Bipartite entanglement of noisy stabilizer states through the lens of stabilizer codes

TL;DR

This paper explores the entanglement properties of noisy stabilizer states using stabilizer codes, revealing how their spectra relate to code characteristics and identifying states resilient to noise for quantum networks.

Contribution

It introduces a novel approach linking stabilizer state entanglement to stabilizer code properties, including a new perspective on resilience against noise and a proof relating stabilizer and graph codes.

Findings

Spectra of reduced states relate to stabilizer code properties

Coherent information links to syndrome entropy of codes

Identifies stabilizer states resilient to noise for quantum networks

Abstract

Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states across a bipartition. We show that the spectra of the corresponding reduced states can be expressed in terms of properties of an associated stabilizer code. In particular, this allows us to show that the coherent information is related to the so-called syndrome entropy of the underlying code. We use this viewpoint to find stabilizer states that are resilient against noise, allowing for more robust entanglement distribution in near-term quantum networks. We specialize our results to the case of graph states, where the found connections with stabilizer codes reduces back to classical linear codes for dephasing noise. On our way we provide an alternative proof of the fact that every qubit stabilizer code is equivalent up to single-qubit Clifford gates to a graph code.