Ensemble basis-free coherence for quantum communication

Abstract

The resource theory of coherence quantifies the quantum properties of states and their role in quantum information processing. Extending coherence theory to ensembles, the natural objects in quantum communication, remains an active research direction, with their operational potential still being explored. In this work, we establish a maximally coherent ensemble in every finite dimension: the continuous ensemble of pure states distributed according to the normalized Haar measure attains the tight upper bound on basis-free relative entropy ensemble coherence. We then prove that ensemble coherence bounds the effective informational advantage of postselective measurements over the Holevo quantity for two equiprobable pure states. Finally, for the qubit B92 QKD protocol, we show that the coherence of Alice's ensemble upper-bounds the secret key rate in the asymptotic regime. These results give ensemble coherence a quantitative operational meaning in quantum communication and cryptography