10,034 research outputs found
A new bound of the â2[0, T]-induced norm and applications to model reduction
We present a simple bound on the finite horizon â2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ââ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics
A complete family of separability criteria
We introduce a new family of separability criteria that are based on the
existence of extensions of a bipartite quantum state to a larger number
of parties satisfying certain symmetry properties. It can be easily shown that
all separable states have the required extensions, so the non-existence of such
an extension for a particular state implies that the state is entangled. One of
the main advantages of this approach is that searching for the extension can be
cast as a convex optimization problem known as a semidefinite program (SDP).
Whenever an extension does not exist, the dual optimization constructs an
explicit entanglement witness for the particular state. These separability
tests can be ordered in a hierarchical structure whose first step corresponds
to the well-known Positive Partial Transpose (Peres-Horodecki) criterion, and
each test in the hierarchy is at least as powerful as the preceding one. This
hierarchy is complete, in the sense that any entangled state is guaranteed to
fail a test at some finite point in the hierarchy, thus showing it is
entangled. The entanglement witnesses corresponding to each step of the
hierarchy have well-defined and very interesting algebraic properties that in
turn allow for a characterization of the interior of the set of positive maps.
Coupled with some recent results on the computational complexity of the
separability problem, which has been shown to be NP-hard, this hierarchy of
tests gives a complete and also computationally and theoretically appealing
characterization of mixed bipartite entangled states.Comment: 21 pages. Expanded introduction. References added, typos corrected.
Accepted for publication in Physical Review
Population inversion of driven two-level systems in a structureless bath
We derive a master equation for a driven double-dot damped by an unstructured
phonon bath, and calculate the spectral density. We find that bath mediated
photon absorption is important at relatively strong driving, and may even
dominate the dynamics, inducing population inversion of the double dot system.
This phenomenon is consistent with recent experimental observations.Comment: 4 Pages, Added Reference [30] to Dykman, 1979, available at
http://www.pa.msu.edu/people/dykman/pub/Sov.J.LowTemp.Phys_5.pd
Network Synthesis of Linear Dynamical Quantum Stochastic Systems
The purpose of this paper is to develop a synthesis theory for linear
dynamical quantum stochastic systems that are encountered in linear quantum
optics and in phenomenological models of linear quantum circuits. In
particular, such a theory will enable the systematic realization of
coherent/fully quantum linear stochastic controllers for quantum control,
amongst other potential applications. We show how general linear dynamical
quantum stochastic systems can be constructed by assembling an appropriate
interconnection of one degree of freedom open quantum harmonic oscillators and,
in the quantum optics setting, discuss how such a network of oscillators can be
approximately synthesized or implemented in a systematic way from some linear
and non-linear quantum optical elements. An example is also provided to
illustrate the theory.Comment: Revised and corrected version, published in SIAM Journal on Control
and Optimization, 200
Optimal tracking for pairs of qubit states
In classical control theory, tracking refers to the ability to perform
measurements and feedback on a classical system in order to enforce some
desired dynamics. In this paper we investigate a simple version of quantum
tracking, namely, we look at how to optimally transform the state of a single
qubit into a given target state, when the system can be prepared in two
different ways, and the target state depends on the choice of preparation. We
propose a tracking strategy that is proved to be optimal for any input and
target states. Applications in the context of state discrimination, state
purification, state stabilization and state-dependent quantum cloning are
presented, where existing optimality results are recovered and extended.Comment: 15 pages, 8 figures. Extensive revision of text, optimality results
extended, other physical applications include
Semiclassical theory of cavity-assisted atom cooling
We present a systematic semiclassical model for the simulation of the
dynamics of a single two-level atom strongly coupled to a driven high-finesse
optical cavity. From the Fokker-Planck equation of the combined atom-field
Wigner function we derive stochastic differential equations for the atomic
motion and the cavity field. The corresponding noise sources exhibit strong
correlations between the atomic momentum fluctuations and the noise in the
phase quadrature of the cavity field. The model provides an effective tool to
investigate localisation effects as well as cooling and trapping times. In
addition, we can continuously study the transition from a few photon quantum
field to the classical limit of a large coherent field amplitude.Comment: 10 pages, 8 figure
Arkansas Cotton Variety Test 2004
The primary aim of the Arkansas Cotton Variety Test is to provide unbiased data regarding the agronomic performance of cotton varieties and advanced breeding lines in the major cotton-growing areas of Arkansas. This information helps seed dealers establish marketing strategies and assists producers in choosing varieties to plant
Applying matrix product operators to model systems with long-range interactions
An algorithm is presented which computes a translationally invariant matrix
product state approximation of the ground state of an infinite 1D system; it
does this by embedding sites into an approximation of the infinite
``environment'' of the chain, allowing the sites to relax, and then merging
them with the environment in order to refine the approximation. By making use
of matrix product operators, our approach is able to directly model any
long-range interaction that can be systematically approximated by a series of
decaying exponentials. We apply our techniques to compute the ground state of
the Haldane-Shastry model and present results.Comment: 7 pages, 3 figures; manuscript has been expanded and restructured in
order to improve presentation of the algorith
Study of radiation hazards to man on extended near earth missions
Radiation hazards to man on extended near earth mission
Comparing Experiments to the Fault-Tolerance Threshold
Achieving error rates that meet or exceed the fault-tolerance threshold is a
central goal for quantum computing experiments, and measuring these error rates
using randomized benchmarking is now routine. However, direct comparison
between measured error rates and thresholds is complicated by the fact that
benchmarking estimates average error rates while thresholds reflect worst-case
behavior when a gate is used as part of a large computation. These two measures
of error can differ by orders of magnitude in the regime of interest. Here we
facilitate comparison between the experimentally accessible average error rates
and the worst-case quantities that arise in current threshold theorems by
deriving relations between the two for a variety of physical noise sources. Our
results indicate that it is coherent errors that lead to an enormous mismatch
between average and worst case, and we quantify how well these errors must be
controlled to ensure fair comparison between average error probabilities and
fault-tolerance thresholds.Comment: 5 pages, 2 figures, 13 page appendi
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