Symmetry-resolved entanglement detection using partial transpose moments

We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The k-th condition involves comparing moments of the partially transposed density operator up to order k. Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.

Influence of Air Temperature on School Teachers’ Mood and the Perception of Students’ Behavior

This study investigates how temperature, inside and outside the classroom, influence teachers’ mood and mental fatigue as well as the perceived students’ behavior. Two daily random measurements of the temperature inside various classrooms were taken for 7 months. Mood, mental fatigue, and perception of students’ behavior were evaluated for the teachers. Daily external temperature data were obtained from the State Agency of Meteorology. Results showed that indoor temperature, indoor humidity, and the difference between outdoor/indoor temperature significantly explain a worse perception of mood of the teachers and a worse perception of students’ behavior that influences perception of students’ behavior.

The relation between second-trimester placental elasticity and poor obstetric outcomes in low-risk pregnancies

ObjectivesIncreased placental stiffness is associated with various pathological conditions. Our objective was to evaluate the relation between the second-trimester placental elasticity value in low-risk pregnant women and poor obstetric outcomes.MethodsA total of 143 pregnant women were enrolled. Placental elasticity values were measured using the transabdominal point shear wave elastography method. 10 random measurements were obtained from different areas of the placenta. The mean was accepted as the mean placental elasticity value. Logistic regression analyses were performed to identify independent variables associated with obstetric outcomes.ResultsSecond-trimester placental elasticity value was significantly and positively associated with the poor obstetric outcomes (p=0.038). We could predict a poor outcome with 69.2% sensitivity and 60.7% specificity if we defined the placental elasticity cut-off as 3.19 kPa. Furthermore, in the multiple regression model, the placental elasticity value added significantly to the prediction of birth weight (p=0.043).ConclusionsOur results showed that the pregnancies with a stiffer placenta in the second trimester were associated with an increased likelihood of exhibiting poor obstetric outcomes. Also, placental elasticity was independently associated with birth weight.

Super Sub-Nyquist Single-Pixel Imaging by Means of Cake-Cutting Hadamard Basis Sort

Single-pixel imaging via compressed sensing can reconstruct high-quality images from a few linear random measurements of an object known a priori to be sparse or compressive, by using a point/bucket detector without spatial resolution. Nevertheless, random measurements still have blindness, limiting the sampling ratios and leading to a harsh trade-off between the acquisition time and the spatial resolution. Here, we present a new compressive imaging approach by using a strategy we call cake-cutting, which can optimally reorder the deterministic Hadamard basis. The proposed method is capable of recovering images of large pixel-size with dramatically reduced sampling ratios, realizing super sub-Nyquist sampling and significantly decreasing the acquisition time. Furthermore, such kind of sorting strategy can be easily combined with the structured characteristic of the Hadamard matrix to accelerate the computational process and to simultaneously reduce the memory consumption of the matrix storage. With the help of differential modulation/measurement technology, we demonstrate this method with a single-photon single-pixel camera under the ulta-weak light condition and retrieve clear images through partially obscuring scenes. Thus, this method complements the present single-pixel imaging approaches and can be applied to many fields.