Entropy of a quantum error correction code
arXiv:0811.1621
Abstract
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme conditions and the entropy exchange computed with respect to any initial state supported on the code. In general the entropy of a code can be viewed as a measure of how close it is to the minimal entropy case, which is given by unitarily correctable codes (including decoherence-free subspaces), or the maximal entropy case, which from dynamical Choi matrix considerations corresponds to non-degenerate codes. We consider several examples, including a detailed analysis in the case of binary unitary channels, and we discuss an extension of the entropy to operator quantum error correcting subsystem codes.
13 pages, 1 figure, to appear in Open Systems & Information Dynamics
References in corpus (19)
- Mixed State Entanglement and Quantum Error Correction
- Decoherence Free Subspaces for Quantum Computation
- Noiseless Quantum Codes
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- A Theory of Quantum Error-Correcting Codes
- Preserving coherence in quantum computation by pairing quantum bits
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Stabilizer Formalism for Operator Quantum Error Correction
- A Unified and Generalized Approach to Quantum Error Correction
- Stabilizing Quantum Information
- Error correction for continuous quantum variables
- Analog quantum error correction
- The structure of preserved information in quantum processes
- Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems
- Approximate quantum error correction, random codes, and quantum channel capacity
- Operator quantum error correction for continuous dynamics
- Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes
- Elementary constructive approach to the higher-rank numerical ranges of unitary matrices
- Quantum decay cannot be completely reversed. The 5% rule