Superadditivity for Entanglement-Assisted Communication

2026-07-16

AI Summary

This study addresses the additivity of communication reliability in entanglement-assisted quantum channels, focusing on whether the error exponent can be enhanced through joint encoding across multiple channel uses. By integrating tools from quantum information theory, Petz–Rényi entropy analysis, and measurement channel modeling, the work establishes—for the first time—that the Petz–Rényi channel information is strictly superadditive for all α ∈ [1/2, 1). Remarkably, this gain is achievable even with separable (non-entangled) input states across channel copies. These findings demonstrate that classical correlations across independent channel uses can substantially improve communication reliability, even when the channel capacity itself is additive. The result rigorously confirms the superadditivity of the entanglement-assisted random coding error exponent for measurement channels.

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.

Problem

• entanglement-assisted communication
• superadditivity
• communication reliability
• quantum channel
• error exponent

Innovation

• superadditivity
• entanglement-assisted communication
• error exponent
• Petz-Rényi information
• measurement channels