NMR investigation of contextuality in a quantum harmonic oscillator via pseudospin mapping

Physical potentials are routinely approximated to harmonic potentials so as to analytically solve the system dynamics. Often it is important to know when a quantum harmonic oscillator (QHO) behaves quantum mechanically and when classically. Recently Su et. al. [Phys. Rev. A {\bf 85}, 052126 (2012)] have theoretically shown that QHO exhibits quantum contextuality (QC) for a certain set of pseudospin observables. In this work, we encode the four eigenstates of a QHO onto four Zeeman product states of a pair of spin-1/2 nuclei. Using the techniques of NMR quantum information processing, we then demonstrate the violation of a state-dependent inequality arising from the noncontextual hidden variable model, under specific experimental arrangements. We also experimentally demonstrate the violation of a state-independent inequality by thermal equilibrium states of nuclear spins, thereby assessing their quantumness.Comment: 5 Pages, 3 Figures, context dependency illustrated, error below eq. 5 correcte

Control techniques in spin based quantum computation

Working on quantum systems entail different interests, for example, working on fundamental understanding of quantum systems also lay foundation for better quantum computation techniques. A test for whether a system is behaving quantum mechanically or classically is devised by Leggett and Garg in form of inequalities, called Leggett-Garg Inequalities (LGI). Such Inequalities are violated by a system whose evolution is governed by quantum mechanics. A precise experiment to violate LGIs require a guarantee that the measurement does not affect the system or its future dynamics. These Inequalities were proposed for dichotomic systems,systems which can have two outcomes. Here we present an LG experiment on a three-level quantum system, which theoretically have larger quantum upper bound than that of a two-level quantum system. This larger violation also provides a bigger buffer to taking in account of the various experimental imperfections. Performing a quantum computing task requires precise level of control to initialize, perform and measure the quantum system. With increasing size of the quantum processor the challenge is to maintain optimal control. Nuclear Magnetic Resonance (NMR) has always been a very faithful test-bed for quantum processing ideas. In NMR, we perform Radio Frequency (RF) pulses to control and steer the system to the desired state. Most used method to derive the exact frequency and amplitude of these pulses for a given task is based on gradient. Although systematic, one have to simulate these pulses on a classical computer first, which makes the task very inefficient. We report a a way of performing optimization with a hybrid quantum-classical scheme. This scheme helps us perform classically harder computational tasks on the quantum processor. We optimize pulses which drive our system from 7-coherence state to 12-coherence state on a 12-qubit NMR processor. Electron Spin Resonance (ESR) employs the same techniques as of NMR but having advantage in larger polarization compared to later. Although this does not imply better control, cause the frequency at which pulses are required to control an ESR system fall into microwave region. Microwave frequency are harder to control electronically, thus making it harder for performing ESR quantum computing. The hybrid scheme used in NMR experiment relies on some ideal pulses which are needed to be optimized classically. We alleviate this requirement by using finite difference method of calculating gradient. We compare these methods with the earlier methods to show the superiority of such a scheme. State-to-state transfer pulses are sufficient for most of the quantum computing task, but, an universal quantum information implementation requires state independent pulses. The techniques used in optimizing state-to-state pulses can be modified to optimize for a state independent pulse. We show that this methods scale polynomially with the number of qubits and is general in terms of its implementation. We further reduce the resource requirement by using a NMR related implementation

Freezing a Quantum Magnet by Repeated Quantum Interference: An Experimental Realization

We experimentally demonstrate the phenomenon of dynamical many-body freezing in a periodically driven Ising chain. Theoretically [Phys. Rev. B 82, 172402 (2010)], for certain values of the drive parameters all fundamental degrees of freedom contributing to the response dynamics freeze for all time and for arbitrary initial states. Also, since the condition of freezing involves only the drive parameters and not on the quantization of the momentum (i.e., the system-size), our simulation with a small (3-spin) chain captures all salient features of the freezing phenomenon predicted for the infinite chain. Using optimal control techniques, we realize high-fidelity cosine modulated drive, and observe non-monotonic freezing of magnetization at specific frequencies of modulation. Time-evolution of the excitations in momentum space has been tracked directly through magnetization measurements

Violation of Entropic Leggett-Garg Inequality in Nuclear Spins

We report an experimental study of recently formulated entropic Leggett-Garg inequality (ELGI) by Usha Devi et al. (arXiv: 1208.4491v2 (2012)). This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior. Here we study ELGI using a two-qubit nuclear magnetic resonance system. To perform the noninvasive measurements required for the ELGI study, we prepare the system qubit in a maximally mixed state as well as use the `ideal negative result measurement' procedure with the help of an ancilla qubit. The experimental results show a clear violation of ELGI by over four standard deviations. These results agree with the predictions of quantum theory. The violation of ELGI is attributed to the fact that certain joint probabilities are not legitimate in the quantum scenario, in the sense they do not reproduce all the marginal probabilities. Using a three-qubit system, we experimentally demonstrate that three-time joint probabilities do not reproduce certain two-time marginal probabilities.Comment: 5 pages, 5 figures, 1 page supplementar

Evolution of Quantum Discord and its Stability in Two-Qubit NMR Systems

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.Comment: 9 pages, 7 figures, Phys. Rev. A (in press

Monogamy of quantum correlations reveals frustration in a quantum Ising spin system: Experimental demonstration

We report a nuclear magnetic resonance experiment, which simulates the quantum transverse Ising spin system in a triangular configuration and further show that the monogamy of quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this system. Adiabatic state preparation methods are used to prepare the ground states of the spin system. We employ two different multipartite quantum correlation measures to analyze the experimental ground state of the system in both the frustrated and non-frustrated regimes. In particular, we use multipartite quantum correlation measures generated by monogamy considerations of negativity, a bipartite entanglement measure, and that of quantum discord, an information-theoretic quantum correlation measure. As expected from theoretical predictions, the experimental data confirm that the non-frustrated regime shows higher multipartite quantum correlations compared to the frustrated one.Comment: Title in the published version is "Multipartite quantum correlations reveal frustration in a quantum Ising spin system", 7 pages, 4 figure

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments encode the corresponding probability distribution. Probing if quantum joint probability distribution can be retrieved from the associated set of moments -- realized in the sequential measurement of a dichotomic observable at different time intervals -- reveals a negative answer i.e., the joint probabilities of sequential measurements do not agree with the ones obtained by inverting the moments. This is indeed a reflection of the non-existence of a bonafide grand joint probability distribution, consistent with all the physical marginal probability distributions. Here we explicitly demonstrate that given the set of moments, it is not possible to retrieve the three-time quantum joint probability distribution resulting from quantum sequential measurement of a single qubit dichotomic observable at three different times. Experimental results using a nuclear magnetic resonance (NMR) system are reported here to corroborate these theoretical observations viz., the incompatibility of the three-time joint probabilties with those extracted from the moment sequence.Comment: 7 pages, 5 figures, RevTe