Scalable Bell Inequalities for Qubit Graph States and Robust Self-Testing.

Bell inequalities constitute a key tool in quantum information theory: they not only allow one to reveal nonlocality in composite quantum systems, but, more importantly, they can be used to certify relevant properties thereof. We provide a general construction of Bell inequalities that are maximally violated by the multiqubit graph states and can be used for their robust self-testing. Apart from their theoretical relevance, our inequalities offer two main advantages from an experimental viewpoint: (i) they present a significant reduction of the experimental effort needed to violate them, as the number of correlations they contain scales only linearly with the number of observers; (ii) numerical results indicate that the self-testing statements for graph states derived from our inequalities tolerate noise levels that are met by present experimental data. We also discuss possible generalizations of our approach to entangled states whose stabilizers are not tensor products of Pauli matrices. Our work introduces a promising approach for the certification of complex many-body quantum states.

Device-Independent Witnesses of Entanglement Depth from Two-Body Correlators.

We consider the characterization of entanglement depth in a quantum many-body system from the device-independent perspective; that is, we aim at certifying how many particles are genuinely entangled without relying on assumptions on the system itself nor on the measurements performed. We obtain device-independent witnesses of entanglement depth (DIWEDs) using the Bell inequalities introduced in [J. Tura et al., Science 344, 1256 (2014)SCIEAS0036-807510.1126/science.1247715] and compute their k-producibility bounds. To this end, we exploit two complementary methods: first, a variational one, yielding a possibly optimal k-producible state; second, a certificate of optimality via a semidefinite program, based on a relaxation of the quantum marginal problem. Numerical results suggest a clear pattern on k-producible bounds for large system sizes, which we then tackle analytically in the thermodynamic limit. Contrary to existing DIWEDs, the ones we present here can be effectively measured by accessing only collective measurements and second moments thereof. These technical requirements are met in current experiments, which have already been performed in the context of detecting Bell correlations in quantum many-body systems of 5×10^{2}-5×10^{5} atoms.

Effects of bovine somatotropin on milk yield and composition, dry matter intake, and some physiological functions of Holstein cows during heat stress.

Thirteen Holstein cows (46 to 106 d postpartum) were assigned to a partially balanced incomplete block experiment to evaluate effects of bovine somatotropin (20.6 mg monomer/d) and environment (shade and no shade) on milk yield and composition, feed intake, rectal temperature, respiration rate, and concentrations of hormones in plasma. Two treatment periods were 29 d each, preceded by 10-d preliminary periods. Water and cotton-seed hull-based diet were available ad libitum. Mathematical model for statistical analyses included cow, period, treatment, environment, day, and estimable interactions. Black globe temperature and respiration rate and rectal temperature of cows were higher in no shade. Milk and 3.5% FCM yields and feed intake of cows in no shade were approximately 9.5 and 16% less than for cows in shade. Much of the effect of heat stress was associated with reduced DM intake. The 3.5% FCM, but not milk yield, was increased by injections of bovine somatotropin. Dry matter intake was unaffected, but milk, 3.5% FCM, and component yields were increased by bovine somatotropin when adjusted for DM intake. Response of cows to bovine somatotropin was not different in the two environments, except cows injected with bovine somatotropin had slightly higher body temperature and respiration rate. Increased production responses of heat-stressed cows due to bovine somatotropin were less than in cows injected under more temperate conditions.

Environmental heat effects on growth, plasma T3, and postheat compensatory effects on Holstein calves.

Five Holstein heifers, 5 months of age, were housed in the Missouri Climatic Laboratory and subjected to an experiment to measure the effects of heat stress on rates of growth, plasma triiodothyronine (T3) levels, and ability to compensate in rate of gain and thyroid function following the stress period. The experiment consisted of 3 weeks at thermoneutral (TN1), followed by 5 weeks of individually controlled heat stress conditions (32.5 to 34 degrees C) dependent on heat tolerance of individual animals. This was followed by a 4-week thermoneutral, postheat compensatory period (TN2). Average daily gains were significantly depressed during the heat stress period (HS). Following heat stress the average body weights attained the projected or expected levels within a 21- to 28-day period following return of animals to thermoneutral conditions. Ratios of feed intake/body weight (w0.75) were reduced during heat stress treatment indicating the thermal inhibition. Ratios or amount of feed intake per unit of gain were greater during HS treatment indicating less weight gain per unit of daily feed intake. Plasma T3 was reduced during heat treatment similarly to daily weight gain. Following the postheat treatment period (TN2) plasma T3 increased markedly as did daily weight gains to demonstrate strong compensatory responses in both measures. In summary, these results demonstrated parallel and positive changes of plasma T3 with daily weight gain during thermoneutral, heat, and postheat compensatory periods, and an inverse relationship of rectal temperature to weight gain and plasma T3.