Superadditivity for Entanglement-Assisted Communication
Information Theory
Summary
The authors studied how reliably information can be sent over quantum channels when assisted by entanglement. They found that while the best communication rate doesn’t improve by using multiple channel uses together, the reliability or error rate can actually get better in such cases. This improvement, called superadditivity, happens even without entangling the inputs being sent through the channels. Their findings highlight that correlation between channel uses can make messages more reliable, even if the maximum rate stays the same.
Authors
Hao-Chung Cheng, Mario Berta
Abstract
The entanglement-assisted capacity of a quantum channel admits an additive single-letter characterization, implying that joint encodings across channel uses cannot increase the ultimate communication rate. Here, we show that this additive picture does not extend to communication reliability. Specifically, we prove that the Petz-Rényi channel information can be strictly superadditive for every $α\in[1/2,1)$, yielding a genuine multi-copy enhancement of the entanglement-assisted random-coding error exponent, even though the entanglement-assisted capacity remains additive. We establish this phenomenon analytically already for measurement channels, which are entanglement-breaking and have additive unassisted capacity. Remarkably, this strict superadditivity is witnessed by a separable, classically correlated two-copy channel-input marginal, demonstrating that no entanglement between the transmitted systems is required. Our results show that, although correlations across channel uses cannot increase the ultimate rate of entanglement-assisted communication, they can enhance its reliability.