A Bayesian analysis of classical shadows

The method of classical shadows heralds unprecedented opportunities for quantum estimation with limited measurements [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020)]. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations -- such as high-fidelity ground truth states -- which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.Comment: 8 pages, 5 figure

Estimation and uncertainty quantification for the output from quantum simulators

The problem of estimating certain distributions over $\{0,1\}^d$ is considered here. The distribution represents a quantum system of $d$ qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is adopted to reconstruct the distribution from exact moments or observed empirical moments. The Robbins Monro algorithm is used to solve the intractable maximum entropy problem, by constructing an unbiased estimator of the un-normalized target with a sequential Monte Carlo sampler at each iteration. In the case of empirical moments, this coincides with a maximum likelihood estimator. A Bayesian formulation is also considered in order to quantify posterior uncertainty. Several approaches are proposed in order to tackle this challenging problem, based on recently developed methodologies. In particular, unbiased estimators of the gradient of the log posterior are constructed and used within a provably convergent Langevin-based Markov chain Monte Carlo method. The methods are illustrated on classically simulated output from quantum simulators

Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths

We characterize a periodically poled KTP crystal that produces an entangled, two-mode, squeezed state with orthogonal polarizations, nearly identical, factorizable frequency modes, and few photons in unwanted frequency modes. We focus the pump beam to create a nearly circular joint spectral probability distribution between the two modes. After disentangling the two modes, we observe Hong-Ou-Mandel interference with a raw (background corrected) visibility of 86 % (95 %) when an 8.6 nm bandwidth spectral filter is applied. We measure second order photon correlations of the entangled and disentangled squeezed states with both superconducting nanowire single-photon detectors and photon-number-resolving transition-edge sensors. Both methods agree and verify that the detected modes contain the desired photon number distributions

Efficacy of a low-dose ferric-EDTA in reducing iron deficiency anaemia among underfive children living in malaria-holoendemic district of Mvomero, Tanzania

Iron deficiency anaemia is a public health problem in Tanzania especially among children under the age of five years. In malaria holoendemic areas, control of anaemia by supplementation with iron has been reported to increase serious adverse events. The World Health Organization recommends that, programs to control anaemia in such areas should go concurrently with malaria control programmes. The objectives of the study were to: (i) to determine if a supplement providing 2.5 mg of iron as ferric EDTA and 2.5 mg of iron as ferrous lactate (low dose) is as effective in correcting anaemia as a supplement providing the standard 10 mg of iron as ferrous lactate (high dose); and ii) determine if iron supplementation increased the risk of malaria. This study was carried out in Mvomero District of east-central Tanzania. Two groups (69 and 70 subjects per treatment) of moderately anaemic children (7.0–9.1 g of Hb/dl), received one of the two micronutrient supplements differing only in iron content for a period of 60 days. Results showed that, the average haemoglobin (Hb) concentration improved from 8.30±0.60 g/dl to 11.08±1.25 g/dl. The average weight-for-age for all children increased from 16.0 to 20.6% while their weight-for-height increased from 4.0 to 13.3%. The incidence of asymptomatic and symptomatic malaria ranged from 10.0 to 10.4% at all time points with no apparent increase in malaria severity due to iron supplementation. Overall, there was a significant reduction in anaemia during the 60 day supplementation period. This study demonstrated that, micronutrient supplements containing low-dose ferric-EDTA is just as effective as the high dose iron in reducing anaemia and can be safely utilized in malaria holoendemic areas to control iron deficiency anaemia. It is recommended that, a large study should be conducted to affirm the effectiveness of the low-dose ferric-EDTA in controlling iron deficiency anaemia among underfive children

Normalized ghost imaging

We present an experimental comparison between different iterative ghost imaging algorithms. Our experimental setup utilizes a spatial light modulator for generating known random light fields to illuminate a partially-transmissive object. We adapt the weighting factor used in the traditional ghost imaging algorithm to account for changes in the efficiency of the generated light field. We show that our normalized weighting algorithm can match the performance of differential ghost imaging

Viscosity Is Not a Parameter of Postdeglutitive Pharyngeal Residue: Quantification and Analysis with Scintigraphy

The aim of this study was to explore the influence of viscosity on pharyngeal residue in normal healthy volunteers. Scintigraphy was used to measure pharyngeal residue in 11 healthy volunteers after swallowing three different substances (age = 20.2–48.3 years). The first substance was a 10-ml solution of tap water with 0.5% xanthan with a viscosity of 4500 mPa s, comparable to a yogurt drink. The second and third substances were a 0.75% xanthan and a 1.00% xanthan solution, with viscosities of 10,500 and 21,000 mPa s, comparable to low-fat yogurt and 3% fat yogurt, respectively. Tap water was used as the control substance. Mean pharyngeal residue after swallowing tap water was 2.3% (SD = 1.2) of the initial volume in the oral cavity. Pharyngeal residue after swallowing 0.5% xanthan solution was 1.8% (SD = 0.8), after swallowing 0.75% xanthan solution 2.6% (SD = 2.2), and after swallowing 1.00% xanthan solution 2.8% (SD = 1.7). No significant correlation between increase of viscosity and pharyngeal residue was found. In healthy persons viscosity does not seem to be a significant parameter for pharyngeal residue for boluses with viscosities ranging from tap water to solutions having a viscosity comparable to 3% fat yogurt

Nature of light correlations in ghost imaging

We investigate the nature of correlations in Gaussian light sources used for ghost imaging. We adopt methods from quantum information theory to distinguish genuinely quantum from classical correlations. Combining a microscopic analysis of speckle-speckle correlations with an effective coarse-grained description of the beams, we show that quantum correlations exist even in `classical'-like thermal light sources, and appear relevant for the implementation of ghost imaging in the regime of low illumination. We further demonstrate that the total correlations in the thermal source beams effectively determine the quality of the imaging, as quantified by the signal-to-noise ratio.Comment: 12 pages, 5 figures. To appear in Scientific Reports (NPG

Схеми скорочення необхідного об'єму вимірювань у методі контролю стаціонарної підйомної установки

Предлагается последовательная процедура принятия решения относительно вектора характеристик контролируемой стационарной подъемной установки, которая является некоторым обобщением процедуры Вальда и позволяет получить выигрыш в среднем объеме испытаний, аналогичный обычному «вальдовскому» выигрышу для случая двух гипотез. Предлагаемая последовательная процедура позволяет учитывать дополнительную информацию и за счет этого получить добавочный выигрыш в объеме контроля стационарной подъемной установки.Offers a consistent decision-making procedure for the vector characteristics of the controlled stationary hoist, which is a generalization of Wald's procedure and provides a gain in the average volume of tests, similar to the usual "of Wald's" winning the case of two hypotheses. The proposed sequential procedure takes into account the additional information and thereby obtain additional gains in the amount of control a stationary hoist