Quantum state tomography for quadrupolar nuclei using global rotations of the spin system

Abstract

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.

NMR quadrupolar system described as Bose–Einstein-condensate-like system

“…These experimental results correspond to the evolution of the V͑ ͒ operator. 28 The solid lines are the numerical predictions using the BEC Hamiltonian ͑2͒, i.e., they correspond to the evolution defined by the U͑ ͒ operator. As we can see, there is an exact correspondence between the behavior of the NMR description in the HP representation and BEC systems.…”

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

“…However, because the maximum nuclear spin quantum number available for NMR experiments is limited, it is convenient that the method be extended to coupled spin systems. Such an extension was already carried out and can be appreciated in Teles et al [10], where, by using the irreducible tensor product, the QST method was applied to a fictitious homonuclear three-spin 1 2 system.…”

“…Now, a short account will be given of how the QST of quadrupolar nuclei in NMR can be performed exclusively by global rotations of the spin system [10]. Non-selective pulses have the property of performing almost ideal rotations of the spin system.…”

“…Therefore, the implemented operation is equivalent to the search process of one among the four functions f y . The corresponding Grover operators are denoted by G 00 , G 01 , G 10 and G 11 .…”

Writing Electronic Ferromagnetic States in a High-Temperature Paramagnetic Nuclear Spin System

“…In this case, the states |00 , |01 , |10 , and |11 can be associated to the four energy levels of the spin 3/2 system and pseudo-pure states and rotation operators that act independently in each qubit can be built, in complete analogy with the spin 1/2 system. A convenient manner of creating the pseudo-pure states and the qubit selective rotation in this system is using a numerically optimized pulse sequence, named Strongly Modulated Pulses (SMP) [34][35][36][37]. Therefore, because in our experiments we used the quadrupolar spin 3/2, all rotation operators were implemented with the SMP technique, and the experimental density matrices were reconstructed with the quantum state tomography method described in Ref.…”