Optimal trace inequalities are derived for single-shot quantum information, replacing prior constants with a smaller Lambert-W prefactor for logarithmic traces and providing optimal two-sided collision-divergence bounds.
Cheng and P.-C
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abstract
In this work, we prove a one-shot random coding bound for classical-quantum channel coding, a problem conjectured by Burnashev and Holevo in 1998. By choosing the optimal input distribution, the bound implies the optimal error exponent (i.e., the reliability function) of classical-quantum channels for rates above the critical rate, even in infinite-dimensional Hilbert spaces. Our result extends to various quantum packing-type problems, including classical communication over any fully quantum channel with or without entanglement-assistance, constant composition codes, and classical data compression with quantum side information via fixed-length or variable-length coding. Our technical ingredient is to establish an operator layer cake theorem - the directional derivative of an operator logarithm admits an integral representation of certain projections. This shows that a kind of pretty-good measurement is equivalent to a randomized Holevo-Helstrom measurement, which provides an operational explanation of why the pretty-good measurement is pretty good.
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quant-ph 4years
2026 4representative citing papers
Quantum noncommutativity uniquely selects the Umegaki relative entropy as the only additive measure compatible with single-shot optimal discrimination in binary guessing games.
Establishes dimension-free one-shot pairwise bounds for multiple quantum hypothesis testing, resolves Audenaert-Mosonyi conjecture, and proves achievability of multiple quantum Chernoff distance for arbitrary separable Hilbert spaces.
Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
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Sufficiency and Petz recovery for positive maps
Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.