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Heisenberg-Weyl Observables: Bloch vectors in phase space

Ali Asadian, Paul Erker, Marcus Huber, and Claude Klöckl
Phys. Rev. A 94, 010301(R) – Published 19 July 2016
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Abstract

We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions. Furthermore, we derive bounds on the sum of expectation values of any set of anticommuting observables. Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first nontrivial example beyond the dichotomic case.

  • Figure
  • Received 4 January 2016
  • Revised 11 May 2016

DOI:https://doi.org/10.1103/PhysRevA.94.010301

©2016 American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Ali Asadian1, Paul Erker2,3,4, Marcus Huber5,2,6,7, and Claude Klöckl2

  • 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
  • 2Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
  • 3Faculty of Informatics, Università della Svizzera italiana, Via G. Buffi 13, 6900 Lugano, Switzerland
  • 4Facoltà indipendente di Gandria, Lunga scala, 6978 Gandria, Switzerland
  • 5Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
  • 6ICFO-Institut de Ciencies Fotoniques, 08860 Castelldefels, Barcelona, Spain
  • 7Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, A-1090 Vienna, Austria

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Issue

Vol. 94, Iss. 1 — July 2016

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