Description
Stub.
Children
- Classical-quantum (c-q) code
- Entanglement-assisted hybrid classical-quantum (EACQ) code — EACQ codes utilize additional ancillary subsystems in a pre-shared entangled state, but reduce to operator-algebra QECCs when said subsystems are interpreted as noiseless physical subsystems.
- Error-correcting code (ECC) — Any ECC can be embedded into a quantum Hilbert space, and thus passed through a quantum channel, by associating elements of the alphabet with basis vectors in a Hilbert space over the complex numbers. For example, a bit of information can be embedded into a two-dimensional vector space by associating the two bit values with two basis vectors for the space.
- Quantum error-correcting code (QECC)
- Subsystem quantum error-correcting code
Cousin
- Holographic code — Properties of holographic codes are often quantified in the Heisenberg picture, i.e., in terms of operator algebras [7][8].
References
- [1]
- Greg Kuperberg, “The capacity of hybrid quantum memory”. quant-ph/0203105
- [2]
- C. Bény, A. Kempf, and D. W. Kribs, “Generalization of Quantum Error Correction via the Heisenberg Picture”, Physical Review Letters 98, (2007). DOI; quant-ph/0608071
- [3]
- C. Bény, A. Kempf, and D. W. Kribs, “Quantum error correction of observables”, Physical Review A 76, (2007). DOI; 0705.1574
- [4]
- Greg Kuperberg and Nik Weaver, “A von Neumann algebra approach to quantum metrics”. 1005.0353
- [5]
- C. BÉNY, D. W. KRIBS, and A. PASIEKA, “ALGEBRAIC FORMULATION OF QUANTUM ERROR CORRECTION”, International Journal of Quantum Information 06, 597 (2008). DOI
- [6]
- K. Furuya, N. Lashkari, and S. Ouseph, “Real-space RG, error correction and Petz map”, Journal of High Energy Physics 2022, (2022). DOI; 2012.14001
- [7]
- A. Almheiri, X. Dong, and D. Harlow, “Bulk locality and quantum error correction in AdS/CFT”, Journal of High Energy Physics 2015, (2015). DOI; 1411.7041
- [8]
- F. Pastawski and J. Preskill, “Code Properties from Holographic Geometries”, Physical Review X 7, (2017). DOI; 1612.00017
Page edit log
- Victor V. Albert (2021-11-24) — most recent
Zoo code information
Cite as:
“Operator-algebra error-correcting code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/oaecc
Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/oaecc.yml.