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The algebra of Grassmann canonical anticommutation relations and its applications to fermionic systems

Source: J. Math. Phys. 51, 023522 (2010); doi:10.1063/1.3282845

Published 8 February 2010

KEYWORDS and PACS
Keywords
PACS
  • 05.30.Fk
    Fermion systems and electron gas (quantum statistical mechanics)
  • 03.65.Ud
    Entanglement and quantum nonlocality
  • 02.30.Px
    Abstract harmonic analysis
  • 02.10.-v
    Logic, set theory, and algebra
  • 03.65.Fd
    Algebraic methods in quantum mechanics
  • 03.65.Db
    Functional analytical methods in quantum mechanics
  • YEAR: 2010
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PUBLICATION DATA
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Michael Keyl and Dirk-M. Schlingemann
Quantum Information Theory Unit, ISI Foundation, Viale S. Severo 65, 10133 Torino, Italy and Institut für Mathematische Physik, Technische Universität Braunschweig, Mendelssohnstraße 3, 38106 Braunschweig, Germany
We present an approach to a noncommutativelike phase space which allows to analyze quasifree states on the algebra of canonical anti-commutation relations (CAR) in analogy to quasifree states on the algebra of canonical commutation relations (CCR). The used mathematical tools are based on a new algebraic structure the “Grassmann algebra of canonical anticommutation relations” (GAR algebra) which is given by the twisted tensor product of a Grassmann and a CAR algebra. As a new application, the corresponding theory provides an elegant tool for calculating the fidelity of two quasifree fermionic states which is needed for the study of entanglement distillation within fermionic systems. ©2010 American Institute of Physics
History: Received 4 September 2009; accepted 10 December 2009; published 8 February 2010
Permalink: http://link.aip.org/link/?JMAPAQ/51/023522/1

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