Description
QECC whose encoding and decoding utilizes pre-shared entanglement between sender and receiver.
Parents
- 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 hybrid classical-quantum (EACQ) code
Children
Cousins
- 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. [3].
- 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). DOI; quant-ph/0608027
- [2]
- T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting Quantum Errors with Entanglement”, Science 314, 436 (2006). DOI; quant-ph/0610092
- [3]
- 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). DOI; 2010.07902
Page edit log
- Victor V. Albert (2022-05-31) — most recent
Zoo code information
Cite as:
“Entanglement-assisted (EA) QECC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/eaqecc
Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/eaqecc.yml.