10,474 research outputs found
Bures distance between two displaced thermal states
The Bures distance between two displaced thermal states and the corresponding
geometric quantities (statistical metric, volume element, scalar curvature) are
computed. Under nonunitary (dissipative) dynamics, the statistical distance
shows the same general features previously reported in the literature by
Braunstein and Milburn for two--state systems. The scalar curvature turns out
to have new interesting properties when compared to the curvature associated
with squeezed thermal states.Comment: 3 pages, RevTeX, no figure
A priori probability that a qubit-qutrit pair is separable
We extend to arbitrarily coupled pairs of qubits (two-state quantum systems)
and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181),
which was concerned with the simplest instance of entangled quantum systems,
pairs of qubits. As in that analysis -- again on the basis of numerical
(quasi-Monte Carlo) integration results, but now in a still higher-dimensional
space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical
distinguishability) probability that arbitrarily paired qubits and qutrits are
separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where
u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive
primes). This is considerably less than the conjectured value of the Bures/SD
probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these
conjectures, in turn, rely upon ones to the effect that the SD volumes of
separable states assume certain remarkable forms, involving "primorial"
numbers. We also estimate the SD area of the boundary of separable qubit-qutrit
states, and provide preliminary calculations of the Bures/SD probability of
separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact
computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures
volume of mixed quantum states" to refine our conjecture
On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere
Single variable hypergeometric functions pFq arise in connection with the
power series solution of the Schrodinger equation or in the summation of
perturbation expansions in quantum mechanics. For these applications, it is of
interest to obtain analytic expressions, and we present the reduction of a
number of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and related
series have additional applications in quantum and statistical physics and
chemistry.Comment: 17 pages, no figure
Electron shielding of the nuclear magnetic moment in hydrogen-like atom
The correction to the wave function of the ground state in a hydrogen-like
atom due to an external homogenous magnetic field is found exactly in the
parameter . The projection of the correction to the wave
function of the state due to the external homogeneous magnetic field
is found for arbitrary . The projection of the correction to the
wave function of the state due to the nuclear magnetic moment is
also found for arbitrary . Using these results, we have calculated the
shielding of the nuclear magnetic moment by the electron.Comment: 15 page
Volume of the quantum mechanical state space
The volume of the quantum mechanical state space over -dimensional real,
complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean
measure is computed, and explicit formulas are presented for the expected value
of the determinant in the general setting too. The case when the state space is
endowed with a monotone metric or a pull-back metric is considered too, we give
formulas to compute the volume of the state space with respect to the given
Riemannian metric. We present the volume of the space of qubits with respect to
various monotone metrics. It turns out that the volume of the space of qubits
can be infinite too. We characterize those monotone metrics which generates
infinite volume.Comment: 17 page
High-Temperature Expansions of Bures and Fisher Information Priors
For certain infinite and finite-dimensional thermal systems, we obtain ---
incorporating quantum-theoretic considerations into Bayesian thermostatistical
investigations of Lavenda --- high-temperature expansions of priors over
inverse temperature beta induced by volume elements ("quantum Jeffreys' priors)
of Bures metrics. Similarly to Lavenda's results based on volume elements
(Jeffreys' priors) of (classical) Fisher information metrics, we find that in
the limit beta -> 0, the quantum-theoretic priors either conform to Jeffreys'
rule for variables over [0,infinity], by being proportional to 1/beta, or to
the Bayes-Laplace principle of insufficient reason, by being constant. Whether
a system adheres to one rule or to the other appears to depend upon its number
of degrees of freedom.Comment: Six pages, LaTeX. The title has been shortened (and then further
modified), at the suggestion of a colleague. Other minor change
The value-added of primary schools: what is it really measuring?
This paper compares the official value-added scores in 2005 for all primary schools in three adjacent LEAs in England with the raw-score Key Stage 2 results for the same schools. The correlation coefficient for the raw- and value-added scores of these 457 schools is around +0.75. Scatterplots show that there are no low attaining schools with average or higher value-added, and no high attaining schools with below average value-added. At least some of the remaining scatter is explained by the small size of some schools. Although some relationship between these measures is to be expected – so that schools adding considerable value would tend to have high examination outcome scores – the relationship shown is too strong for this explanation to be considered sufficient. Value-added analysis is intended to remove the link between a schools’ intake scores and their raw-score outcomes at KS2. It should lead to an estimate of the differential progress made by pupils, assessed between schools. In fact, however, the relationship between value-added and raw scores is of the same size as the original relationship between intake scores and raw-scores that the value-added is intended to overcome. Therefore, however appealing the calculation of value-added figures is, their development is still at the stage where they are not ready to move from being a research tool to an instrument of judgement on schools. Such figures may mislead parents, governors and teachers and, even more importantly, they are being used in England by OFSTED to pre-determine the results of school inspections
The effect of distressing imagery on attention to and persuasiveness of an anti-alcohol message: a gaze-tracking approach
Density Functional Theory for the Photoionization Dynamics of Uracil
Photoionization dynamics of the RNA base Uracil is studied in the framework
of Density Functional Theory (DFT). The photoionization calculations take
advantage of a newly developed parallel version of a multicentric approach to
the calculation of the electronic continuum spectrum which uses a set of
B-spline radial basis functions and a Kohn-Sham density functional hamiltonian.
Both valence and core ionizations are considered. Scattering resonances in
selected single-particle ionization channels are classified by the symmetry of
the resonant state and the peak energy position in the photoelectron kinetic
energy scale; the present results highlight once more the site specificity of
core ionization processes. We further suggest that the resonant structures
previously characterized in low-energy electron collision experiments are
partly shifted below threshold by the photoionization processes. A critical
evaluation of the theoretical results providing a guide for future experimental
work on similar biosystems
Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities
Employing Hilbert-Schmidt measure, we explicitly compute and analyze a number
of determinantal product (bivariate) moments |rho|^k |rho^{PT}|^n,
k,n=0,1,2,3,..., PT denoting partial transpose, for both generic
(9-dimensional) two-rebit (alpha = 1/2) and generic (15-dimensional) two-qubit
(alpha=1) density matrices rho. The results are, then, incorporated by Dunkl
into a general formula (Appendix D6), parameterized by k, n and alpha, with the
case alpha=2, presumptively corresponding to generic (27-dimensional)
quaternionic systems. Holding the Dyson-index-like parameter alpha fixed, the
induced univariate moments (|rho| |rho^{PT}|)^n and |rho^{PT}|^n are inputted
into a Legendre-polynomial-based (least-squares) probability-distribution
reconstruction algorithm of Provost (Mathematica J., 9, 727 (2005)), yielding
alpha-specific separability probability estimates. Since, as the number of
inputted moments grows, estimates based on |rho| |rho^{PT}| strongly decrease,
while ones employing |rho^{PT}| strongly increase (and converge faster), the
gaps between upper and lower estimates diminish, yielding sharper and sharper
bounds. Remarkably, for alpha = 2, with the use of 2,325 moments, a
separability-probability lower-bound 0.999999987 as large as 26/323 = 0.0804954
is found. For alpha=1, based on 2,415 moments, a lower bound results that is
0.999997066 times as large as 8/33 = 0.242424, a (simpler still) fractional
value that had previously been conjectured (J. Phys. A, 40, 14279 (2007)).
Furthermore, for alpha = 1/2, employing 3,310 moments, the lower bound is
0.999955 times as large as 29/64 = 0.453125, a rational value previously
considered (J. Phys. A, 43, 195302 (2010)).Comment: 47 pages, 12 figures; slightly expanded and modified for journal
publication; this paper incorporates and greatly extends arXiv:1104.021
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