Effective noise channels for encoded quantum systems

TL;DR

This paper introduces a framework for analyzing effective noise channels in encoded quantum systems, simplifying the study of entanglement and error correction performance by reducing system complexity.

Contribution

It presents a novel approach to model physical noise as logical noise channels, aiding in understanding entanglement dynamics and error correction in quantum computing.

Findings

Lower bounds on entanglement lifetime were calculated.

Negativity of encoded states was analyzed.

Framework simplifies understanding of error correction codes.

Abstract

We investigate effective noise channels for encoded quantum systems with and without active error correction. Noise acting on physical qubits forming a logical qubit is thereby described as a logical noise channel acting on the logical qubits, which leads to a significant decrease of the effective system dimension. This provides us with a powerful tool to study entanglement features of encoded quantum systems. We demonstrate this framework by calculating lower bounds on the lifetime of distillable entanglement and the negativity for encoded multipartite qubit states with different encodings. At the same time, this approach leads to a simple understanding of the functioning of (concatenated) error correction codes.