EAOA qubit stabilizer code[1]
Root code for the Qubit Kingdom
Description
Entanglement-assisted qubit stabilizer code in the operator-algebra framework. In the generalized stabilizer formalism of [1], such a code is specified on an extended qubit space by Pauli data consisting of stabilizer, gauge, logical, and sector-labeling operators, and is viewed on the original system as using noiseless ebits shared with a receiver. Such codes are denoted by \([[n,k; r,e,c_b]]\) or \([[n,k,d; r,e,c_b]]\), where \(n\) is the number of transmitted physical qubits, \(k\) is the number of logical qubits, \(r\) is the number of gauge qubits, \(e\) is the number of ebits, and \(c_b\) is the number of classical strings encoded. When the hybrid component encodes \(c\) classical bits, one has \(c_b=2^c\). This family encompasses ordinary entanglement-assisted qubit stabilizer codes, entanglement-assisted subsystem stabilizer codes, entanglement-assisted hybrid stabilizer codes, and operator-algebra generalizations described within that stabilizer formalism.Protection
For stabilizer-described qubit subclasses, the EAOAQEC framework yields explicit Pauli error-correction conditions for errors acting on the sender’s qubits under the usual assumption that the receiver’s halves of the ebits are noiseless [1].Cousin
- Operator-algebra (OA) qubit stabilizer code— EAOA qubit stabilizer codes utilize additional ancillary subsystems in a pre-shared entangled state, but reduce to OA qubit stabilizer codes when said subsystems are interpreted as noiseless physical subsystems.
Member of code lists
Primary Hierarchy
Parents
A generalized stabilizer formalism of entanglement-assisted operator-algebra codes over qubits yields EAOA qubit stabilizer codes.
EAOA qubit stabilizer code
Children
An EAOA qubit stabilizer code with no gauge or hybrid structure is an EA qubit stabilizer code. EA hybrid stabilizer codes can be defined [2]. The quantum logical space can be repurposed to encode classical information, and the classical logical space can instead be used to protect against more errors [2; Thm. 6].
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
- [2]
- I. Kremsky, M.-H. Hsieh, and T. A. Brun, “Classical enhancement of quantum-error-correcting codes”, Physical Review A 78, (2008) arXiv:0802.2414 DOI
Page edit log
- Victor V. Albert (2026-03-27) — most recent
Cite as:
“EAOA qubit stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/eaoa_stabilizer