No information transmission through quantum channels above capacity

2026-09-08

AI Summary

该研究证明了量子信道容量标志着一个相变点，超过此容量的信息传输将因保真度和成功概率的指数衰减而失败，并采用Arimoto策略结合Rényi信息量的新积分表示法来证明。

Abstract

We show that the capacity of a quantum channel demarcates a phase transition: while reliable transmission below capacity is always possible, any attempt to transmit information above it fails catastrophically. Specifically, we prove exponential strong converse theorems for unassisted quantum and classical communication over arbitrary finite-dimensional memoryless quantum channels. At rates beyond the respective capacity, the entanglement-generation fidelity and the success probability for classical communication decay exponentially with the number of channel uses. This rules out transmission above capacity even when one tolerates arbitrarily large errors. Our proof follows the classical Arimoto strategy, augmented by a crucial new ingredient: integral representations of R\'enyi information measures that lead to asymptotic continuity bounds for R\'enyi capacities.

Problem

• quantum channel
• capacity
• information transmission

Innovation

• quantum channel capacity
• exponential strong converse theorems
• Rényi information measures
• asymptotic continuity bounds