General entanglement-assisted quantum error-correcting codes
arXiv:0708.2142 · doi:10.1103/PhysRevA.76.062313
Abstract
Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-existing entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs which can only be constructed from dual-containing codes. Operator quantum error-correcting codes (OQECCs) allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement-assisted quantum error correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction (EAOQEC), is the most general and powerful quantum error-correcting technique known, retaining the advantages of both entanglement-assistance and passive correction. We present the formalism, show the considerable freedom in constructing EAOQECCs from classical codes, and demonstrate the construction with examples.
7 pages, no figure
References in corpus (12)
- Good Quantum Error-Correcting Codes Exist
- Decoherence Free Subspaces for Quantum Computation
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Correcting Quantum Errors with Entanglement
- Stabilizer Formalism for Operator Quantum Error Correction
- A Unified and Generalized Approach to Quantum Error Correction
- Entanglement required in achieving entanglement-assisted channel capacities
- Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems
- Algebraic and information-theoretic conditions for operator quantum error-correction
- Computation on a Noiseless Quantum Code and Symmetrization
- Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes
- Clifford Code Constructions of Operator Quantum Error Correcting Codes
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