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DOI: 10.4230/LIPIcs.TQC.2015.245

Interferometric Versus Projective Measurement of Anyons

Authors: Claire Levaillant and Michael Freedman

Published in: LIPIcs, Volume 44, 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)

Abstract

Two distinct methods for measuring topological charge in a nonabelian anyonic system have been discussed in the literature: projective measurement of a single point-like quasiparticle and interferometric measurement of the total topological charge of a group of quasiparticles. Projective measurement by definition is only applied near a point and will project to a topological charge sector near that point. Thus, if it is to be applied to a group of anyons to project to a total charge, then the anyons must first be fused one by one to obtain a single anyon carrying the collective charge. We show that interferometric measurement is strictly stronger: Any protocol involving projective measurement can be simulated at low overhead by another protocol involving only interferometric measurement.

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Claire Levaillant and Michael Freedman. Interferometric Versus Projective Measurement of Anyons. In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. 245-249, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{levaillant_et_al:LIPIcs.TQC.2015.245,
  author =	{Levaillant, Claire and Freedman, Michael},
  title =	{{Interferometric Versus Projective Measurement of Anyons}},
  booktitle =	{10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)},
  pages =	{245--249},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-96-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{44},
  editor =	{Beigi, Salman and K\"{o}nig, Robert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2015.245},
  URN =		{urn:nbn:de:0030-drops-55600},
  doi =		{10.4230/LIPIcs.TQC.2015.245},
  annote =	{Keywords: anyons, measurement, interferometry, physics}
}

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Interferometric Versus Projective Measurement of Anyons

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