Narrow Bounds for the Quantum Capacity of Thermal Attenuators

TL;DR

This paper derives improved upper bounds on the quantum capacity of thermal attenuator channels, crucial for quantum communication, by introducing degradable channel extensions and applying the bottleneck inequality, achieving near-accurate capacity estimates in practical scenarios.

Contribution

The paper introduces new upper bounds for the quantum capacity of thermal attenuators using degradable channel extensions and channel decomposition techniques.

Findings

Bounds are tighter than previous estimates across various attenuation and noise levels.

The approach allows near-accurate quantum capacity estimation for practical low-noise conditions.

The extended degradable channels provide a single-letter quantum capacity bound for complex thermal channels.

Abstract

Thermal attenuator channels model the decoherence of quantum systems interacting with a thermal bath, e.g., a two-level system subject to thermal noise and an electromagnetic signal travelling through a fiber or in free-space. Hence determining the quantum capacity of these channels is an outstanding open problem for quantum computation and communication. Here we derive several upper bounds on the quantum capacity of qubit and bosonic thermal attenuators. We introduce an extended version of such channels which is degradable and hence has a single-letter quantum capacity, bounding that of the original thermal attenuators. Another bound for bosonic attenuators is given by the bottleneck inequality applied to a particular channel decomposition. With respect to previously known bounds we report better results in a broad range of attenuation and noise: we can now approximate the quantum capacity up to a negligible uncertainty for most practical applications, e.g., for low thermal noise.