In this paper, we describe a quantum state tomography method based on global rotations of the spin system which, together with a coherence selection scheme, enables the complete density matrix reconstruction. The main advantage of this technique, in respect to previous proposals, is the use of much shorter rf pulses, which decreases significantly the time necessary for algorithm quantum state tomography. In this case, under adequate experimental conditions, the rf pulses correspond to simple spatial rotations of the spin states, and its analytical description is conveniently given in the irreducible tensor formalism. Simulated results show the feasibility of the method for a single spin 72 nucleus. As an experimental result, we exemplify the application of this method by tomographing the steps during the implementation of the Deutsch algorithm. The algorithm was implemented in a (23)Na quadrupole nucleus using the strongly modulated pulses technique. We also extended the tomography method for a 3-coupled homonuclear spin 12 system, where an additional evolution under the internal Hamiltonian is necessary for zero order coherences evaluation.

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Second-order dipolar order in magic-angle spinning nuclear magnetic resonance J. Chem. Phys. 135, 154507 (2011) Single crystal nuclear magnetic resonance in spinning powders J. Chem. Phys. 135, 144201 (2011) Resistive detection of optically pumped nuclear polarization with spin phase transition peak at Landau level filling factor 2/3 Appl. Phys. Lett. 99, 112106 (2011) High-resolution 13C nuclear magnetic resonance evidence of phase transition of Rb,Cs-intercalated singlewalled nanotubes J. Appl. Phys. 110, 054306 (2011) Introduction of the Floquet-Magnus expansion in solid-state nuclear magnetic resonance spectroscopy J. Chem. Phys. 135, 044109 (2011) Additional information on J. Chem. Phys. This paper presents a description of nuclear magnetic resonance ͑NMR͒ of quadrupolar systems using the Holstein-Primakoff ͑HP͒ formalism and its analogy with a Bose-Einstein condensate ͑BEC͒ system. Two nuclear spin systems constituted of quadrupolar nuclei I =3/ 2 ͑ 23 Na͒ and I =7/ 2 ͑ 133 Cs͒ in lyotropic liquid crystals were used for experimental demonstrations. Specifically, we derived the conditions necessary for accomplishing the analogy, executed the proper experiments, and compared with quantum mechanical prediction for a Bose system. The NMR description in the HP representation could be applied in the future as a workbench for BEC-like systems, where the statistical properties may be obtained using the intermediate statistic, first established by Gentile. The description can be applied for any quadrupolar systems, including new developed solid-state NMR GaAS nanodevices.

Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1 2 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1 2 , are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover's algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3 2 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1 2 and quadrupolar spin 3 2 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.

In this paper we use the Nuclear Magnetic Resonance (NMR) to write eletronic states of a ferromagnetic system into a high-temperature paramagnetic nuclear spins. Through the control of phase and duration of radiofrequency pulses we set the NMR density matrix populations, and apply the technique of quantum state tomography to experimentally obtain the matrix elements of the system, from which we calculate the temperature dependence of magnetization for different magnetic fields. The effects of the variation of temperature and magnetic field over the populations can be mapped in the angles of spins rotations, carried out by the RF pulses. The experimental results are compared to the Brillouin functions of ferromagnetic ordered systems in the mean field approximation for two cases: the mean field is given by (i) B = B0 + λM and (ii) B = B0 + λM + λ ′ M 3 , where B0 is the external magnetic field, and λ, λ ′ are mean field parameters. The first case exhibits second order transition, whereas the second case has first order transition with temperature hysteresis. The NMR simulations are in good agreement with the magnetic predictions.

In this work, we present an implementation of quantum logic gates and algorithms in a three effective qubits system, represented by a (I = 7/2) NMR quadrupolar nuclei. To implement these protocols we have used the strong modulating pulses (SMP). The various stages of each implementation were verified by quantum state tomography (QST). It is presented here the results for the computational base states, Toffolli logic gates, and Deutsch-Jozsa and Grover algorithms.Also, we discuss the difficulties and advantages of implementing such protocols using the SMP technique in quadrupolar systems.

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.