Entanglement-assisted Coding Theory
arXiv:0807.2080
Abstract
In this dissertation, I present a general method for studying quantum error correction codes (QECCs). This method not only provides us an intuitive way of understanding QECCs, but also leads to several extensions of standard QECCs, including the operator quantum error correction (OQECC), the entanglement-assisted quantum error correction (EAQECC). Furthermore, we can combine both OQECC and EAQECC into a unified formalism, the entanglement-assisted operator formalism. This provides great flexibility of designing QECCs for different applications. Finally, I show that the performance of quantum low-density parity-check codes will be largely improved using entanglement-assisted formalism.
PhD dissertation, 102 pages
References in corpus (26)
- Mixed State Entanglement and Quantum Error Correction
- Good Quantum Error-Correcting Codes Exist
- Decoherence Free Subspaces for Quantum Computation
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- A Theory of Quantum Error-Correcting Codes
- Quantum Error Correction and Orthogonal Geometry
- Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Correcting Quantum Errors with Entanglement
- Sparse Graph Codes for Quantum Error-Correction
- Stabilizer Formalism for Operator Quantum Error Correction
- A Unified and Generalized Approach to Quantum Error Correction
- Stabilizing Quantum Information
- A Resource Framework for Quantum Shannon Theory
- A family of quantum protocols
- Distilling common randomness from bipartite quantum states
- Entanglement required in achieving entanglement-assisted channel capacities
- Convolutional and tail-biting quantum error-correcting codes
- Entanglement in the stabilizer formalism
- Topological Protection and Quantum Noiseless Subsystems
- GHZ extraction yield for multipartite stabilizer states
- Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems
- Algebraic and information-theoretic conditions for operator quantum error-correction
- Constructions and performance of classes of quantum LDPC codes
- Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes
- Efficiently implementable codes for quantum key expansion