Entanglement-assisted operator-algebra QECC (EAOA QECC)[1]
Description
A code family that encompasses ordinary (i.e., subspace) codes, subsystem codes, classical-quantum codes, hybrid codes, and their entanglement-assisted counterparts using an operator-algebraic framework. In the EAOAQEC framework, the original EAQEC, EAOQEC, and EACQ formalisms appear as special cases, and the operator-algebra perspective also yields EA hybrid subspace and EA subsystem codes beyond those earlier settings [1].Protection
For Pauli noise with noiseless receiver ebits, the EAOAQEC framework gives a unified error-correction criterion and an associated distance notion that specialize to the corresponding conditions for EAQEC, EAOQEC, and EACQ codes [1].Cousin
- Operator-algebra QECC (OAQECC)— EAOA QECCs use pre-shared entangled ancillary subsystems, while OAQECCs recover the same operator-algebraic structures when those ancillary subsystems are instead treated as noiseless physical subsystems.
Member of code lists
Primary Hierarchy
Parents
Entanglement-assisted operator-algebra QECC (EAOA QECC)
Children
An EAOA QECC that has no gauge structure (e.g., gauge qubits), that has a block structure that corresponds to a classical code, and that utilizes pre-shared entanglement is an EA hybrid QECC.
An EAOA QECC that has 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 EAOQECC.
An EAOA QECC 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.
An EAOA QECC defined over qubits is an EAOA qubit code.
References
- [1]
- P. J. Nadkarni, S. Adonsou, G. Dauphinais, D. W. Kribs, and M. Vasmer, “Unified and Generalized Approach to Entanglement-Assisted Quantum Error Correction”, (2024) arXiv:2411.14389
Page edit log
- Victor V. Albert (2024-12-10) — most recent
Cite as:
“Entanglement-assisted operator-algebra QECC (EAOA QECC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/eaoaecc
Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/eaoaecc.yml.