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Hierarchy of Rényi Coherent Information in Stabilizer Codes
arxiv.orgpaper

Hierarchy of Rényi Coherent Information in Stabilizer Codes

This arXiv paper proves that the Renyi-n coherent information, a computable proxy for von Neumann coherent information used to study decodability transitions in noisy quantum error-correcting codes, is nondecreasing in n for stabilizer codes under independent Pauli noise, resolving a monotonicity gap in the prior theory. It also gives an operational meaning to the Renyi-n coherent information via postselection on matching syndromes across auxiliary code blocks, showing its saturation is equivalent to asymptotically perfect recovery, and that it upper-bounds achievable coherent information after any syndrome-conditioned recovery.

TL;DR Proves monotonicity and gives an operational postselected-channel meaning to Renyi coherent information for stabilizer quantum error-correcting codes.
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What it claims

The Rényi-$n$ coherent information is nondecreasing in $n \in \mathbb{Z}^+$ for stabilizer codes under Pauli noise from independent Bernoulli events. Beyond the stabilizer-code result the summary already states, the page names the general lemma that carries it and states the result generalizes past quantum codes.

How it works

The monotonicity is a corollary of a purely information-theoretic theorem: if independent random bits are mapped linearly to a fine label $T$ and a coarse label $C$, then the Rényi entropy difference $H_n(C) - H_n(T)$ is nondecreasing in $n$. The paper instantiates this for stabilizer codes by taking $T$ = the joint syndrome–logical class and $C$ = the syndrome, so that $H_n(C) - H_n(T)$ equals the Rényi-$n$ coherent information up to a constant. Because the theorem only needs independent bits mapped linearly, the same argument covers classical linear codes and independent detector error models, not just stabilizer codes — the linearity and independence, not the quantum structure, is what does the work.

On the operational side (the postselection-across-auxiliary-blocks construction the summary describes), the page adds one qualifier the summary omits: the authors explicitly determine when the postselected construction defines a valid quantum channel, rather than assuming it always does.

Limits

  • The monotonicity proof requires noise from independent Bernoulli events and the map from bits to labels to be linear; correlated noise or nonlinear structure is outside the theorem. The operational-meaning results hold for arbitrary stochastic Pauli noise, but the two contributions have different scopes — do not assume the monotonicity extends to the general stochastic setting.
  • This is an abstract-only page; no proofs, worked codes, numerical thresholds, or comparison against specific decoders are visible. The claim that saturation is equivalent to asymptotically perfect recovery, and the upper-bound-on-recovery claim, are stated without the conditions or constants that would let you apply them to a concrete code.
  • Submitted 10 Sep 2026, v1; no code, data, or associated media are linked from the page.

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