278 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
Testing of quantum phase in matter wave optics
Various phase concepts may be treated as special cases of the maximum
likelihood estimation. For example the discrete Fourier estimation that
actually coincides with the operational phase of Noh, Fouge`res and Mandel is
obtained for continuous Gaussian signals with phase modulated mean.Since
signals in quantum theory are discrete, a prediction different from that given
by the Gaussian hypothesis should be obtained as the best fit assuming a
discrete Poissonian statistics of the signal. Although the Gaussian estimation
gives a satisfactory approximation for fitting the phase distribution of almost
any state the optimal phase estimation offers in certain cases a measurable
better performance. This has been demonstrated in neutron--optical experiment.Comment: 8 pages, 4 figure
Magnetic soft modes in the locally distorted triangular antiferromagnet alpha-CaCr2O4
In this paper we explore the phase diagram and excitations of a distorted
triangular lattice antiferromagnet. The unique two-dimensional distortion
considered here is very different from the 'isosceles'-type distortion that has
been extensively investigated. We show that it is able to stabilize a 120{\deg}
spin structure for a large range of exchange interaction values, while new
structures are found for extreme distortions. A physical realization of this
model is \alpha-CaCr2O4 which has 120{\deg} structure but lies very close to
the phase boundary. This is verified by inelastic neutron scattering which
reveals unusual roton-like minima at reciprocal space points different from
those corresponding to the magnetic order.Comment: 5 pages, 3 figures and lots of spin-wave
Quantum inference of states and processes
The maximum-likelihood principle unifies inference of quantum states and
processes from experimental noisy data. Particularly, a generic quantum process
may be estimated simultaneously with unknown quantum probe states provided that
measurements on probe and transformed probe states are available. Drawbacks of
various approximate treatments are considered.Comment: 7 pages, 4 figure
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
Neutron wave packet tomography
A tomographic technique is introduced in order to determine the quantum state
of the center of mass motion of neutrons. An experiment is proposed and
numerically analyzed.Comment: 4 pages, 3 figure
Maximum likelihood estimation of photon number distribution from homodyne statistics
We present a method for reconstructing the photon number distribution from
the homodyne statistics based on maximization of the likelihood function
derived from the exact statistical description of a homodyne experiment. This
method incorporates in a natural way the physical constraints on the
reconstructed quantities, and the compensation for the nonunit detection
efficiency.Comment: 3 pages REVTeX. Final version, to appear in Phys. Rev. A as a Brief
Repor
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
Reconstruction of motional states of neutral atoms via MaxEnt principle
We present a scheme for a reconstruction of states of quantum systems from
incomplete tomographic-like data. The proposed scheme is based on the Jaynes
principle of Maximum Entropy. We apply our algorithm for a reconstruction of
motional quantum states of neutral atoms. As an example we analyze the
experimental data obtained by the group of C. Salomon at the ENS in Paris and
we reconstruct Wigner functions of motional quantum states of Cs atoms trapped
in an optical lattice
Optimal, reliable estimation of quantum states
Accurately inferring the state of a quantum device from the results of
measurements is a crucial task in building quantum information processing
hardware. The predominant state estimation procedure, maximum likelihood
estimation (MLE), generally reports an estimate with zero eigenvalues. These
cannot be justified. Furthermore, the MLE estimate is incompatible with error
bars, so conclusions drawn from it are suspect. I propose an alternative
procedure, Bayesian mean estimation (BME). BME never yields zero eigenvalues,
its eigenvalues provide a bound on their own uncertainties, and it is the most
accurate procedure possible. I show how to implement BME numerically, and how
to obtain natural error bars that are compatible with the estimate. Finally, I
briefly discuss the differences between Bayesian and frequentist estimation
techniques.Comment: RevTeX; 14 pages, 2 embedded figures. Comments enthusiastically
welcomed
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