Entanglement-assisted codeword stabilized quantum codes

TL;DR

This paper explores how entanglement can enhance quantum error correction by enabling the construction of both additive and non-additive codes from classical codes, potentially improving quantum communication reliability.

Contribution

It introduces a framework for constructing entanglement-assisted quantum codes, including non-additive codes, from classical linear codes without the dual-containing constraint.

Findings

Constructed new entanglement-assisted non-additive quantum codes.

Demonstrated improved code parameters such as ((5,16,2;1)) and ((7,4,5;4)).

Showed that the framework simplifies encoding and error correction processes.

Abstract

Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the dual-containing constraint. We show that it is possible to construct both additive and non-additive quantum codes using the codeword stabilized quantum code framework. Nonadditive codes may offer improved performance over the more common sta- bilizer codes. Like other entanglement-assisted codes, the encoding procedure acts only the qubits on Alice's side, and only these qubits are assumed to pass through the channel. However, errors the codeword stabilized quantum code framework gives rise to effective Z errors on Bob side. We use this scheme to construct new entanglement-assisted non-additive quantum codes, in particular, ((5,16,2;1)) and ((7,4,5;4)) codes.