Amplitude Damping for single-qubit System with single-qubit mixed-state Environment

TL;DR

This paper investigates the capabilities of a single-qubit mixed-state environment to simulate generalized amplitude damping channels, revealing a significantly smaller volume of simulatable channels compared to two-qubit environments.

Contribution

It provides a geometric analysis of the amplitude damping channel with a single-qubit mixed environment, quantifying the limited set of channels that can be simulated.

Findings

The volume of simulatable channels is about 8% of the total.

This volume is much smaller than that for generalized depolarizing channels.

Single-qubit mixed environments have limited simulation capabilities.

Abstract

We study a generalized amplitude damping channel when environment is initially in the single-qubit mixed state. Representing the affine transformation of the generalized amplitude damping by a three-dimensional volume, we plot explicitly the volume occupied by the channels simulatable by a single-qubit mixed-state environment. As expected, this volume is embedded in the total volume by the channels which is simulated by two-qubit enviroment. The volume ratio is approximately 0.08 which is much smaller than 3/8, the volume ratio for generalized depolarizing channels.