One of the most important properties of orbital angular momentum (OAM) of photons is that the Hilbert space required to describe a general quantum state is infinite dimensional. In principle, this could allow for encoding arbitrarily large amounts of quantum information per photon, but in practice, this potential is limited by decoherence and errors. To determine whether photons with OAM are suitable for quantum communication, we numerically simulated their passage through a turbulent atmosphere and the resulting errors. We also proposed an encoding scheme to protect the photons from these errors, and characterized its effectiveness by the channel fidelity.

In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first-order approximation of a small deviation in the probability distribution, and study the robustness of standard weak measurement and postselected weak measurements against systematic errors. We show that, with a large weak value, the systematic error of a postselected weak measurement when the probe undergoes decoherence can be significantly lower than that of a standard weak measurement. This indicates another advantage of weak value amplification in improving the performance of parameter estimation. We illustrate the results by an exact numerical simulation of decoherence arising from a bosonic mode and compare it to the first-order analytical result we obtain.

Statistical modeling of the dependence within applied stochastic models has become an important goal in many fields of science, since Pearson's correlation does not provide a complete description of the dependence structure of the random variables, being strongly affected from extreme endpoints, and correlation zero does not imply independence, except in the case of multivariate normal distributions. The construction of bounds for the variability of the distributions of some applied stochastic models when there is only partial information on the dependence structure of the models is the main purpose of this paper. We consider stochastic models in engineering, hydrology, and biosciences, that are defined by mixtures with stochastic environmental parameters. We study stochastic monotonicity and directional convexity properties of some functionals of random variables that are used to define these models. Variability comparisons between the mixture models in terms of the dependence between the stochastic environments are obtained. Stochastic bounds and examples are derived from modeling the dependence structure by some known notions.

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