Entanglement-assisted (EA) QECC[13] 

Also known as Catalytic QECC.

Description

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

Protection

The original EAQECC Singleton bound [2,3] was shown to be erroneous [4] and corrected in Ref. [5].

Rate

Bounds on the minimum entanglement required to achieve the entanglement-assisted channel capacity are derived [1].

Notes

See Ref. [6] for an introduction to EAQECCs.

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. [5].
  • Linear \(q\)-ary code — Any linear \(q\)-ary code can be used to construct an EAQECC.
  • Entanglement-assisted (EA) hybrid quantum code — An EA hybrid QECC storing no classical information reduces to an EA QECC. Conversely, any EA QECC can be converted into an EA hybrid QECC by using a portion of its logical subspace to store only classical information.
  • Entanglement-assisted (EA) subsystem QECC — An EA subsystem QECC reduces to an EA QECC when the gauge subsystem is trivial. Conversely, any EA QECC with a tensor-product logical subspace can be turned into an EA subsystem QECC by treating a logical tensor factor as a gauge subsystem.
  • 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.
  • \([[3, 1, 3;2]]\) EA code — The \([[3, 1, 3;2]]\) EA code is the first EA code.

References

[1]
G. Bowen, “Entanglement required in achieving entanglement-assisted channel capacities”, Physical Review A 66, (2002) arXiv:quant-ph/0205117 DOI
[2]
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
[3]
T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting Quantum Errors with Entanglement”, Science 314, 436 (2006) arXiv:quant-ph/0610092 DOI
[4]
M. Grassl, “Entanglement-assisted quantum communication beating the quantum Singleton bound”, Physical Review A 103, (2021) arXiv:2007.01249 DOI
[5]
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
[6]
T. A. Brun and M.-H. Hsieh, “Entanglement-assisted quantum error-correcting codes”, Quantum Error Correction 181 (2013) 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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Cite as:

“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.