580 research outputs found
Explicit product ensembles for separable quantum states
We present a general method for constructing pure-product-state
representations for density operators of quantum bits. If such a
representation has nonnegative expansion coefficients, it provides an explicit
separable ensemble for the density operator. We derive the condition for
separability of a mixture of the Greenberger-Horne-Zeilinger state with the
maximally mixed state.Comment: 15 pages, no figure
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.
Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics
We re-examine the problem of the "Loschmidt echo", which measures the
sensitivity to perturbation of quantum chaotic dynamics. The overlap squared
of two wave packets evolving under slightly different Hamiltonians is
shown to have the double-exponential initial decay in the main part of phase space. The
coefficient is the self-averaging Lyapunov exponent. The average
decay is single exponential with a different
coefficient . The volume of phase space that contributes to
vanishes in the classical limit for times less than the
Ehrenfest time . It is only after
the Ehrenfest time that the average decay is representative for a typical
initial condition.Comment: 4 pages, 4 figures, [2017: fixed broken postscript figures
Compatibility of quantum states
We introduce a measure of the compatibility between quantum states--the
likelihood that two density matrices describe the same object. Our measure is
motivated by two elementary requirements, which lead to a natural definition.
We list some properties of this measure, and discuss its relation to the
problem of combining two observers' states of knowledge.Comment: 4 pages, no figure
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