Noiseless subsystems for collective rotation channels in quantum information theory
arXiv:math/0402105
Abstract
Collective rotation channels are a fundamental class of channels in quantum computing and quantum information theory. The commutant of the noise operators for such a channel is a C*-algebra which is equal to the set of fixed points for the channel. Finding the precise spatial structure of the commutant algebra for a set of noise operators associated with a channel is a core problem in quantum error prevention. We draw on methods of operator algebras, quantum mechanics and combinatorics to explicitly determine the structure of the commutant for the class of collective rotation channels.
21 pages, preprint version
References in corpus (13)
- Decoherence Free Subspaces for Quantum Computation
- Noiseless Quantum Codes
- Reliable Quantum Computers
- A Theory of Quantum Error-Correcting Codes
- Preserving coherence in quantum computation by pairing quantum bits
- Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
- Stabilizing Quantum Information
- Classical and quantum communication without a shared reference frame
- Constructing Qubits in Physical Systems
- Introduction to Quantum Error Correction
- Topological Protection and Quantum Noiseless Subsystems
- Quantum Computation using Decoherence-Free States of the Physical Operator Algebra
- Exploring Noiseless Subsystems via Nuclear Magnetic Resonance