35 research outputs found
Characterizing the width of entanglement
We introduce the concept of entanglement width as measure of the spatial
distribution of entanglement in multiparticle systems. We develop criteria to
detect the width of entanglement using global observables such as energy and
magnetic susceptibility. Therefore, the introduced entanglement criteria can be
applied to systems where addressing of single particles is not possible. We
apply the criteria to different examples such as the J1-J2- Heisenberg model
and point out the difference between entanglement depth and entanglement width.Comment: 10 pages, 5 figures, major revision including new examples and
criteria for entanglement widt
Quantum dynamics of trapped ions in a dynamic field gradient using dressed states
Novel ion traps that provide either a static or a dynamic magnetic gradient
field allow for the use of radio frequency (rf) radiation for coupling internal
and motional states of ions, which is essential for conditional quantum logic.
We show that the coupling mechanism in the presence of a dynamic gradient is
the same, in a dressed state basis, as in the case of a static gradient. Then,
it is shown how demanding experimental requirements arising when using a
dynamic gradient could be overcome. Thus, using dressed states in a dynamic
gradient field could decisively reduce experimental complexity on the route
towards a scalable device for quantum information science based on rf-driven
trapped ions.Comment: 5 page
Optimal distributed sensing in noisy environments
We consider distributed sensing of non-local quantities. We introduce quantum
enhanced protocols to directly measure any (scalar) field with a specific
spatial dependence by placing sensors at appropriate positions and preparing a
spatially distributed entangled quantum state. Our scheme has optimal
Heisenberg scaling and is completely unaffected by noise on other processes
with different spatial dependence than the signal. We consider both Fisher and
Bayesian scenarios, and design states and settings to achieve optimal scaling.
We explicitly demonstrate how to measure coefficients of spatial Taylor and
Fourier series, and show that our approach can offer an exponential advantage
as compared to strategies that do not make use of entanglement between
different sites.Comment: 7 pages (4+3), 4 figure
A unified approach to entanglement criteria using the Cauchy-Schwarz and H\"older inequalities
We present unified approach to different recent entanglement criteria.
Although they were developed in different ways, we show that they are all
applications of a more general principle given by the Cauchy-Schwarz
inequality. We explain this general principle and show how to derive with it
not only already known but also new entanglement criteria. We systematically
investigate its potential and limits to detect bipartite and multipartite
entanglement.Comment: 11 pages, 1 figur
Estimation of gradients in quantum metrology
We develop a general theory to estimate magnetic field gradients in quantum
metrology. We consider a system of particles distributed on a line whose
internal degrees of freedom interact with a magnetic field. Usually gradient
estimation is based on precise measurements of the magnetic field at two
different locations, performed with two independent groups of particles. This
approach, however, is sensitive to fluctuations of the off-set field
determining the level-splitting of the particles and results in collective
dephasing. In this work we use the framework of quantum metrology to assess the
maximal accuracy for gradient estimation. For arbitrary positioning of
particles, we identify optimal entangled and separable states allowing the
estimation of gradients with the maximal accuracy, quantified by the quantum
Fisher information. We also analyze the performance of states from the
decoherence-free subspace (DFS), which are insensitive to the fluctuations of
the magnetic offset field. We find that these states allow to measure a
gradient directly, without the necessity of estimating the magnetic offset
field. Moreover, we show that DFS states attain a precision for gradient
estimation comparable to the optimal entangled states. Finally, for the above
classes of states we find simple and feasible measurements saturating the
quantum Cram\'er-Rao bound.Comment: 22 pages, 8 figures. See also the related work by I. Apellaniz et al.
arXiv: 1703.09056 (2017
Generalized Effective Operator Formalism for Decaying Systems
Systems of neutral kaons can be used to observe entanglement and the
violation of Bell inequalities. The decay of these particles poses some
problems, however, and recently an effective formalism for treating such
systems has been derived. We generalize this formalism and make it applicable
to other quantum systems that can be made to behave in a similar manner. As
examples, we discuss two possible implementations of the generalized formalism
using trapped ions such as Yb or Yb, which may be used to
simulate kaonic behavior in a quantum optical system.Comment: 11 pages, 20 figure
Optimized parameter estimation in the presence of collective phase noise
We investigate phase and frequency estimation with different measurement
strategies under the effect of collective phase noise. First, we consider the
standard linear estimation scheme and present an experimentally realisable
optimization of the initial probe states by collective rotations. We identify
the optimal rotation angle for different measurement times. Second, we show
that sub-shot noise sensitivity - up to the Heisenberg limit - can be reached
in presence of collective phase noise by using differential interferometry,
where one part of the system is used to monitor the noise. For this, not only
GHZ states but also symmetric Dicke states are suitable. We investigate the
optimal splitting for a general symmetric Dicke state at both inputs and
discuss possible experimental realisations of differential interferometry.Comment: 17 pages, 6 figures, v2: small revisions, final versio
State selective detection of hyperfine qubits
In order to faithfully detect the state of an individual two-state quantum
system (qubit) realized using, for example, a trapped ion or atom, state
selective scattering of resonance fluorescence is well established. The
simplest way to read out this measurement and assign a state is the threshold
method. The detection error can be decreased by using more advanced detection
methods like the time-resolved method or the -pulse detection method.
These methods were introduced to qubits with a single possible state change
during the measurement process. However, there exist many qubits like the
hyperfine qubit of where several state change are possible. To
decrease the detection error for such qubits, we develope generalizations of
the time-resolved method and the -pulse detection method for such qubits.
We show the advantages of these generalized detection methods in numerical
simulations and experiments using the hyperfine qubit of . The
generalized detection methods developed here can be implemented in an efficient
way such that experimental real time state discrimination with improved
fidelity is possible.Comment: 22 pages, 9 figure
Distinguishing between statistical and systematic errors in quantum process tomography
It is generally assumed that every process in quantum physics can be
described mathematically by a completely positive map. However, experimentally
reconstructed processes are not necessarily completely positive due to
statistical or systematic errors. In this paper, we introduce a test for
discriminating statistical from systematic errors which is necessary to
interpret experimentally reconstructed, non-completely positive
maps.Wedemonstrate the significance of the test using several examples given by
experiments and simulations. In particular, we demonstrate experimentally how
an initial correlation between the system to be measured and its environment
leads to an experimentally reconstructed map with negative eigenvalues. These
experiments are carried out using atomic 171Yb+ ions confined in a linear Paul
trap, addressed and coherently manipulated by radio frequency radiation.Comment: 11 pages, 5 figure
Radio-frequency sideband cooling and sympathetic cooling of trapped ions in a static magnetic field gradient
We report a detailed investigation on near-ground state cooling of one and
two trapped atomic ions. We introduce a simple sideband cooling method for
confined atoms and ions, using RF radiation applied to bare ionic states in a
static magnetic field gradient, and demonstrate its application to ions
confined at secular trap frequencies, kHz.
For a single \ybplus ion, the sideband cooling cycle reduces the average phonon
number, from the Doppler limit to
0.30(12). This is in agreement with the
theoretically estimated lowest achievable phonon number in this experiment. We
extend this method of RF sideband cooling to a system of two \ybplus ions,
resulting in a phonon number of 1.1(7) in
the center-of-mass mode. Furthermore, we demonstrate the first realisation of
sympathetic RF sideband cooling of an ion crystal consisting of two
individually addressable identical isotopes of the same species.Comment: 8 pages, 7 figure