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Title: Number of representations providing noiseless subsystems

Abstract

This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and also has applications to the understanding of quantum decoherence. We prove that for Hilbert spaces of sufficiently high dimension, decoherence-free (DF) subspaces exist for almost all representations of the error algebra. For decoherence-free subsystems, we plot the function f{sub d}(n) which is the fraction of all d-dimensional quantum systems which preserve n bits of information through DF subsystems, and note that this function fits an inverse beta distribution. The mathematical tools which arise include techniques from classical number theory.

Authors:
 [1]
  1. Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138 (United States)
Publication Date:
OSTI Identifier:
20786291
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.062328; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ALGEBRA; DISTRIBUTION; ERRORS; HILBERT SPACE; LIE GROUPS; QUANTUM COMPUTERS; QUANTUM DECOHERENCE

Citation Formats

Ritter, William Gordon. Number of representations providing noiseless subsystems. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Ritter, William Gordon. Number of representations providing noiseless subsystems. United States. doi:10.1103/PHYSREVA.72.0.
Ritter, William Gordon. Thu . "Number of representations providing noiseless subsystems". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786291,
title = {Number of representations providing noiseless subsystems},
author = {Ritter, William Gordon},
abstractNote = {This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and also has applications to the understanding of quantum decoherence. We prove that for Hilbert spaces of sufficiently high dimension, decoherence-free (DF) subspaces exist for almost all representations of the error algebra. For decoherence-free subsystems, we plot the function f{sub d}(n) which is the fraction of all d-dimensional quantum systems which preserve n bits of information through DF subsystems, and note that this function fits an inverse beta distribution. The mathematical tools which arise include techniques from classical number theory.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 6,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}