Entanglement-assisted (EA) QECC

Entanglement-assisted (EA) QECC[1–3]

Also known as Catalytic QECC.

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

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

See Ref. [5] for an introduction to EAQECCs.

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.

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.

[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]: T. A. Brun and M.-H. Hsieh, “Entanglement-assisted quantum error-correcting codes”, Quantum Error Correction 181 (2013) DOI

Page edit log

“Entanglement-assisted (EA) QECC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/eaqecc