31 research outputs found
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