Analysis and optimization of quantum adaptive measurement protocols with the framework of preparation games.

A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. Many experimental tasks in quantum information, such as entanglement quantification or magic state detection, can be cast as preparation games. In this paper, we introduce general methods to design n-round preparation games, with tight bounds on the performance achievable by players with arbitrarily constrained preparation devices. We illustrate our results by devising new adaptive measurement protocols for entanglement detection and quantification. Surprisingly, we find that the standard procedure in entanglement detection, namely, estimating n times the average value of a given entanglement witness, is in general suboptimal for detecting the entanglement of a specific quantum state. On the contrary, there exist n-round experimental scenarios where detecting the entanglement of a known state optimally requires adaptive measurement schemes.

Erratum: Entanglement Detection beyond Measuring Fidelities [Phys. Rev. Lett. 124, 200502 (2020)].

This corrects the article DOI: 10.1103/PhysRevLett.124.200502.

Entanglement Detection beyond Measuring Fidelities.

One of the most widespread methods to determine if a quantum state is entangled, or to quantify its entanglement dimensionality, is by measuring its fidelity with respect to a pure state. In this Letter, we find a large class of states whose entanglement cannot be detected in this manner; we call them unfaithful. We find that unfaithful states are ubiquitous in information theory. For small dimensions, we check numerically that most bipartite states are both entangled and unfaithful. Similarly, numerical searches in low dimensions show that most pure entangled states remain entangled but become unfaithful when a certain amount of white noise is added. We also find that faithfulness can be self-activated, i.e., there exist instances of unfaithful states whose tensor powers are faithful. To explore how the fidelity approach limits the quantification of entanglement dimensionality, we generalize the notion of an unfaithful state to that of a D unfaithful state, one that cannot be certified as D-dimensionally entangled by measuring its fidelity with respect to a pure state. For describing such states, we additionally introduce a hierarchy of semidefinite programming relaxations that fully characterizes the set of states of Schmidt rank at most D.

General stabilizing effects of plant diversity on grassland productivity through population asynchrony and overyielding.

Insurance effects of biodiversity can stabilize the functioning of multispecies ecosystems against environmental variability when differential species' responses lead to asynchronous population dynamics. When responses are not perfectly positively correlated, declines in some populations are compensated by increases in others, smoothing variability in ecosystem productivity. This variance reduction effect of biodiversity is analogous to the risk-spreading benefits of diverse investment portfolios in financial markets. We use data from the BIODEPTH network of grassland biodiversity experiments to perform a general test for stabilizing effects of plant diversity on the temporal variability of individual species, functional groups, and aggregate communities. We tested three potential mechanisms: reduction of temporal variability through population asynchrony; enhancement of long-term average performance through positive selection effects; and increases in the temporal mean due to overyielding. Our results support a stabilizing effect of diversity on the temporal variability of grassland aboveground annual net primary production through two mechanisms. Two-species communities with greater population asynchrony were more stable in their average production over time due to compensatory fluctuations. Overyielding also stabilized productivity by increasing levels of average biomass production relative to temporal variability. However, there was no evidence for a performance-enhancing effect on the temporal mean through positive selection effects. In combination with previous work, our results suggest that stabilizing effects of diversity on community productivity through population asynchrony and overyielding appear to be general in grassland ecosystems.

Molecular hydrogen (H2) emissions from gasoline and diesel vehicles.

This study assesses individual-vehicle molecular hydrogen (H2) emissions in exhaust gas from current gasoline and diesel vehicles measured on a chassis dynamometer. Absolute H2 emissions were found to be highest for motorcycles and scooters (141+/-38.6 mg km(-1)), approximately 5 times higher than for gasoline-powered automobiles (26.5+/-12.1 mg km(-1)). All diesel-powered vehicles emitted marginal amounts of H2 ( approximately 0.1 mg km(-1)). For automobiles, the highest emission factors were observed for sub-cycles subject to a cold-start (mean of 53.1+/-17.0 mg km(-1)). High speeds also caused elevated H2 emission factors for sub-cycles reaching at least 150 km h(-1) (mean of 40.4+/-7.1 mg km(-1)). We show that H2/CO ratios (mol mol(-1)) from gasoline-powered vehicles are variable (sub-cycle means of 0.44-5.69) and are typically higher (mean for automobiles 1.02, for 2-wheelers 0.59) than previous atmospheric ratios characteristic of traffic-influenced measurements. The lowest mean individual sub-cycle ratios, which correspond to high absolute emissions of both H2 and CO, were observed during cold starts (for automobiles 0.48, for 2-wheelers 0.44) and at high vehicle speeds (for automobiles 0.73, for 2-wheelers 0.45). This finding illustrates the importance of these conditions to observed H2/CO ratios in ambient air. Overall, 2-wheelers displayed lower H2/CO ratios (0.48-0.69) than those from gasoline-powered automobiles (0.75-3.18). This observation, along with the lower H2/CO ratios observed through studies without catalytic converters, suggests that less developed (e.g. 2-wheelers) and older vehicle technologies are largely responsible for the atmospheric H2/CO ratios reported in past literature.