Petz–Rényi Channel Information Is Superadditive for Every α Between 1/2 and 1

A new theoretical study has revealed that using multiple copies of a quantum communication channel in a correlated way can improve transmission reliability without increasing the maximum communication rate. Hao-Chung Cheng of the National Taiwan University and Mario Berta of the RWTH Aachen University prove that the Petz–Rényi channel information is strictly superadditive for every Rényi parameter α between 1/2 and 1, demonstrating that entanglement-assisted quantum communication can become more reliable through joint channel use even though its capacity remains fundamentally additive.

Entanglement-assisted communication allows a sender and receiver to share entanglement before transmitting information through a quantum channel. While previous results established that joint encodings across multiple channel uses cannot increase the ultimate communication rate, the new work shows that they can enhance the probability of successful communication by improving the random-coding error exponent, a measure of how rapidly transmission errors decrease as larger codes are used.

The researchers establish this phenomenon analytically for measurement channels, a class of entanglement-breaking channels whose unassisted communication capacity is already known to be additive. Despite their inability to preserve quantum entanglement, these channels still exhibit a genuine multi-copy reliability enhancement under entanglement-assisted communication.

Remarkably, the improvement does not require entanglement between the transmitted channel inputs. Instead, the superadditivity is demonstrated using a separable, classically correlated two-copy input state, showing that classical correlations alone are sufficient to produce the reliability gain. This finding highlights an unexpected role for correlations beyond entanglement in quantum communication protocols.

Rather than increasing the amount of information that can ultimately be transmitted, the work shows that correlated channel use makes communication more robust against errors. The results distinguish communication reliability from communication capacity and reveal that additive capacity does not imply additive reliability, opening new directions for optimizing quantum communication protocols and understanding the role of correlations in quantum information theory.