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Medida da dinâmica de correlações quânticas em ressonância magnética nuclear

Isabela Almeida Silva

Published Jul 22, 2013• 0 citations
Publisher

Abstract

We present a study of the decoherence processes in Nuclear Magnetic Resonance (NMR) quantum systems and their effects on the temporal evolution of non-classical correlations.For that, we review some quantum discord quantifiers, such as entropic and geometric discord as well as negativity of quantumness.To describe the relaxation of NMR systems, we use Kraus operators phase and generalized amplitude damping channels.The experimental demonstrations were achieved in 2 qubits systems implemented by J coupled spins 1/2 as well as spins 3/2 subject to quadrupolar interaction.We demonstrate the freezing phenomenon of quantum discord in a 2 spins 1/2 system, subject to phase and amplitude damping channel, and the phenomenon of double sudden-change in a spin 3/2 system, subject to amplitude damping channel.Furthermore, for spin 1/2 system, we introduce a method to selectively measure density matrix elements, that provide the necessary information to calculate discord quantifiers, without needing the full reconstruction provided by usual quantum state tomography.

DOI
10.11606/d.76.2013.tde-19092013-105634

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We present a study of the decoherence processes in Nuclear Magnetic Resonance (NMR) quantum systems and their effects on the temporal evolution of non-classical correlations.For that, we review some quantum discord quantifiers, such as entropic and geometric discord as well as negativity of quantumness.To describe the relaxation of NMR systems, we use Kraus operators phase and generalized amplitude damping channels.The experimental demonstrations were achieved in 2 qubits systems implemented by J coupled spins 1/2 as well as spins 3/2 subject to quadrupolar interaction.We demonstrate the freezing phenomenon of quantum discord in a 2 spins 1/2 system, subject to phase and amplitude damping channel, and the phenomenon of double sudden-change in a spin 3/2 system, subject to amplitude damping channel.Furthermore, for spin 1/2 system, we introduce a method to selectively measure density matrix elements, that provide the necessary information to calculate discord quantifiers, without needing the full reconstruction provided by usual quantum state tomography.
"We review the theoretical and the experimental researches aimed at quantifying or identifying quantum correlations in liquid-state nuclear magnetic resonance (NMR) systems at room temperature. We first overview, at the formal level, a method to determine the quantum discord and its classical counterpart in systems described by a deviation matrix. Next, we describe an experimental implementation of that method. Previous theoretical analysis of quantum discord decoherence had predicted the time dependence of the discord to change suddenly under the influence of phase noise. The experiment attests to the robustness of the effect, sufficient to confirm the theoretical prediction even under the additional influence of a thermal environment. Finally, we discuss an observable witness for the quantumness of correlations in two-qubit systems and its first NMR implementation. Should the nature, not the amount, of the correlation be under scrutiny, the witness offers the most attractive alternative."
Quantum discord is a more general measure of quantum correlations than entanglement and has been proposed as a resource in certain quantum information processing tasks. The computation of discord is mostly confined to two-qubit systems for which an analytical calculational scheme is available. The utilization of quantum correlations in quantum information-based applications is limited by the problem of decoherence, i.e., the loss of coherence due to the inevitable interaction of a quantum system with its environment. The dynamics of quantum correlations due to decoherence may be studied in the Kraus operator formalism for different types of quantum channels representing system-environment interactions. In this review, we describe the salient features of the dynamics of classical and quantum correlations in a two-qubit system under Markovian (memoryless) time evolution. The two-qubit state considered is described by the reduced density matrix obtained from the ground state of a spin model. The models considered include the transverse-field XY model in one dimension, a special case of which is the transverse-field Ising model, and the XXZ spin chain. The quantum channels studied include the amplitude damping, bit-flip, bit-phase-flip and phase-flip channels. The Kraus operator formalism is briefly introduced and the origins of different types of dynamics discussed. One can identify appropriate quantities associated with the dynamics of quantum correlations which provide signatures of quantum phase transitions in the spin models. Experimental observations of the different types of dynamics are also mentioned.
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.
We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.
We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any 2 ⊗ d system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state.
Nuclear magnetic resonance (NMR) was successfully employed to test several protocols and ideas in quantum information science. In most of these implementations, the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this paper, we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogue of the single-photon Mach-Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrates how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present.