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<p>We provide a tight asymptotic characterization of the error exponent for classical-quantum channel coding assisted by activated non-signaling correlations. Namely, we find that the optimal exponent—also called reliability function—is equal to the well-known sphere packing bound, which can be written as a single-letter formula optimized over Petz-Rényi divergences. Remarkably, there is no critical rate and as such our characterization remains tight for arbitrarily low rates below the capacity. On the achievability side, we further extend our results to fully quantum channels. Our proofs rely on semi-definite program duality and a dual representation of the Petz-Rényi divergences via Young inequalities.</p>

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Error exponent of activated non-signaling-assisted classical-quantum channel coding

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • Aadil Oufkir,
  • Marco Tomamichel,
  • Mario Berta

摘要

We provide a tight asymptotic characterization of the error exponent for classical-quantum channel coding assisted by activated non-signaling correlations. Namely, we find that the optimal exponent—also called reliability function—is equal to the well-known sphere packing bound, which can be written as a single-letter formula optimized over Petz-Rényi divergences. Remarkably, there is no critical rate and as such our characterization remains tight for arbitrarily low rates below the capacity. On the achievability side, we further extend our results to fully quantum channels. Our proofs rely on semi-definite program duality and a dual representation of the Petz-Rényi divergences via Young inequalities.