Entanglement-Assisted Codes Outside the Stabilizer Framework

TL;DR

This paper introduces a novel method to construct entanglement-assisted quantum codes from arbitrary codes by leveraging erasure channel properties, expanding beyond traditional stabilizer frameworks.

Contribution

It presents a new approach to create entanglement-assisted codes from any quantum code, including non-stabilizer codes, and explores their properties and potential advantages.

Findings

Entanglement-assisted codes can be derived from arbitrary quantum codes.

Receiver's bipartite state can be compressed in degenerate codes.

Examples include permutation-invariant and XP-stabilizer codes outside traditional frameworks.

Abstract

We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms the receiver's share of a bipartite state that can be used for entanglement-assisted communications, both in the noiseless and noisy ebit error models. In the case of degenerate codes, we show that the receiver's share of the bipartite state can sometimes be compressed, at the cost of potentially reduced error-correction ability in the noisy ebit error model. We also give examples of permutation-invariant and XP-stabilizer entanglement-assisted codes, the first outside of the stabilizer and codeword-stabilized frameworks.