Nonclassical correlation in NMR quadrupolar systems

Abstract

The existence of quantum correlation (as revealed by quantum discord), other than entanglement and its role in quantum-information processing (QIP), is a current subject for discussion. In particular, it has been suggested that this nonclassical correlation may provide computational speedup for some quantum algorithms. In this regard, bulk nuclear magnetic resonance (NMR) has been successfully used as a test bench for many QIP implementations, although it has also been continuously criticized for not presenting entanglement in most of the systems used so far. In this paper, we report a theoretical and experimental study on the dynamics of quantum and classical correlations in an NMR quadrupolar system. We present a method for computing the correlations from experimental NMR deviation-density matrices and show that, given the action of the nuclear-spin environment, the relaxation produces a monotonic time decay in the correlations. Although the experimental realizations were performed in a specific quadrupolar system, the main results presented here can be applied to whichever system uses a deviation-density matrix formalism.

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

“…Note that, despite being a rather small number (e ≈ 10 −5 ), this value is beyond the NMR detection limit because only the deviation density matrix, from which the quantum correlation is calculated, is detected in NMR measurements. This demonstrates the existence of quantum correlations of separable states in the spin 3 2 system under consideration [14]. The effect of the environment on the quantum correlations was also experimentally monitored [14], by preparing the state (4.5) and characterizing its evolution by following the procedure described in §4a.…”

“…This demonstrates the existence of quantum correlations of separable states in the spin 3 2 system under consideration [14]. The effect of the environment on the quantum correlations was also experimentally monitored [14], by preparing the state (4.5) and characterizing its evolution by following the procedure described in §4a. The mutual information, classical and quantum correlations were then calculated for each step of the evolution.…”

“…Considering a typical two-qubit NMR density matrix, it can be shown that both the mutual information and classical correlations can be obtained directly from the deviation matrix Dr [14], so that it is possible to calculate the quantum discord directly from experimentally tomographed NMR deviation matrices. By this means, the quantum discord was experimentally measured for the first time in NMR with the quadrupolar spin 3 2 systems described in §5, in an X -type PPS (prepared using the SMP method) by the following deviation matrix:…”

“…To achieve that, we first describe the relaxation of quadrupolar spin 3 2 systems in terms of both the more NMR-friendly Redfield formalism [11,22] and quantum channels [13], more familiar in the QIP community [23,24]. Furthermore, the effect of the system-environment interaction on the behaviour of the classical and quantum correlation of spin 1 2 [25] and spin 3 2 [14] NMR systems is described, and the origin of the difference in behaviour is discussed.…”

Quantum State Tomography and Quantum Logical Operations in a Three Qubits NMR Quadrupolar System

“…Thus, a new method for tomography [21], based on nonselective pulses [22], was proposed and generalized to any spin system. Previous works, that used nonselective pulses to implement QST, explored a spin 3/2 quadrupolar system (an effective two-qubits system) showing the great acurracy of the technique [12,21] also for relaxation studies [23][24][25][26] and simulation of quantum systems [27] .…”