12,717 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
Cortical pain responses in human infants
Despite the recent increase in our understanding of the development of pain processing, it is still not known whether premature infants are capable of processing pain at a cortical level. In this study, changes in cerebral oxygenation over the somatosensory cortex were measured in response to noxious stimulation using real-time near-infrared spectroscopy in 18 infants aged between 25 and 45 weeks postmenstrual age. The noxious stimuli were heel lances performed for routine blood sampling; no blood tests were performed solely for the purpose of the study. Noxious stimulation produced a clear cortical response, measured as an increase in total hemoglobin concentration [HbT] in the contralateral somatosensory cortex, from 25 weeks (mean Delta[HbT] = 7.74 mu mol/L; SE, 1.10). Cortical responses were significantly greater in awake compared with sleeping infants, with a mean difference of 6.63 mu mol/L [95% confidence interval (CI) limits: 2.35, 10.91 mu mol/L; mean age, 35.2 weeks]. In awake infants, the response in the contralateral somatosensory cortex increased with age ( regression coefficient, 0.698 mu mol/L/week; 95% CI limits: 0.132, 1.265 mu mol/L/week) and the latency decreased with age (regression coefficient, -0.9861 mu mol/L/week; 95% CI limits: -1.5361, -0.4361 mu mol/L/week; age range, 25-38 weeks). The response was modality specific because no response was detected after non-noxious stimulation of the heel, even when accompanied by reflex withdrawal of the foot. We conclude that noxious information is transmitted to the preterm infant cortex from 25 weeks, highlighting the potential for both higher-level pain processing and pain-induced plasticity in the human brain from a very early age
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
Traveling sealer for contoured table Patent
Sealing apparatus for joining two pieces of frangible material
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
Structure and Response in the World Trade Network
We examine how the structure of the world trade network has been shaped by
globalization and recessions over the last 40 years. We show that by treating
the world trade network as an evolving system, theory predicts the trade
network is more sensitive to evolutionary shocks and recovers more slowly from
them now than it did 40 years ago, due to structural changes in the world trade
network induced by globalization. We also show that recession-induced change to
the world trade network leads to an \emph{increased} hierarchical structure of
the global trade network for a few years after the recession.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let
Testing nonlocality over 12.4 km of underground fiber with universal time-bin qubit analyzers
We experimentally demonstrate that the nonlocal nature of time-bin entangled
photonic qubits persists when one or two qubits of the pair are converted to
polarization qubits. This is possible by implementing a novel Universal
Time-Bin Qubit Analyzer (UTBA), which, for the first time, allows analyzing
time-bin qubits in any basis. We reveal the nonlocal nature of the emitted
light by violating the Clauser-Horne-Shimony-Holt inequality with measurement
bases exploring all the dimensions of the Bloch sphere. Moreover, we conducted
experiments where one qubit is transmitted over a 12.4 km underground fiber
link and demonstrate the suitability of our scheme for use in a real-world
setting. The resulting entanglement can also be interpreted as hybrid
entanglement between different types of degrees of freedom of two physical
systems, which could prove useful in large scale, heterogeneous quantum
networks. This work opens new possibilities for testing nonlocality and for
implementing new quantum communication protocols with time-bin entanglement.Comment: 6 pages, 5 figure
EVALUATION OF THE 2006/7 AGRICULTURAL INPUT SUBSIDY PROGRAMME, MALAWI. FINAL REPORT
This report evaluates the 2006/7 Malawi Government Agricultural Input Subsidy Programme (AISP). The main objective of the evaluation is to assess the impact and implementation of the AISP in order to provide lessons for future interventions in growth and social protection. The evaluation combined qualitative and quantitative methods of data collection and analysis. Quantitative data were collected through a national survey in 2007 of 2,491 households who were previously interviewed in the 2004/05 Integrated Household Survey, a survey of retail shops selling inputs in six districts and data on stocks and sales from manufacturers, large-scale importers and dealers of fertilizers and seeds. The quantitative data was triangulated by qualitative data from focus group discussions with smallholder farmers in 12 districts, and key informant interviews with government staff, input distributors and beneficiary and non-beneficiary households. The analysis is based on descriptive statistics, econometric modelling and livelihood and rural economy modelling. An Interim Report in March 2007 provides fuller details of the implementation of the programme.Agribusiness, Agricultural and Food Policy, Community/Rural/Urban Development, Food Consumption/Nutrition/Food Safety, Food Security and Poverty, Productivity Analysis,
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
An experimental test of all theories with predictive power beyond quantum theory
According to quantum theory, the outcomes of future measurements cannot (in
general) be predicted with certainty. In some cases, even with a complete
physical description of the system to be measured and the measurement
apparatus, the outcomes of certain measurements are completely random. This
raises the question, originating in the paper by Einstein, Podolsky and Rosen,
of whether quantum mechanics is the optimal way to predict measurement
outcomes. Established arguments and experimental tests exclude a few specific
alternative models. Here, we provide a complete answer to the above question,
refuting any alternative theory with significantly more predictive power than
quantum theory. More precisely, we perform various measurements on distant
entangled photons, and, under the assumption that these measurements are chosen
freely, we give an upper bound on how well any alternative theory could predict
their outcomes. In particular, in the case where quantum mechanics predicts two
equally likely outcomes, our results are incompatible with any theory in which
the probability of a prediction is increased by more than ~0.19. Hence, we can
immediately refute any already considered or yet-to-be-proposed alternative
model with more predictive power than this.Comment: 13 pages, 4 figure
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