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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes.

Jianzhang Chen¹, Wanchuan Fang¹, Shuo Zhou¹

¹College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou 350002, China.

Entropy (Basel, Switzerland)

|December 23, 2023

Summary

This summary is machine-generated.

New asymmetric quantum error-correcting codes are developed to better protect quantum information. These codes overcome limitations of existing methods by using entanglement and algebraic structures for enhanced asymmetry.

Keywords:

asymmetric entanglement-assisted quantum codes constacyclic codes maximal-distance separable codes

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Area of Science:

Quantum Information Science
Quantum Error Correction
Coding Theory

Background:

Quantum errors are often asymmetric, with phase-shift errors more frequent than qubit-flip errors.
Existing asymmetric quantum error-correcting (QEC) codes, primarily within the Calderbank-Shor-Steane (CSS) framework, face limitations in asymmetry due to the dual-containing condition.
This restricts the full potential of QEC in safeguarding quantum information in asymmetric channels.

Purpose of the Study:

To develop novel asymmetric quantum error-correcting codes with enhanced asymmetry.
To overcome the limitations imposed by the dual-containing condition in existing CSS-based codes.
To construct codes that more effectively protect quantum information transmitted through asymmetric quantum channels.

Main Methods:

Utilizing entanglement-assisted technology to enhance code asymmetry.
Exploiting the algebraic structure of cyclotomic cosets of constacyclic codes.
Generalizing the decomposition method of the defining set for constacyclic codes and counting pre-shared entangled states.

Main Results:

Construction of four new classes of asymmetric entanglement-assisted quantum maximal-distance separable (EAQMDS) codes.
The constructed EAQMDS codes satisfy the asymmetric entanglement-assisted quantum Singleton bound.
The new codes offer greater asymmetry and more general code lengths and pre-shared entangled states compared to existing literature.

Conclusions:

The developed method successfully enhances the asymmetry of quantum error-correcting codes.
The new classes of EAQMDS codes provide improved solutions for quantum information protection in asymmetric channels.
This work expands the toolkit for designing advanced quantum error correction strategies.