Quantum error correction and Young tableaux
Year: 2004
Type: preprint
Abstract: . A quantum channel is a completely positive trace preserving map which acts on the set of operators for the Hilbert space associated with a given quantum system. Analysis of such channels is central to quantum computing and quantum information theory. We present and investigate a new class of quantum channels that includes the class of collective rotation channels as a special case. We use the phrase ‘universal collective rotation channels ’ for this class. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this operator algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We apply classical representation theory of the symmetric group via Young tableaux and give a computationally amenable method for explicitly finding this structure for the class of universal collective rotation channels. 1.
Source: arXiv (Cornell University)
Authors: Marius Junge, Peter T. Kim, David W. Kribs
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2794734703