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We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cramér–Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of radiometer and expectation–maximization (EM) algorithms in the estimation of the force noise power. When applied to experimental data, the EM estimator is found to have the lowest error and follow the Cramér–Rao bound most closely. Our analytic results are envisioned to be valuable to optomechanical experiment design, while the EM algorithm, with its ability to estimate most of the system parameters, is envisioned to be useful for optomechanical sensing, atomic magnetometry and fundamental tests of quantum mechanics. [ABSTRACT FROM AUTHOR]

A probability density characterization of multipartite entanglement is tested on the one-dimensional quantum Ising model in a transverse field. The average and second moment of the probability distribution are numerically shown to be good indicators of the quantum phase transition. We comment on multipartite entanglement generation at a quantum phase transition. [ABSTRACT FROM AUTHOR]

How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these kind of strategies usually do not consider that medical institutes may have limited vaccine resources available. In this manuscript, we explore the susceptible-infected-recovered model with local dynamic vaccination, and considering limited vaccines. In this model, susceptibles in contact with an infected individual, are vaccinated -with probability ω- and then get infected -with probability β. However, when the fraction of immunized individuals reaches a threshold VL, the vaccination stops, after which only the infection is possible. In the steady state, besides the critical points βc and ωc that separate a non-epidemic from an epidemic phase, we find for a range of VL another transition points, β* > βc and ω* < ωc, which correspond to a novel discontinuous phase transition. This critical value separates a phase where the amount of vaccines is sufficient, from a phase where the disease is strong enough to exhaust all the vaccination units. For a disease with fixed β, the vaccination probability ω can be controlled in order to drastically reduce the number of infected individuals, using efficiently the available vaccines. Furthermore, the temporal evolution of the system close to β* or ω*, shows that after a peak of infection the system enters into a quasi-stationary state, with only a few infected cases. But if there are no more vaccines, these few infected individuals could originate a second outbreak, represented by a second peak of infection. This state of apparent calm, could be dangerous since it may lead to misleading conclusions and to an abandon of the strategies to control the disease. [ABSTRACT FROM AUTHOR]

A complete single-point statistical description of a narrow-band partially polarized optical field is developed in terms of the 2D period-averaged probability density function (PA-PDF) of the electrical field vector. This statistic can be measured using the coherent (heterodyne) detection. PA-PDF carries more information about the partially polarized light than the traditional Stokes vector. For a simple Gaussian partially polarized field the PA-PDF depends on 13 real parameters in contrast to the four parameters of the Stokes vector or coherence tensor. We show on several examples that the polarization state of the wave, as described by PA-PDF can vary significantly even while Stokes vector remains fixed. [ABSTRACT FROM AUTHOR]

In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it doubles the success probability of many quantum spatial search algorithms. For example, this allows Grover's unstructured search problem to be solved with certainty, rather than with probability 1/2 if only the walker's position is measured, so the additional measurement yields a search algorithm that is twice as fast as without it, on average. Thus the internal state of discrete-time quantum walks holds valuable information that can be utilized to improve algorithms. Furthermore, we determine conditions for which spatial search problems on regular graphs are amenable to this doubling of the success probability, and this involves diagrammatically analyzing search using degenerate perturbation theory and deriving a useful formula for how the quantum walk acts in its reduced subspace. [ABSTRACT FROM AUTHOR]

We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of self-adjoint Hamiltonians which are quantum mechanically equivalent to the non-self-adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of self-adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrödinger equations generated by the non-self-adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual self-adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-self-adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have self-adjoint Hamiltonians that correspond to the non-self-adjoint ones found in Harrison’s article. [ABSTRACT FROM AUTHOR]

We introduce a discrete-time distributed consensus process on multi-layered complex networks represented by multiplex graphs. The proposed consensus process can be characterized with a multiplex Markov chain (MC) composed of a mixture of interlayer and intralayer MCs. The interlayer MC is characterized by a parameter which represents the probability that the chain will switch between different layers of the multiplex network. Surprisingly, for large regions of the parameter space the convergence speed of the multiplex MC is determined only by the convergence speed of the interlayer MC. Moreover, as the number of layers in the network is increased, these regions increase until they encompass the whole parameter space. We also show that for some regions of the parameter space, the multiplex MC has a faster convergence speed than the MCs on top of the individual layers, thus complementing previous results on diffusion on multiplex networks. [ABSTRACT FROM AUTHOR]

The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory. This review paper tries to present the framework and recent results to a broader readership in an accessible manner. To achieve this, we follow a constructive approach. Starting from a few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory. Furthermore, we characterize consistency conditions limiting the range of possible extensions. In this framework classical and quantum theory appear as special cases, and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature. It turns out that non-classical features of single systems can equivalently result from higher-dimensional classical theories that have been restricted. Entanglement and non-locality, however, are shown to be genuine non-classical features. [ABSTRACT FROM AUTHOR]