Quantum channels have a strict limit on reliable information transfer
No information transmission through quantum channels above capacity
Information Theory
Summary
This paper shows that quantum communication channels have a clear boundary for how much information they can send correctly. If you try to send information below this limit, it works well. But if you go above it, the chances of successful communication drop very fast, even if you allow many errors. The authors prove this for both quantum and classical information over quantum channels. They use advanced mathematical tools to show that this limit behaves like a sharp phase change.
quantum channelquantum capacityclassical communicationmemoryless channelentanglement fidelitystrong converse theoremRényi information measuresphase transitionasymptotic continuitychannel capacity
Authors
Hao-Chung Cheng, Marco Tomamichel
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 Rényi information measures that lead to asymptotic continuity bounds for Rényi capacities.