Normalization procedure for relaxation studies in NMR quantum information processing

  • Authors:

  • A. Gavini-Viana;A. M. Souza;D. O. Soares-Pinto;J. Teles;R. S. Sarthour;E. R. Deazevedo;T. J. Bonagamba;I. S. Oliveira

  • Affiliations:

  • Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil 22290-180;Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Canada N2L 3G1;Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, Brazil 13560-970;Instituto de Ciências Exatas e da Terra, Campus do Médio Araguaia, Universidade Federal de Mato Grosso, Pontal do Araguaia, Brazil 78698-000;Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil 22290-180;Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, Brazil 13560-970;Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, Brazil 13560-970;Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil 22290-180

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2010

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Abstract

NMR quantum information processing studies rely on the reconstruction of the density matrix representing the so-called pseudo-pure states (PPS). An initially pure part of a PPS state undergoes unitary and non-unitary (relaxation) transformations during a computation process, causing a "loss of purity" until the equilibrium is reached. Besides, upon relaxation, the nuclear polarization varies in time, a fact which must be taken into account when comparing density matrices at different instants. Attempting to use time-fixed normalization procedures when relaxation is present, leads to various anomalies on matrices populations. On this paper we propose a method which takes into account the time-dependence of the normalization factor. From a generic form for the deviation density matrix an expression for the relaxing initial pure state is deduced. The method is exemplified with an experiment of relaxation of the concurrence of a pseudo-entangled state, which exhibits the phenomenon of sudden death, and the relaxation of the Wigner function of a pseudo-cat state.