arXiv subjects

J. A. Holbrook

Publications and source records attributed to J. A. Holbrook.

2 recordsLinked to original sources

arXiv2004

Noiseless subsystems for collective rotation channels in quantum information theory

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.

math.OA↗

arXiv2004

Noiseless subsystems and the structure of the commutant in quantum error correction

The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of this set of operators. This led to the discovery of noiseless subsystems. They are described by a set of operators obtained from the commutant of the noise generators. In this paper we derive a general method to compute the structure of this commutant in the case of unital noise.

quant-ph↗