Parts | Days | Selection | Search | Updates | Downloads | Help

MON: Monday Contributed Sessions

MON 17: Quantum Communication and Networks: Theory

MON 17.1: Talk

Monday, September 8, 2025, 16:30–16:45, ZHG006

Resolution of Holevo’s Conjecture on Classical-Quantum Channel Coding via Uncertainty Relations — •Joseph M. Renes — Institute for Theoretical Physics, ETH Zurich, Switzerland

The notion of complementarity is fundamental to quantum theory, as evidenced by the uncertainty principle. In quantum information theory complementarity and uncertainty relations have become important tools in designing and analyzing information processing protocols, e.g. in quantum key distribution. Here I report on another use, in determining the error exponent of classical-quantum (CQ) channels.

The error exponent of a given channel W and rate R is the constant E(W, R) which governs the exponential decay of decoding error when using ever larger optimal codes of fixed rate R to communicate over ever more (memoryless) instances of a given channel W. Here I show a lower bound on the error exponent of communication over arbitrary CQ channels which matches Dalai’s sphere-packing upper bound for rates above a critical value, exactly analogous to the known results for the case of classical channels. This resolves a conjecture made by Holevo in 2000 from his investigation of the problem.

Unlike the classical case, however, the argument does not proceed via a refined analysis of a suitable decoder, but instead by leveraging a bound by Hayashi on the error exponent of the cryptographic task of privacy amplification. This bound is then related to the coding problem via tight entropic uncertainty relations, providing another illustration of their use in quantum information theory.

Keywords: quantum communication; entropic uncertainty relations; quantum channel coding; classical-quantum channels; quantum Shannon theory