5,670 research outputs found
A Quantitative Analysis of IRAS Maps of Molecular Clouds
We present an analysis of IRAS maps of five molecular clouds: Orion,
Ophiuchus, Perseus, Taurus, and Lupus. For the classification and description
of these astrophysical maps, we use a newly developed technique which considers
all maps of a given type to be elements of a pseudometric space. For each
physical characteristic of interest, this formal system assigns a distance
function (a pseudometric) to the space of all maps; this procedure allows us to
measure quantitatively the difference between any two maps and to order the
space of all maps. We thus obtain a quantitative classification scheme for
molecular clouds. In this present study we use the IRAS continuum maps at
100m and 60m to produce column density (or optical depth) maps for
the five molecular cloud regions given above. For this sample of clouds, we
compute the ``output'' functions which measure the distribution of density, the
distribution of topological components, the self-gravity, and the filamentary
nature of the clouds. The results of this work provide a quantitative
description of the structure in these molecular cloud regions. We then order
the clouds according to the overall environmental ``complexity'' of these star
forming regions. Finally, we compare our results with the observed populations
of young stellar objects in these clouds and discuss the possible environmental
effects on the star formation process. Our results are consistent with the
recently stated conjecture that more massive stars tend to form in more
``complex'' environments.Comment: 27 pages Plain TeX, submitted to ApJ, UM-AC 93-15, 15 figures
available upon reques
Adiabatic Elimination in Compound Quantum Systems with Feedback
Feedback in compound quantum systems is effected by using the output from one
sub-system (``the system'') to control the evolution of a second sub-system
(``the ancilla'') which is reversibly coupled to the system. In the limit where
the ancilla responds to fluctuations on a much shorter time scale than does the
system, we show that it can be adiabatically eliminated, yielding a master
equation for the system alone. This is very significant as it decreases the
necessary basis size for numerical simulation and allows the effect of the
ancilla to be understood more easily. We consider two types of ancilla: a
two-level ancilla (e.g. a two-level atom) and an infinite-level ancilla (e.g.
an optical mode). For each, we consider two forms of feedback: coherent (for
which a quantum mechanical description of the feedback loop is required) and
incoherent (for which a classical description is sufficient). We test the
master equations we obtain using numerical simulation of the full dynamics of
the compound system. For the system (a parametric oscillator) and feedback
(intensity-dependent detuning) we choose, good agreement is found in the limit
of heavy damping of the ancilla. We discuss the relation of our work to
previous work on feedback in compound quantum systems, and also to previous
work on adiabatic elimination in general.Comment: 18 pages, 12 figures including two subplots as jpeg attachment
Quantum error correction for continuously detected errors
We show that quantum feedback control can be used as a quantum error
correction process for errors induced by weak continuous measurement. In
particular, when the error model is restricted to one, perfectly measured,
error channel per physical qubit, quantum feedback can act to perfectly protect
a stabilizer codespace. Using the stabilizer formalism we derive an explicit
scheme, involving feedback and an additional constant Hamiltonian, to protect
an ()-qubit logical state encoded in physical qubits. This works for
both Poisson (jump) and white-noise (diffusion) measurement processes. In
addition, universal quantum computation is possible in this scheme. As an
example, we show that detected-spontaneous emission error correction with a
driving Hamiltonian can greatly reduce the amount of redundancy required to
protect a state from that which has been previously postulated [e.g., Alber
\emph{et al.}, Phys. Rev. Lett. 86, 4402 (2001)].Comment: 11 pages, 1 figure; minor correction
Reconsidering Rapid Qubit Purification by Feedback
This paper reconsiders the claimed rapidity of a scheme for the purification
of the quantum state of a qubit, proposed recently in Jacobs 2003 Phys. Rev.
A67 030301(R). The qubit starts in a completely mixed state, and information is
obtained by a continuous measurement. Jacobs' rapid purification protocol uses
Hamiltonian feedback control to maximise the average purity of the qubit for a
given time, with a factor of two increase in the purification rate over the
no-feedback protocol. However, by re-examining the latter approach, we show
that it mininises the average time taken for a qubit to reach a given purity.
