11,234 research outputs found
Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems
We seek to derive the probability--expressed in terms of the Hilbert-Schmidt
(Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit
system is separable, by implementing the well-known Peres-Horodecki test on the
partial transposes (PT's) of the associated 4 x 4 density matrices). But the
full implementation of the test--requiring that the determinant of the PT be
nonnegative for separability to hold--appears to be, at least presently,
computationally intractable. So, we have previously implemented--using the
auxiliary concept of a diagonal-entry-parameterized separability function
(DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal
minors of the PT. This yielded an exact upper bound on the separability
probability of 1024/{135 pi^2} =0.76854$. Here, we piece together
(reflection-symmetric) results obtained by requiring that each of the four 3 x
3 principal minors of the PT, in turn, be nonnegative, giving an
improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a
still further improved upper bound of 1129/2100 = 0.537619 can be found by
similarly piecing together the (reflection-symmetric) results of enforcing the
simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors.
In deriving our improved upper bounds, we rely repeatedly upon the use of
certain integrals over cubes that arise. Finally, we apply an independence
assumption to a pair of DESF's that comes close to reproducing our numerical
estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the
end are correcte
Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence
The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional
and 15-dimensional in nature, respectively. The total volumes of the spaces
they occupy with respect to the Hilbert-Schmidt and Bures metrics are
obtainable as special cases of formulas of Zyczkowski and Sommers. We claim
that if one could determine certain metric-independent 3-dimensional
"eigenvalue-parameterized separability functions" (EPSFs), then these formulas
could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes
occupied by only the separable two-qubit states (and hence associated
separability probabilities). Motivated by analogous earlier analyses of
"diagonal-entry-parameterized separability functions", we further explore the
possibility that such 3-dimensional EPSFs might, in turn, be expressible as
univariate functions of some special relevant variable--which we hypothesize to
be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical
results we obtain are rather closely supportive of this hypothesis. Both the
real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude
roughly 50% at C=1/2, as well as a number of additional matching
discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.
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
Hilbert-Schmidt Separability Probabilities and Noninformativity of Priors
The Horodecki family employed the Jaynes maximum-entropy principle, fitting
the mean (b_{1}) of the Bell-CHSH observable (B). This model was extended by
Rajagopal by incorporating the dispersion (\sigma_{1}^2) of the observable, and
by Canosa and Rossignoli, by generalizing the observable (B_{\alpha}). We
further extend the Horodecki one-parameter model in both these manners,
obtaining a three-parameter (b_{1},\sigma_{1}^2,\alpha) two-qubit model, for
which we find a highly interesting/intricate continuum (-\infty < \alpha <
\infty) of Hilbert-Schmidt (HS) separability probabilities -- in which, the
golden ratio is featured. Our model can be contrasted with the three-parameter
(b_{q}, \sigma_{q}^2,q) one of Abe and Rajagopal, which employs a
q(Tsallis)-parameter rather than , and has simply q-invariant HS
separability probabilities of 1/2. Our results emerge in a study initially
focused on embedding certain information metrics over the two-level quantum
systems into a q-framework. We find evidence that Srednicki's recently-stated
biasedness criterion for noninformative priors yields rankings of priors fully
consistent with an information-theoretic test of Clarke, previously applied to
quantum systems by Slater.Comment: 26 pages, 12 figure
On the nucleon-nucleon interaction leading to a standing wave instability in symmetric nuclear matter
We examine a recently proposed nucleon-nucleon interaction, claimed by its
authors both realistic and leading to a standing wave instability in symmetric
nuclear matter. Contrary to these claims, we find that this interaction leads
to a serious overbinding of 4He, 16O and 40Ca nuclei when the Hartree-Fock
method is properly applied. The resulting nuclear densities contradict the
experimental data and all realistic Hartree-Fock results.Comment: 4 pages, 1 figur
