Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement

TL;DR

This paper derives an additive capacity formula for classical information transmission over noisy quantum channels with limited entanglement assistance, applicable to various protocols including Gaussian and covariant channels.

Contribution

It introduces a new capacity formula considering mixed state signal-ancilla pairs and proves its additivity, simplifying analysis of quantum communication and security.

Findings

Capacity formula is additive for separable encoding.

Closed-form formula for covariant channels.

Upper bounds on information gain in quantum key distribution.

Abstract

We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver's pre-shared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a "witness". Thus, the signal-witness correlation limits the resource available from the signal-ancilla correlation. Our formula characterizes the utility of different forms of resources, including noisy or limited entanglement assistance, for classical communication. With separable encoding, the sender's signals across multiple channel uses are still allowed to be entangled, yet our capacity formula is additive. In particular, for generalized covariant channels our capacity formula has a simple closed-form. Moreover, our additive capacity formula upper bounds the general coherent attack's information gain in various two-way quantum key distribution protocols. For Gaussian protocols, the additivity of the formula indicates that the collective Gaussian attack is the most powerful.