In fact, the average time taken for the no-feedback protocol beats that for
Jacobs' protocol by a factor of two. We discuss how this is compatible with
Jacobs' result, and the usefulness of the different approaches.Comment: 11 pages, 3 figures. Final version, accepted for publication in New
J. Phy
On quantum error-correction by classical feedback in discrete time
We consider the problem of correcting the errors incurred from sending
quantum information through a noisy quantum environment by using classical
information obtained from a measurement on the environment. For discrete time
Markovian evolutions, in the case of fixed measurement on the environment, we
give criteria for quantum information to be perfectly corrigible and
characterize the related feedback. Then we analyze the case when perfect
correction is not possible and, in the qubit case, we find optimal feedback
maximizing the channel fidelity.Comment: 11 pages, 1 figure, revtex
Optimal states and almost optimal adaptive measurements for quantum interferometry
We derive the optimal N-photon two-mode input state for obtaining an estimate
\phi of the phase difference between two arms of an interferometer. For an
optimal measurement [B. C. Sanders and G. J. Milburn, Phys. Rev. Lett. 75, 2944
(1995)], it yields a variance (\Delta \phi)^2 \simeq \pi^2/N^2, compared to
O(N^{-1}) or O(N^{-1/2}) for states considered by previous authors. Such a
measurement cannot be realized by counting photons in the interferometer
outputs. However, we introduce an adaptive measurement scheme that can be thus
realized, and show that it yields a variance in \phi very close to that from an
optimal measurement.Comment: 4 pages, 4 figures, journal versio
Adaptive Phase Measurements in Linear Optical Quantum Computation
Photon counting induces an effective nonlinear optical phase shift on certain
states derived by linear optics from single photons. Although this no
nlinearity is nondeterministic, it is sufficient in principle to allow scalable
linear optics quantum computation (LOQC). The most obvious way to encode a
qubit optically is as a superposition of the vacuum and a single photon in one
mode -- so-called "single-rail" logic. Until now this approach was thought to
be prohibitively expensive (in resources) compared to "dual-rail" logic where a
qubit is stored by a photon across two modes. Here we attack this problem with
real-time feedback control, which can realize a quantum-limited phase
measurement on a single mode, as has been recently demonstrated experimentally.
We show that with this added measurement resource, the resource requirements
for single-rail LOQC are not substantially different from those of dual-rail
LOQC. In particular, with adaptive phase measurements an arbitrary qubit state
can be prepared deterministically
State and dynamical parameter estimation for open quantum systems
Following the evolution of an open quantum system requires full knowledge of
its dynamics. In this paper we consider open quantum systems for which the
Hamiltonian is ``uncertain''. In particular, we treat in detail a simple system
similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]:
a radiatively damped atom driven by an unknown Rabi frequency (as
would occur for an atom at an unknown point in a standing light wave). By
measuring the environment of the system, knowledge about the system state, and
about the uncertain dynamical parameter, can be acquired. We find that these
two sorts of knowledge acquisition (quantified by the posterior distribution
for , and the conditional purity of the system, respectively) are quite
distinct processes, which are not strongly correlated. Also, the quality and
quantity of knowledge gain depend strongly on the type of monitoring scheme. We
compare five different detection schemes (direct, adaptive, homodyne of the
quadrature, homodyne of the quadrature, and heterodyne) using four
different measures of the knowledge gain (Shannon information about ,
variance in , long-time system purity, and short-time system purity).Comment: 14 pages, 18 figure
Entanglement under restricted operations: Analogy to mixed-state entanglement
We show that the classification of bi-partite pure entangled states when
local quantum operations are restricted yields a structure that is analogous in
many respects to that of mixed-state entanglement. Specifically, we develop
this analogy by restricting operations through local superselection rules, and
show that such exotic phenomena as bound entanglement and activation arise
using pure states in this setting. This analogy aids in resolving several
conceptual puzzles in the study of entanglement under restricted operations. In
particular, we demonstrate that several types of quantum optical states that
possess confusing entanglement properties are analogous to bound entangled
states. Also, the classification of pure-state entanglement under restricted
operations can be much simpler than for mixed-state entanglement. For instance,
in the case of local Abelian superselection rules all questions concerning
distillability can be resolved.Comment: 10 pages, 2 figures; published versio
Decoherence and the conditions for the classical control of quantum systems
We find the conditions for one quantum system to function as a classical
controller of another quantum system: the controller must be an open system and
rapidly diagonalised in the basis of the controller variable that is coupled to
the controlled system. This causes decoherence in the controlled system that
can be made small if the rate of diagonalisation is fast. We give a detailed
example based on the quantum optomechanical control of a mechanical resonator.
The resulting equations are similar in structure to recently proposed models
for consistently combining quantum and classical stochastic dynamics
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