Entanglement estimation in non-optimal qubit states

In the last years, a relationship has been established between the quantum Fisher information (QFI) and quantum entanglement. In the case of two-qubit systems, all pure entangled states can be made useful for sub-shot-noise interferometry while their QFI meets a necessary and sufficient condition [1]. In M-qubit systems, the QFI provides just a sufficient condition in the task of detecting the degree of entanglement of a generic state [2]. In our work, we show analytically that, for a large class of one-parameter non-optimal two-qubit states, the maximally entangled states are associated with stationary points of the QFI, as a function of such parameter. We show, via numerical simulations, that this scenario is maintained for the generalisation of this class of states to a generic M-qubit system. Furthermore, we suggest a scheme for an interferometer able to detect the entanglement in a large class of two-spin states.Comment: 7 pages, 7 figure

Quantum topological data analysis via the estimation of the density of states

We develop a quantum topological data analysis (QTDA) protocol based on the estimation of the density of states (DOS) of the combinatorial Laplacian. Computing topological features of graphs and simplicial complexes is crucial for analyzing datasets and building explainable AI solutions. This task becomes computationally hard for simplicial complexes with over sixty vertices and high-degree topological features due to a combinatorial scaling. We propose to approach the task by embedding underlying hypergraphs as effective quantum Hamiltonians and evaluating their density of states from the time evolution. Specifically, we compose propagators as quantum circuits using the Cartan decomposition of effective Hamiltonians and sample overlaps of time-evolved states using multi-fidelity protocols. Next, we develop various post-processing routines and implement a Fourier-like transform to recover the rank (and kernel) of Hamiltonians. This enables us to estimate the Betti numbers, revealing the topological features of simplicial complexes. We test our protocol on noiseless and noisy quantum simulators and run examples on IBM quantum processors. We observe the resilience of the proposed QTDA approach to real-hardware noise even in the absence of error mitigation, showing the promise to near-term device implementations and highlighting the utility of global DOS-based estimators.Comment: 15 pages, 8 figure

Entanglement distance for an arbitrary state of M qubits

We propose a measure of entanglement that can be computed for any pure state of an $M$-qubit system. The entanglement measure has the form of a distance that we derive from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and defined as trace of a suitable metric that we derive, the entanglement metric $\tilde{g}$. Furthermore, the analysis of the eigenvalues of $\tilde{g}$ gives information about the robustness of entanglement.Comment: 6 pages, 5 figure

Colour variation of the Maltese wall lizards (Podarcis filfolensis) at population and individual levels in the Linosa island

AbstractThe research on animal colouration has always been of great interest for biologists but since the last decades it has grown exponentially thanks to multidisciplinary approaches. Animals have found several ways to deal with the camouflage/communication trade-off in colouration, leading to the evolution of alternative patterns of variation of colourations at different levels including signal partitioning and spatial resolution of colouration. In this paper we analyse the variability of dorsal and ventral colouration in males and females of Maltese wall lizards in three populations on Linosa. We collected high-resolution digital images of dorsal, ventral and throat colouration from 61 lizards (32 males and 29 females). We showed that the colouration differs among sexes and body regions within the same individual. Colourations are also variable among individuals within population, as well as among different populations across the Island. Finally, we detected a lizard's colouration shifts with increasing body size. Those result supports the hypothesis that colouration in this species evolved under the competing pressures of natural and sexual selection to promote signals that are visible to conspecifics while being less perceptible to avian predators. Graphic abstrac

Graph theory approach to exceptional points in wave scattering

In this paper, we use graph theory to solve wave scattering problems in the discrete dipole approximation. As a key result of this work, in the presence of active scatterers, we show how one can find arbitrary large-order zero eigenvalue exceptional points (EPs) in parameter space by solving a set of non-linear equations. We interpret these equations in a graph theory picture as vanishing sums of scattering events. We also show how the total field of the system responds to parameter perturbations at the EP. Finally, we investigate the sensitivity of the power output to imaginary perturbation in the design frequency. This perturbation can be employed to trade sensitivity for a different dissipation balance of the system.Comment: 15 pages, 11 figure

A tribute to Hubert Saint Girons: niche separation between Vipera aspis and V. berus on the basis of distribution models

Interspecific competition in contact areas is a major topic in ecological studies. A number of studies were carried out on European vipers, focusing on contact areas between two or three species characterized as appropriate by ecological needs more or less similar. The aim of this study is to extend the analysis of this topic to the case of Vipera aspis and V. berus in an alpine area of northern Italy, by comparing suitability models to verify which ecological factors affect their occurrence and to assess a possible niche separation. Potential distribution was modelled using the maximum entropy method, using six non-correlated ecogeographical variables as predictors. The models fitted well for both species (mean AUC = 0.926; 87.4% of testing data correctly classified). The most informative variables were: habitat, altitude and solar radiation for the asp viper; altitude and habitat for the adder. Deciduous woods, meadows and urban areas had a positive effect on V. aspis distribution as wetlands, meadows and rocks vegetation did on V. berus. However, the variable best separating the species was the elevation, the adder occurring more frequently at higher altitude than the asp viper. Our data showed that the two vipers were mutually exclusive, as already observed by Saint Girons in 1975. Vipera aspis is more thermophilic and lives at low altitude, while Vipera berus lives under cool and humid areas typical of alpine pastures. A similar pattern were found in the contact areas between European vipers belonging to the V. aspis and Pelias group respectively

Morphometric differences between extant and extinct Italian populations of the adder, Vipera berus (Linnaeus, 1758)

Vipera berus (Linnaeus, 1758) is the terrestrial snake showing the widest distribution in the world, occuring from Great Britain, France and Northern Italy to the Sakhalin Island and North Korea (Nilson, 1980; Saint Girons, 1980; Nilson et al., 1994; Nilson & Andrén, 1997a). However, adders do not occur uniformly over their distribution area, but are scattered in several isolated populations (Nilson & Andrén, 1997a). Frequently, ecological traits of borderline and isolated populations differ from those living in the core area of the distribution range of the species, and might be subjected to higher risks of stochastic extinction and higher differentiation rates (Mayr, 1970). For example, meadow vipers (Vipera ursinii) show a highly fragmented distribution, many of isolated groups being different subspecies (Nilson & Andrén, 1997b, 2001)