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Normalization procedure for relaxation studies in NMR quantum information processing

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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.

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Correspondence to A. Gavini-Viana.

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Gavini-Viana, A., Souza, A.M., Soares-Pinto, D.O. et al. Normalization procedure for relaxation studies in NMR quantum information processing. Quantum Inf Process 9, 575–589 (2010). https://doi.org/10.1007/s11128-009-0158-1

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