We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our criteria are simple functions of the given quantum state and detect genuine multipartite entanglement that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed.

We introduce an intuitive measure of genuine multipartite entanglement which is based on the well-known concurrence. We show how lower bounds on this measure can be derived that also meet important characteristics of an entanglement measure. These lower bounds are experimentally implementable in a feasible way enabling quantification of multipartite entanglement in a broad variety of cases.

The definition of the inequality for detecting genuine multipartite entanglement in Dicke states, Eq. (1), contains a typographical error. The sets {γ } = {{α},{β}}, which are summed over, in fact, have to satisfy |{α} ∩ {β}| = m − 1 instead of 1 such that x = {α}\{β} and y = {β}\{α} satisfy |x| = |y| = 1.This does not affect the proof of the criterion nor the conclusion of the paper. The detection behavior of the criterion, however, is slightly altered (except for the case m = 2, where the incorrect and the correct versions coincide). FIG. 1. (Color online) Illustration of the detection quality of the presented criterion compared to the fidelity witness. * marcus.huber@univie.ac.at † paul.erker@univie.ac.at FIG. 2. (Color online) Detection threshold p of the state ρ = (1 − p)|D n m D n m | + p 2 n 1 for different values of m starting with m = 1 and gradually approaching m = 33.The value of the constant N D in the criterion has to be corrected to m(n − m − 1) such that the maximal violation of the n-qubit m-Dicke state inequality is m (irrespective of n).Evidently, this correction also slightly alters the numerical examples.Six qubits: The correct plot for the detection quality of six-qubit states is shown in Fig. 1.n qubits: The general noise threshold for detection of the state ρ = (1 − p)|D n m D n m | + p 2 n 1 iswhich is shown in Fig. 2.We would like to thank Zhi-Hao Ma for pointing out the error in our paper.

Using a recently introduced framework, we derive criteria for quantum k-separability, which are easily computed. In the case k=2, our criteria are equally strong to the best methods known so far, while in all other cases there are currently no comparable criteria known. We also show how the criteria can be implemented experimentally.

Entanglement and its consequences-in particular the violation of Bell inequalities, which defies our concepts of realism and locality-have been proven to play key roles in Nature by many experiments for various quantum systems. Entanglement can also be found in systems not consisting of ordinary matter and light, i.e. in massive meson-antimeson systems. Bell inequalities have been discussed for these systems, but up to date no direct experimental test to conclusively exclude local realism was found. This mainly stems from the fact that one only has access to a restricted class of observables and that these systems are also decaying. In this Letter we put forward a Bell inequality for unstable systems which can be tested at accelerator facilities with current technology. Herewith, the long awaited proof that such systems at different energy scales can reveal the sophisticated "dynamical" nonlocal feature of Nature in a direct experiment gets feasible. Moreover, the role of entanglement and CP violation, an asymmetry between matter and antimatter, is explored, a special feature offered only by these meson-antimeson systems.

We present a general framework that reveals substructures of genuine multipartite entanglement. Via simple inequalities it is possible to discriminate different sets of multipartite qubit states. These inequalities are beneficial regarding experimental examinations as only local measurements are required. Furthermore, the number of observables scales favorably with system size. In exemplary cases we demonstrate the noise resistance and discuss implementations.

We construct a set of criteria detecting genuine multipartite entanglement in arbitrary dimensional multipartite systems. These criteria are optimally suited for detecting multipartite entanglement in n-qubit Dicke states with m excitations, as shown in exemplary cases. Furthermore, they can be employed to detect multipartite entanglement in different states related to quantum cloning, decoherence-free communication, and quantum secret sharing. In a detailed analysis, we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore, it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.

The magnitude of public concerns about agricultural innovations has often been underestimated, as past examples, such as pesticides, nanotechnology, and cloning, demonstrate. Indeed, studies have proven that the agricultural sector presents an area of tension and often attracts skepticism concerning new technologies. Digital technologies have become increasingly popular in agriculture. Yet there are almost no investigations on the public acceptance of digitalization in agriculture so far. Our online survey provides initial insights to reduce this knowledge gap. The sample (n = 2012) represents the German population in terms of gender, age (minimum 18 years), education and size of place of residence. Results showed that if the potential of digital farming technologies (DFT) regarding animal welfare and environmental protection was described, respondents reacted positively. Thus, the general attitudes of respondents toward the benefits of DFT were mostly positive. The approval to increasing adoption rates of particular DFT by providing subsidies was also high. Linear regression models showed that the dominant positive influences on respondents' attitudes toward the benefits of DFT were a generally positive attitude toward farming and a strong trust in farmers in Germany. Confronting respondents with pictures showing DFT resulted in many spontaneous negative associations and general criticism of agricultural production. The latter holds true for DFT in animal husbandry in particular. However, as agriculture as a whole is criticized by many groups in Germany, it is unlikely that benefits from digitalization will significantly increase the public acceptance of agriculture as a whole.