280 research outputs found
Diluted maximum-likelihood algorithm for quantum tomography
We propose a refined iterative likelihood-maximization algorithm for
reconstructing a quantum state from a set of tomographic measurements. The
algorithm is characterized by a very high convergence rate and features a
simple adaptive procedure that ensures likelihood increase in every iteration
and convergence to the maximum-likelihood state.
We apply the algorithm to homodyne tomography of optical states and quantum
tomography of entangled spin states of trapped ions and investigate its
convergence properties.Comment: v2: Convergence proof adde
Convex probability domain of generalized quantum measurements
Generalized quantum measurements with N distinct outcomes are used for
determining the density matrix, of order d, of an ensemble of quantum systems.
The resulting probabilities are represented by a point in an N-dimensional
space. It is shown that this point lies in a convex domain having at most d^2-1
dimensions.Comment: 7 pages LaTeX, one PostScript figure on separate pag
Reconstruction of the spin state
System of 1/2 spin particles is observed repeatedly using Stern-Gerlach
apparatuses with rotated orientations. Synthesis of such non-commuting
observables is analyzed using maximum likelihood estimation as an example of
quantum state reconstruction. Repeated incompatible observations represent a
new generalized measurement. This idealized scheme will serve for analysis of
future experiments in neutron and quantum optics.Comment: 4 pages, 1 figur
Lost and found: the radial quantum number of Laguerre-Gauss modes
We introduce an operator linked with the radial index in the Laguerre-Gauss
modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We
discuss ladder operators for this variable, and confirm that they obey the
commutation relations of the su(1,1) algebra. Using this fact, we examine how
basic quantum optical concepts can be recast in terms of radial modes.Comment: Some minor typos fixed
Quantum estimation via minimum Kullback entropy principle
We address quantum estimation in situations where one has at disposal data
from the measurement of an incomplete set of observables and some a priori
information on the state itself. By expressing the a priori information in
terms of a bias toward a given state the problem may be faced by minimizing the
quantum relative entropy (Kullback entropy) with the constraint of reproducing
the data. We exploit the resulting minimum Kullback entropy principle for the
estimation of a quantum state from the measurement of a single observable,
either from the sole mean value or from the complete probability distribution,
and apply it as a tool for the estimation of weak Hamiltonian processes. Qubit
and harmonic oscillator systems are analyzed in some details.Comment: 7 pages, slightly revised version, no figure
Minimax mean estimator for the trine
We explore the question of state estimation for a qubit restricted to the
- plane of the Bloch sphere, with the trine measurement. In our earlier
work [H. K. Ng and B.-G. Englert, eprint arXiv:1202.5136[quant-ph] (2012)],
similarities between quantum tomography and the tomography of a classical die
motivated us to apply a simple modification of the classical estimator for use
in the quantum problem. This worked very well. In this article, we adapt a
different aspect of the classical estimator to the quantum problem. In
particular, we investigate the mean estimator, where the mean is taken with a
weight function identical to that in the classical estimator but now with
quantum constraints imposed. Among such mean estimators, we choose an optimal
one with the smallest worst-case error-the minimax mean estimator-and compare
its performance with that of other estimators. Despite the natural
generalization of the classical approach, this minimax mean estimator does not
work as well as one might expect from the analogous performance in the
classical problem. While it outperforms the often-used maximum-likelihood
estimator in having a smaller worst-case error, the advantage is not
significant enough to justify the more complicated procedure required to
construct it. The much simpler adapted estimator introduced in our earlier work
is still more effective. Our previous work emphasized the similarities between
classical and quantum state estimation; in contrast, this paper highlights how
intuition gained from classical problems can sometimes fail in the quantum
arena.Comment: 18 pages, 3 figure
Characterizing Quantum Microwave Radiation and its Entanglement with Superconducting Qubits using Linear Detectors
Recent progress in the development of superconducting circuits has enabled
the realization of interesting sources of nonclassical radiation at microwave
frequencies. Here, we discuss field quadrature detection schemes for the
experimental characterization of itinerant microwave photon fields and their
entanglement correlations with stationary qubits. In particular, we present
joint state tomography methods of a radiation field mode and a two-level
system. Including the case of finite quantum detection efficiency, we relate
measured photon field statistics to generalized quasi-probability distributions
and statistical moments for one-channel and two-channel detection. We also
present maximum-likelihood methods to reconstruct density matrices from
measured field quadrature histograms. Our theoretical investigations are
supported by the presentation of experimental data, for which microwave quantum
fields beyond the single-photon and Gaussian level have been prepared and
reconstructed.Comment: 14 pages, 5 figure
Electron-phonon coupling in the conventional superconductor YNiBC at high phonon energies studied by time-of-flight neutron spectroscopy
We report an inelastic neutron scattering investigation of phonons with
energies up to 159 meV in the conventional superconductor YNiBC. Using
the SWEEP mode, a newly developed time-of-flight technique involving the
continuous rotation of a single crystal specimen, allowed us to measure a four
dimensional volume in (Q,E) space and, thus, determine the dispersion surface
and linewidths of the (~ 102 meV) and (~ 159 meV) type phonon
modes for the whole Brillouin zone. Despite of having linewidths of , modes do not strongly contribute to the total electron-phonon
coupling constant . However, experimental linewidths show a remarkable
agreement with ab-initio calculations over the complete phonon energy range
demonstrating the accuracy of such calculations in a rare comparison to a
comprehensive experimental data set.Comment: accepted for publication in PR
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