Normalization procedure for relaxation studies in NMR quantum information processing |
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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 |
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Affiliation: | (1) Department of Physics Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW London, UK;(2) Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW London, UK |
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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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