# Information-theoretic aspects of the generalized amplitude damping channel

## TL;DR

This paper provides an in-depth information-theoretic analysis of the generalized amplitude damping channel (GADC), including capacity bounds and conditions for entanglement breaking and anti-degradability, improving understanding of noise in quantum systems.

## Contribution

It offers new upper bounds on the classical, quantum, and private capacities of the GADC, tightening previous bounds and exploring various capacity limits using advanced information-theoretic techniques.

## Key findings

- Tighter upper bounds on the quantum capacity of the GADC.
- Identification of parameter ranges where the GADC is entanglement breaking.
- Establishment of bounds on two-way assisted quantum and private capacities.

## Abstract

The generalized amplitude damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. It can be viewed as the qubit analogue of the bosonic thermal channel, and it thus can be used to model lossy processes in the presence of background noise for low-temperature systems. In this work, we provide an information-theoretic study of the GADC. We first determine the parameter range for which the GADC is entanglement breaking and the range for which it is anti-degradable. We then establish several upper bounds on its classical, quantum, and private capacities. These bounds are based on data-processing inequalities and the uniform continuity of information-theoretic quantities, as well as other techniques. Our upper bounds on the quantum capacity of the GADC are tighter than the known upper bound reported recently in [Rosati et al., Nat. Commun. 9, 4339 (2018)] for the entire parameter range of the GADC, thus reducing the gap between the lower and upper bounds. We also establish upper bounds on the two-way assisted quantum and private capacities of the GADC. These bounds are based on the squashed entanglement, and they are established by constructing particular squashing channels. We compare these bounds with the max-Rains information bound, the mutual information bound, and another bound based on approximate covariance. For all capacities considered, we find that a large variety of techniques are useful in establishing bounds.