Entanglement-assisted (EA) QECC

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Entanglement-assisted (EA) QECC[1–3]

Alternative names: Catalytic QECC.

Description

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

Protection

Pre-shared entanglement can be prepared in a way that is robust to noise [4].

Rate

The EA quantum capacity is the highest rate of quantum information transmission through a quantum channel with arbitrarily small error rate and access to arbitrary amounts of entanglement [5]. The fault-tolerant EA capacity is the capacity for the more general case where the encoding and decoding maps are also assumed to undergo noise [6].

Notes

See Ref. [7] for an introduction to EAQECCs.

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.
Entanglement-assisted (EA) hybrid QECC— 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.

Member of code lists

Primary Hierarchy

Quantum Domain

Quantum code

Entanglement-assisted operator-algebra QECC (EAOAQECC)

Parents

Entanglement-assisted operator-algebra QECC (EAOAQECC)

An EAOAQECC that has no gauge structure (e.g., gauge qubits), that has no block structure that corresponds to a classical code, and that utilizes pre-shared entanglement is an EA QECC.

Entanglement-assisted (EA) QECC

Children

EA bosonic code

EA Galois-qudit codeEA MDS

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. M. Wilde and M.-H. Hsieh, “Entanglement generation with a quantum channel and a shared state”, 2010 IEEE International Symposium on Information Theory (2010) arXiv:0904.1175 DOI
[5]: C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, “Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem”, (2002) arXiv:quant-ph/0106052
[6]: P. Belzig, M. Christandl, and A. Müller-Hermes, “Fault-Tolerant Coding for Entanglement-Assisted Communication”, IEEE Transactions on Information Theory 70, 2655 (2024) arXiv:2210.02939 DOI
[7]: T. A. Brun and M.-H. Hsieh, “Entanglement-assisted quantum error-correcting codes”, Quantum Error Correction 181 (2013) DOI

Page edit log

Victor V. Albert (2022-05-31) — most recent

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.