797 research outputs found
Unknown Quantum States and Operations, a Bayesian View
The classical de Finetti theorem provides an operational definition of the
concept of an unknown probability in Bayesian probability theory, where
probabilities are taken to be degrees of belief instead of objective states of
nature. In this paper, we motivate and review two results that generalize de
Finetti's theorem to the quantum mechanical setting: Namely a de Finetti
theorem for quantum states and a de Finetti theorem for quantum operations. The
quantum-state theorem, in a closely analogous fashion to the original de
Finetti theorem, deals with exchangeable density-operator assignments and
provides an operational definition of the concept of an "unknown quantum state"
in quantum-state tomography. Similarly, the quantum-operation theorem gives an
operational definition of an "unknown quantum operation" in quantum-process
tomography. These results are especially important for a Bayesian
interpretation of quantum mechanics, where quantum states and (at least some)
quantum operations are taken to be states of belief rather than states of
nature.Comment: 37 pages, 3 figures, to appear in "Quantum Estimation Theory," edited
by M.G.A. Paris and J. Rehacek (Springer-Verlag, Berlin, 2004
A C++ library using quantum trajectories to solve quantum master equations
Quantum trajectory methods can be used for a wide range of open quantum
systems to solve the master equation by unraveling the density operator
evolution into individual stochastic trajectories in Hilbert space. This C++
class library offers a choice of integration algorithms for three important
unravelings of the master equation. Different physical systems are modeled by
different Hamiltonians and environment operators. The program achieves
flexibility and user friendliness, without sacrificing execution speed, through
the way it represents operators and states in Hilbert space. Primary operators,
implemented in the form of simple routines acting on single degrees of freedom,
can be used to build up arbitrarily complex operators in product Hilbert spaces
with arbitrary numbers of components. Standard algebraic notation is used to
build operators and to perform arithmetic operations on operators and states.
States can be represented in a local moving basis, often leading to dramatic
savings of computing resources. The state and operator classes are very general
and can be used independently of the quantum trajectory algorithms. Only a
rudimentary knowledge of C++ is required to use this package.Comment: 17 pages standard LaTeX + 3 figures (postscript). Submitted to
Computer Physics Communications. Web site:
http://galisteo.ma.rhbnc.ac.uk/applied/QSD.htm
Quantum state diffusion with a moving basis: computing quantum-optical spectra
Quantum state diffusion (QSD) as a tool to solve quantum-optical master
equations by stochastic simulation can be made several orders of magnitude more
efficient if states in Hilbert space are represented in a moving basis of
excited coherent states. The large savings in computer memory and time are due
to the localization property of the QSD equation. We show how the method can be
used to compute spectra and give an application to second harmonic generation.Comment: 8 pages in RevTeX, 1 uuencoded postscript figure, submitted to Phys.
Rev.
Quantum state diffusion, localization and computation
Numerical simulation of individual open quantum systems has proven advantages
over density operator computations. Quantum state diffusion with a moving basis
(MQSD) provides a practical numerical simulation method which takes full
advantage of the localization of quantum states into wave packets occupying
small regions of classical phase space. Following and extending the original
proposal of Percival, Alber and Steimle, we show that MQSD can provide a
further gain over ordinary QSD and other quantum trajectory methods of many
orders of magnitude in computational space and time. Because of these gains, it
is even possible to calculate an open quantum system trajectory when the
corresponding isolated system is intractable. MQSD is particularly advantageous
where classical or semiclassical dynamics provides an adequate qualitative
picture but is numerically inaccurate because of significant quantum effects.
The principles are illustrated by computations for the quantum Duffing
oscillator and for second harmonic generation in quantum optics. Potential
applications in atomic and molecular dynamics, quantum circuits and quantum
computation are suggested.Comment: 16 pages in LaTeX, 2 uuencoded postscript figures, submitted to J.
Phys.
The Difficult Verses of the Song of Deborah Expounded
The purpose of this thesis is to give a translation of the entire Song and offer a tenable solution of the linguistic difficulties found therein, established on sound biblical exegesis, and not by corrupting the text, as critics have done and yet do; for that mititates against the clear conception or Holy Writ
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