495 research outputs found
Weak measurement and rapid state reduction in bipartite quantum systems
In this paper we consider feedback control algorithms for the rapid
purification of a bipartite state consisting of two qubits, when the observer
has access to only one of the qubits. We show 1) that the algorithm that
maximizes the average purification rate is not the same as that that for a
single qubit, and 2) that it is always possible to construct an algorithm that
generates a deterministic rate of purification for {\em both} qubits. We also
reveal a key difference between projective and continuous measurements with
regard to state-purification.Comment: 4 pages, 3 figure
A discrete invitation to quantum filtering and feedback control
The engineering and control of devices at the quantum-mechanical level--such
as those consisting of small numbers of atoms and photons--is a delicate
business. The fundamental uncertainty that is inherently present at this scale
manifests itself in the unavoidable presence of noise, making this a novel
field of application for stochastic estimation and control theory. In this
expository paper we demonstrate estimation and feedback control of quantum
mechanical systems in what is essentially a noncommutative version of the
binomial model that is popular in mathematical finance. The model is extremely
rich and allows a full development of the theory, while remaining completely
within the setting of finite-dimensional Hilbert spaces (thus avoiding the
technical complications of the continuous theory). We introduce discretized
models of an atom in interaction with the electromagnetic field, obtain
filtering equations for photon counting and homodyne detection, and solve a
stochastic control problem using dynamic programming and Lyapunov function
methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be
found at http://minty.caltech.edu/papers.ph
Scattering of polarized laser light by an atomic gas in free space: a QSDE approach
We propose a model, based on a quantum stochastic differential equation
(QSDE), to describe the scattering of polarized laser light by an atomic gas.
The gauge terms in the QSDE account for the direct scattering of the laser
light into different field channels. Once the model has been set, we can
rigorously derive quantum filtering equations for balanced polarimetry and
homodyne detection experiments, study the statistics of output processes and
investigate a strong driving, weak coupling limit.Comment: 9 pages, 2 figure
Bellman equations for optimal feedback control of qubit states
Using results from quantum filtering theory and methods from classical
control theory, we derive an optimal control strategy for an open two-level
system (a qubit in interaction with the electromagnetic field) controlled by a
laser. The aim is to optimally choose the laser's amplitude and phase in order
to drive the system into a desired state. The Bellman equations are obtained
for the case of diffusive and counting measurements for vacuum field states. A
full exact solution of the optimal control problem is given for a system with
simpler, linear, dynamics. These linear dynamics can be obtained physically by
considering a two-level atom in a strongly driven, heavily damped, optical
cavity.Comment: 10 pages, no figures, replaced the simpler model in section
Functional regeneration at the blood-biomaterial interface
The use of cardiovascular implants is commonplace in clinical practice. However, reproducing the key bioactive and adaptive properties of native cardiovascular tissues with an artificial replacement is highly challenging. Exciting new treatment strategies are under development to regenerate (parts of) cardiovascular tissues directly in situ using immunomodulatory biomaterials. Direct exposure to the bloodstream and hemodynamic loads is a particular challenge, given the risk of thrombosis and adverse remodeling that it brings. However, the blood is also a source of (immune) cells and proteins that dominantly contribute to functional tissue regeneration. This review explores the potential of the blood as a source for the complete or partial in situ regeneration of cardiovascular tissues, with a particular focus on the endothelium, being the natural blood-tissue barrier. We pinpoint the current scientific challenges to enable rational engineering and testing of blood-contacting implants to leverage the regenerative potential of the blood.</p
Non Markovian Quantum Repeated Interactions and Measurements
A non-Markovian model of quantum repeated interactions between a small
quantum system and an infinite chain of quantum systems is presented. By
adapting and applying usual pro jection operator techniques in this context,
discrete versions of the integro-differential and time-convolutioness Master
equations for the reduced system are derived. Next, an intuitive and rigorous
description of the indirect quantum measurement principle is developed and a
discrete non Markovian stochastic Master equation for the open system is
obtained. Finally, the question of unravelling in a particular model of
non-Markovian quantum interactions is discussed.Comment: 22 page
Training a perceptron in a discrete weight space
On-line and batch learning of a perceptron in a discrete weight space, where
each weight can take different values, are examined analytically and
numerically. The learning algorithm is based on the training of the continuous
perceptron and prediction following the clipped weights. The learning is
described by a new set of order parameters, composed of the overlaps between
the teacher and the continuous/clipped students. Different scenarios are
examined among them on-line learning with discrete/continuous transfer
functions and off-line Hebb learning. The generalization error of the clipped
weights decays asymptotically as / in the case of on-line learning with binary/continuous activation
functions, respectively, where is the number of examples divided by N,
the size of the input vector and is a positive constant that decays
linearly with 1/L. For finite and , a perfect agreement between the
discrete student and the teacher is obtained for . A crossover to the generalization error ,
characterized continuous weights with binary output, is obtained for synaptic
depth .Comment: 10 pages, 5 figs., submitted to PR
On the Quantum Phase Operator for Coherent States
In papers by Lynch [Phys. Rev. A41, 2841 (1990)] and Gerry and Urbanski
[Phys. Rev. A42, 662 (1990)] it has been argued that the phase-fluctuation
laser experiments of Gerhardt, B\"uchler and Lifkin [Phys. Lett. 49A, 119
(1974)] are in good agreement with the variance of the Pegg-Barnett phase
operator for a coherent state, even for a small number of photons. We argue
that this is not conclusive. In fact, we show that the variance of the phase in
fact depends on the relative phase between the phase of the coherent state and
the off-set phase of the Pegg-Barnett phase operator. This off-set
phase is replaced with the phase of a reference beam in an actual experiment
and we show that several choices of such a relative phase can be fitted to the
experimental data. We also discuss the Noh, Foug\`{e}res and Mandel [Phys.Rev.
A46, 2840 (1992)] relative phase experiment in terms of the Pegg-Barnett phase
taking post-selection conditions into account.Comment: 8 pages, 8 figures. Typographical errors and misprints have been
corrected. The outline of the paper has also been changed. Physica Scripta
(in press
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