A simple minimax estimator for quantum states

Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting the gathered data into an estimate of the state works very well. For smaller data sets, however, it often suffers from problems of rank deficiency in the estimated state. For many systems of relevance for quantum information processing, the preparation of a very large number of copies of the same quantum state is still a technological challenge, which motivates us to look for estimation strategies that perform well even when there is not much data. In this article, we review the concept of minimax state estimation, and use minimax ideas to construct a simple estimator for quantum states. We demonstrate that, for the case of tomography of a single qubit, our estimator significantly outperforms the ML estimator for small number of copies of the state measured. Our estimator is always full-rank, and furthermore, has a natural dependence on the number of copies measured, which is missing in the ML estimator.Comment: 26 pages, 3 figures. v2 contains minor improvements to the text, and an additional appendix on symmetric measurement

Comment on "Cherenkov Radiation by Neutrinos in a Supernova Core"

Mohanty and Samal have shown that the magnetic-moment interaction with nucleons contributes significantly to the photon dispersion relation in a supernova core, and with an opposite sign relative to the usual plasma effect. Because of a numerical error they overestimated the magnetic-moment term by two orders of magnitude, but it is still of the same order as the plasma effect. It appears that the Cherenkov processes gamma+nu -> nu and nu -> nu+gamma remain forbidden, but a final verdict depends on a more detailed investigation of the dynamical magnetic susceptibility of a hot nuclear medium.Comment: 2 pages, REVTEX. Submitted as a Comment to PR

Nicotine on Children's Hands: Limited Protection of Smoking Bans and Initial Clinical Findings.

BackgroundThirdhand smoke (THS) pollutants, such as nicotine, accumulate on the hands of children who live in homes with smokers and are exposed to secondhand smoke. Our objective was to examine whether levels of hand nicotine in exposed children are associated with demographics, environmental factors, and clinical findings.MethodsParticipants were caregivers who smoke and children (mean age (SD) = 2.6 (3.7) years) who were part of an ongoing 2-group, randomized controlled trial of an emergency department-based tobacco cessation intervention (N = 104). The primary outcome measure was nicotine on the child's hand. Caregivers reported demographics and smoking patterns; children's medical records were abstracted for chief complaint, medical history, and diagnoses.ResultsAll children had detectable hand nicotine (geometric mean [GeoM] = 86.2 ng/wipe; range = 3.5-2, 190.4 ng/wipe). Children in the age group of 2 to 4 years old (GeoM = 185.6 ng/wipe) had higher levels than the children in the age groups of 0 to 1 (GeoM = 68.9 ng/wipe, P < .001), 5 to 9 (GeoM = 77.9 ng/wipe, P = .04), and 10 to 15 years old (GeoM = 74.2 ng/wipe, P = .048). Children whose caregivers smoked 6 to 14 (GeoM = 97.2 ng/wipe, P = .047) and 15 to 40 cigarettes/day (GeoM = 124.0 ng/wipe, P = .01) had higher levels than children whose caregivers smoked 1 to 5 cigarettes/day (GeoM = 59.7 ng/wipe). Children with 6 to 14 cigarettes/day (GeoM = 163.11 ng/wipe, P = .007) and 15 to 40 cigarettes/day (GeoM = 186.1, P = .003) smoked inside the home by all smokers had significantly higher levels than homes with 0 cigarettes (GeoM = 81.3 ng/wipe). Similar differences in hand nicotine levels were found for smoking frequency of all household members in any location. Children with complaints of cough/congestion (GeoM = 97.7 ng/wipe) had higher levels than those without cough/congestion (GeoM = 59.0 ng/wipe, P = .01).ConclusionsThe high hand nicotine levels in children whose caregivers do not necessarily smoke indoor demonstrate that indoor smoking bans do not safeguard against THS exposure and the associations with increased home smoking activity indicate that hand wipes may be a noninvasive way to characterize children's exposure. The findings of associated cough and congestion with higher THS levels need to be examined further

Uses of a small field value which falls from a metastable maximum over cosmological times

We consider a small, metastable maximum vacuum expectation value $b_0$ of order of a few eV, for a pseudoscalar Goldstone-like field, which is related to the scalar inflaton field $\phi$ in an idealized model of a cosmological, spontaneously-broken chiral symmetry. The b field allows for relating semi-quantitatively three distinct quantities in a cosmological context. (1) A very small, residual vacuum energy density or effective cosmological constant of ~ lambda b_0^4 ~ 2.7 x 10^{-47}GeV^4, for lambda ~ 3 x 10^{-14}, the same as an empirical inflaton self-coupling. (2) A tiny neutrino mass, less then b_0. (3) A possible small variation downward of the proton to electron mass ratio over cosmological time. The latter arises from the motion downward of the $b$ field over cosmological time, toward a nonzero limiting value as $t \to \infty$. Such behavior is consistent with an equation of motion. We argue that hypothetical b quanta, potentially inducing new long-range forces, are absent, because of negative, effective squared mass in an equation of motion for $b$-field fluctuations.Comment: version accepted for publication in Mod.Phys.Lett.

Predicting the Deforestation–Trend Under Different Carbon–Prices

Background: Global carbon stocks in forest biomass are decreasing by 1.1 Gt of carbon annually, owing to continued deforestation and forest degradation. Deforestation emissions are partly offset by forest expansion and increases in growing stock primarily in the extra-tropical north. Innovative financial mechanisms would be required to help reducing deforestation. Using a spatially explicit integrated biophysical and socio-economic land use model we estimated the impact of carbon price incentive schemes and payment modalities on deforestation. One payment modality is adding costs for carbon emission, the other is to pay incentives for keeping the forest carbon stock intact. Results, Baseline scenario calculations show that close to 200mil ha or around 5% of today’s forest area will be lost between 2006 and 2025, resulting in a release of additional 17.5 GtC. Today’s forest cover will shrink by around 500 million hectares, which is 1/8 of the current forest cover, within the next 100 years. The accumulated carbon release during the next 100 years amounts to 45 GtC, which is 15% of the total carbon stored in forests today. Incentives of 6 US$/tC for the standing biomass paid every 5 years will bring deforestation down by 50$/year. On the other hand a carbon tax of 12$/tC harvested forest biomass will also cut deforestation by half. The tax income will decrease from 6 billion US$ in 2005 to 4.3 billion US$in 2025 and 0.7 billion US$ in 2100 due to decreasing deforestation speed. Conclusions, Avoiding deforestation requires financial mechanisms that make retention of forests economically competitive with the currently often preferred option to seek profits from other land uses. Incentive payments need to be at a very high level to be effective against deforestation. Taxes on the other hand will generate budgetary revenues by the regions which are already poor. A combination of incentives and taxes could turn out to be a viable solution for this dilemma. Increasing the value of forest land and thereby make it less easily prone to deforestation would act as a strong incentive to increase productivity of agricultural and fuelwood production, which could be supported by revenues generated by the deforestation tax.Deforestation, Carbon Prices