Number of representations providing noiseless subsystems
Abstract
This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finitedimensional 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, decoherencefree (DF) subspaces exist for almost all representations of the error algebra. For decoherencefree subsystems, we plot the function f{sub d}(n) which is the fraction of all ddimensional 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:
 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 finitedimensional 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, decoherencefree (DF) subspaces exist for almost all representations of the error algebra. For decoherencefree subsystems, we plot the function f{sub d}(n) which is the fraction of all ddimensional 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}
}

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