Pursuing the fundamental limits for quantum communication

TL;DR

This paper derives new single-letter upper bounds on the quantum and private capacities of quantum channels, improving understanding of their fundamental limits and providing tighter bounds for key quantum noise channels.

Contribution

It introduces a novel approach using extended channels with specific structures to obtain tighter upper bounds on quantum and private capacities.

Findings

Improved upper bounds for depolarizing channel capacity.

Enhanced bounds for generalized amplitude damping channel.

Applicable to quantum channels relevant in superconducting quantum computing.

Abstract

The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information coherently. In this paper, we derive single-letter upper bounds on the quantum and private capacities of quantum channels. The quantum capacity of a quantum channel is always no larger than the quantum capacity of its extended channels, since the extensions of the channel can be considered as assistance from the environment. By optimizing the parametrized extended channels with specific structures such as the flag structure, we obtain new upper bounds on the quantum capacity of the original quantum channel. Furthermore, we extend our approach to estimating the fundamental limits of private communication and one-way entanglement distillation. As notable applications, we establish improved upper bounds to the quantum and private capacities for fundamental quantum channels of interest in quantum information, some of which are also the sources of noise in superconducting quantum computing. In particular, our upper bounds on the quantum capacities of the depolarizing channel and the generalized amplitude damping channel are strictly better than previously best-known bounds for certain regimes.