3,093 research outputs found
Quantum-state tomography for spin-l systems
We show that the density matrix of a spin-l system can be described entirely
in terms of the measurement statistics of projective spin measurements along a
minimum of 4l+1 different spin directions. It is thus possible to represent the
complete quantum statistics of any N-level system within the spherically
symmetric three dimensional space defined by the spin vector. An explicit
method for reconstructing the density matrix of a spin-1 system from the
measurement statistics of five non-orthogonal spin directions is presented and
the generalization to spin-l systems is discussed.Comment: 10 pages, including 2 tables, minor modifications in section II,
final version for publication in Phys. Rev.
Statistical Reconstruction of Qutrits
We discuss a procedure of measurement followed by the reproduction of the
quantum state of a three-level optical system - a frequency- and spatially
degenerate two-photon field. The method of statistical estimation of the
quantum state based on solving the likelihood equation and analyzing the
statistical properties of the obtained estimates is developed. Using the root
approach of estimating quantum states, the initial two-photon state vector is
reproduced from the measured fourth moments in the field . The developed
approach applied to quantum states reconstruction is based on the amplitudes of
mutually complementary processes. Classical algorithm of statistical estimation
based on the Fisher information matrix is generalized to the case of quantum
systems obeying Bohr's complementarity principle. It has been experimentally
proved that biphoton-qutrit states can be reconstructed with the fidelity of
0.995-0.999 and higher.Comment: Submitted to Physical Review
Chirped-pulse interferometry with finite frequency correlations
Chirped-pulse interferometry is a new interferometric technique encapsulating
the advantages of the quantum Hong-Ou-Mandel interferometer without the
drawbacks of using entangled photons. Both interferometers can exhibit
even-order dispersion cancellation which allows high resolution optical delay
measurements even in thick optical samples. In the present work, we show that
finite frequency correlations in chirped-pulse interferometry and
Hong-Ou-Mandel interferometry limit the degree of dispersion cancellation. Our
results are important considerations in designing practical devices based on
these technologies.Comment: 10 pages, 2 figure
Theory and experiment of entanglement in a quasi-phase-matched two-crystal source
We report new results regarding a source of polarization entangled
photon-pairs created by the process of spontaneous parametric downconversion in
two orthogonally oriented, periodically poled, bulk KTiOPO4 crystals (PPKTP).
The source emits light colinearly at the non-degenerate wavelengths of 810 nm
and 1550 nm, and is optimized for single-mode optical fiber collection and
long-distance quantum communication. The configuration favors long crystals,
which promote a high photon-pair production rate at a narrow bandwidth,
together with a high pair-probability in fibers. The quality of entanglement is
limited by chromatic dispersion, which we analyze by determining the output
state. We find that such a decoherence effect is strongly material dependent,
providing for long crystals an upper bound on the visibility of the coincidence
fringes of 41% for KTiOPO4, and zero for LiNbO3. The best obtained raw
visibility, when canceling decoherence with an extra piece of crystal, was 91
\pm 0.2%, including background counts. We confirm by a violation of the
CHSH-inequality (S = 2.679 \pm 0.004 at 55 s^{-1/2} standard deviations) and by
complete quantum state tomography that the fibers carry high-quality entangled
pairs at a maximum rate of 55 x 10^3 s^{-1}THz^{-1}mW^{-1}.Comment: 12 pages, 10 figures, REVTeX
Quantum Sensors: Improved Optical Measurement via Specialized Quantum States
Classical measurement strategies in many areas are approaching their maximum
resolution and sensitivity levels, but these levels often still fall far short
of the ultimate limits allowed by the laws of physics. To go further,
strategies must be adopted that take into account the quantum nature of the
probe particles and that optimize their quantum states for the desired
application. Here, we review some of these approaches, in which quantum
entanglement, the orbital angular momentum of single photons, and quantum
interferometry are used to produce optical measurements beyond the classical
limit
Quantum tomography for collider physics: Illustrations with lepton pair production
Quantum tomography is a method to experimentally extract all that is
observable about a quantum mechanical system. We introduce quantum tomography
to collider physics with the illustration of the angular distribution of lepton
pairs. The tomographic method bypasses much of the field-theoretic formalism to
concentrate on what can be observed with experimental data, and how to
characterize the data. We provide a practical, experimentally-driven guide to
model-independent analysis using density matrices at every step. Comparison
with traditional methods of analyzing angular correlations of inclusive
reactions finds many advantages in the tomographic method, which include
manifest Lorentz covariance, direct incorporation of positivity constraints,
exhaustively complete polarization information, and new invariants free from
frame conventions. For example, experimental data can determine the
of the production process, which is a
model-independent invariant that measures the degree of coherence of the
subprocess. We give reproducible numerical examples and provide a supplemental
standalone computer code that implements the procedure. We also highlight a
property of that guarantees in a least-squares type fit
that a local minimum of a statistic will be a global minimum: There
are no isolated local minima. This property with an automated implementation of
positivity promises to mitigate issues relating to multiple minima and
convention-dependence that have been problematic in previous work on angular
distributions.Comment: 25 pages, 3 figure
- …