Entanglement-assisted (EA) QECC[1,2] 

Description

QECC whose encoding and decoding utilizes pre-shared entanglement between sender and receiver.

Notes

See Ref. [3] for an introduction to EA QEC.

Parents

Children

Cousins

  • Quantum error-correcting code (QECC) — EA QECCs utilize additional ancillary subsystems in a pre-shared entangled state, but reduce to QECCs when said subsystems are interpreted as noiseless physical subsystems.
  • Modular-qudit code — Pure modular-qudit codes can be used to make EA-QECCs with the same distance and dimension; see Thm. 10 of Ref. [4].
  • Linear binary code — Any linear binary code can be used to construct an EAQECC.
  • Linear \(q\)-ary code — Any linear \(q\)-ary code can be used to construct an EAQECC.
  • Error-corrected sensing code — Metrologically optimal codes can be thought of as being entanglement-assisted because they require error-free ancillas for optimal local parameter estimation, and the estimation procedure uses an entangling gate.

References

[1]
T. A. Brun, I. Devetak, and M.-H. Hsieh, “Catalytic Quantum Error Correction”, IEEE Transactions on Information Theory 60, 3073 (2014) arXiv:quant-ph/0608027 DOI
[2]
T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting Quantum Errors with Entanglement”, Science 314, 436 (2006) arXiv:quant-ph/0610092 DOI
[3]
T. A. Brun and M.-H. Hsieh, “Entanglement-assisted quantum error-correcting codes”, Quantum Error Correction 181 (2013) DOI
[4]
M. Grassl, F. Huber, and A. Winter, “Entropic Proofs of Singleton Bounds for Quantum Error-Correcting Codes”, IEEE Transactions on Information Theory 68, 3942 (2022) arXiv:2010.07902 DOI
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Zoo Code ID: eaqecc

Cite as:
“Entanglement-assisted (EA) QECC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/eaqecc
BibTeX:
@incollection{eczoo_eaqecc, title={Entanglement-assisted (EA) QECC}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/eaqecc} }
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“Entanglement-assisted (EA) QECC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/eaqecc

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/eaqecc.yml.