Fundamental Limit on the Power of Entanglement Assistance in Quantum Communication

TL;DR

This paper proves a long-standing conjecture that the ratio of entanglement-assisted to unassisted classical capacities of finite-dimensional quantum channels is bounded by a function of the input dimension, limiting the advantage of entanglement in such settings.

Contribution

The paper establishes an upper bound on the ratio of entanglement-assisted to unassisted capacities, confirming the conjecture for finite-dimensional quantum channels.

Findings

The ratio is upper bounded by $o(d^2)$, where $d$ is the input dimension.

The bound confirms the finite-dimensional conjecture about entanglement advantage.

Application to noisy quantum communication encoders and decoders is demonstrated.

Abstract

The optimal rate of reliable communication over a quantum channel can be enhanced by pre-shared entanglement. Whereas the enhancement may be unbounded in infinite-dimensional settings even when the input power is constrained, a long-standing conjecture asserts that the ratio between the entanglement-assisted and unassisted classical capacities is bounded in finite-dimensional settings [Bennett et al., IEEE Trans. Inf. Theory 48, 2637 (2002)]. In this work, we prove this conjecture by showing that their ratio is upper bounded by $o(d^2)$, where $d$ is the input dimension of the channel. An application to quantum communication with noisy encoders and decoders is given.