Carbon isotope fractionation during aerobic biodegradation of trichloroethene by Burkholderia cepacia G4: a tool to map degradation mechanisms
The strain Burkholderia cepacia G4 aerobically mineralized trichloroethene (TCE) to CO2 over a time period of similar to20 h. Three biodegradation experiments were conducted with different bacterial optical densities at 540 nm (OD(540)s) in order to test whether isotope fractionation was consistent. The resulting TCE degradation was 93, 83.8, and 57.2% (i.e., 7.0, 16.2, and 42.8% TCE remaining) at OD(540)s of 2.0, 1.1, and 0.6, respectively. ODs also correlated linearly with zero-order degradation rates (1.99, 1.11, and 0.64 mumol h(-1)). While initial nonequilibrium mass losses of TCE produced only minor carbon isotope shifts (expressed in per mille delta C- 13(VPDB)), they were 57.2, 39.6, and 17.0parts per thousand between the initial and final TCE levels for the three experiments, in decreasing order of their OD(540)s. Despite these strong isotope shifts, we found a largely uniform isotope fractionation. The latter is expressed with a Rayleigh enrichment factor, E, and was -18.2 when all experiments were grouped to a common point of 42.8% TCE remaining. Although, decreases of epsilon to -20.7 were observed near complete degradation, our enrichment factors were significantly more negative than those reported for anaerobic dehalogenation of TCE. This indicates typical isotope fractionation for specific enzymatic mechanisms that can help to differentiate between degradation pathways
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
QCD and QED dynamics of the EMC effect
Applying exact QCD sum rules for the baryon charge and energy-momentum we
demonstrate that if nucleons are the only degrees of freedom of nuclear wave
function, the structure function of a nucleus would be the additive sum of the
nucleon distributions at the same Bjorken x = AQ^2/2(p_Aq)< 0.5 up to very
small Fermi motion corrections if x>0.05. Thus the difference of the EMC ratio
from one reveals the presence of non-nucleonic degrees of freedom in nuclei.
Using exact QCD sum rules we show that the ratio R_A(x_p,Q^2) used in
experimental studies, where x_p = Q^2/2q_0 m_p deviates from one even if a
nucleus consists of nucleons with small momenta only. Use of the Bjorken x
leads to additional decrease of R_A(x,Q^2) as compared to the x_p plots.
Coherent contribution of equivalent photons into photon component of parton
wave function of a nucleus unambiguously follows from Lorentz transformation of
the rest frame nucleus Coulomb field. For A~200 photons carry ~0.0065 fraction
of the light momentum of nucleus almost compensates the difference between data
analysis in terms of Bjorken x and x_p. Different role of higher twist effects
for Q^2 probed at electron and muon beams is emphasized. Direct observations of
large and predominantly nucleonic short-range correlations in nuclei pose a
serious challenge for most of the models of the EMC effect for x>0.6. The data
are consistent with a scenario in which the hadronic EMC effect reflects
fluctuations of inter nucleon interaction due to fluctuations of color
distribution in the interacting nucleons. The dynamic realization of this
scenario is the model in which the 3q (3qg) configurations with x > 0.5 parton
have a weaker interaction with nearby nucleons, leading to suppression of such
configurations giving a right magnitude of the EMC effect. The directions for
the future studies and challenging questions are outlined.Comment: The sign in the relation of x_Bj and x_p is corrected and the
following discussion is adjusted accordingly. Discussion of the higher twist
effects is adde
Evaluation of Scheduling Methods for Multiple Runways
Several scheduling strategies are analyzed in order to determine the most efficient means of scheduling aircraft when multiple runways are operational and the airport is operating at different utilization rates. The study compares simulation data for two and three runway scenarios to results from queuing theory for an M/D/n queue. The direction taken, however, is not to do a steady-state, or equilibrium, analysis since this is not the case during a rush period at a typical airport. Instead, a transient analysis of the delay per aircraft is performed. It is shown that the scheduling strategy that reduces the delay depends upon the density of the arrival traffic. For light traffic, scheduling aircraft to their preferred runways is sufficient; however, as the arrival rate increases, it becomes more important to separate traffic by weight class. Significant delay reduction is realized when aircraft that belong to the heavy and small weight classes are sent to separate runways with large aircraft put into the 'best' landing slot
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