holevo information; allowing codewords entangled across multiple uses leads to the channel’s classical capacity, defined through a regularized quantity.
The question is whether that entanglement lets the sender transmit more classical information per use. Wu proves a stronger condition for the channel families in his paper: their Holevo information adds exactly when combined with any partner channel. Applying that result to repeated uses means entangled codewords do not raise the rate above the single-use value.
That claim concerns classical communication through a quantum channel. It does not say entanglement is unhelpful for quantum computing, quantum communication more broadly, or every task involving noisy channels.
A block-entropy inequality links the two results
Wu’s proof introduces what he calls a Schur-weighted block entropy inequality. The estimate relates the entropy of a matrix arranged in blocks to an expression built from the traces of those blocks. He uses it to prove strong additivity for phase-covariant channels, then applies it alongside a separate channel decomposition to obtain the qubit result.
Wu’s manuscript discloses that he used ChatGPT-6 Astra and Claude Opus 5.5 to study a cited OpenAI manuscript and explore generalizations and proofs. It says he verified the results and that the proofs are fully checked in Lean; a companion GitHub repository contains Lean and proof files.
The proof leaves other channel classes open
The result does not establish that entanglement fails to improve rates for every channel. Wu says his argument does not prove strong additivity for channels with higher-dimensional inputs and qubit outputs when the decomposition contains multiple coherent Kraus operators. The paper also leaves open whether other forms of symmetry, beyond phase covariance, guarantee additivity.
Wu frames a broader problem: determine whether there is a dimension threshold below which every channel has additive classical capacity, while higher dimensions admit explicit counterexamples. His paper supplies results for phase-covariant channels at any dimension and for qubit-to-qubit channels, but does not locate that threshold. Which dimensions, if any, mark the boundary between universal additivity and an explicit entanglement advantage?