Directional Distributions

Mardia, Kanti V.; Ley, Christophe

doi:10.1002/9781118445112.stat00962.pub2

Cited by 6 publications

(10 citation statements)

References 70 publications

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“…For the sake of simplicity, let us assume that the random variable φ µ is independent from d µ and ρ µ . Regarding its probability density function, we propose to adopt a convenient statistical model for angular random variables, namely the Wrapped-Gaussian Distribution (WGD), with average value φ and variance σ 2 φ [40]. The definition and main properties of WGD's, which basically correspond to normal probability distributions 'wrapped' around the unit circle, are recalled in Appendix D. Using these properties, the ensemble-averaged Mueller matrix of the sample is:…”

Section: A Stochastic Depolarization Model Of An Ensemble Of Random L...mentioning

confidence: 99%

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus

Ortega-Quijano¹,

Fade²,

Roche³

et al. 2016

J. Opt. Soc. Am. A

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Polarimetric sensing by orthogonality breaking has been recently proposed as an alternative technique for performing direct and fast polarimetric measurements using a specific dual-frequency dual-polarization (DFDP) source. Based on the instantaneous Stokes-Mueller formalism to describe the high-frequency evolution of the DFDP beam intensity, we thoroughly analyze the interaction of such a beam with birefringent, dichroic and depolarizing samples. This allows us to confirm that orthogonality breaking is produced by the sample diattenuation, whereas this technique is immune to both birefringence and diagonal depolarization. We further analyze the robustness of this technique when polarimetric sensing is performed through a birefringent waveguide, and the optimal DFDP source configuration for fiber-based endoscopic measurements is subsequently identified. Finally, we consider a stochastic depolarization model based on an ensemble of random linear diattenuators, which makes it possible to understand the progressive vanishing of the detected orthogonality breaking signal as the spatial heterogeneity of the sample increases, thus confirming the insensitivity of this method to diagonal depolarization. The fact that the orthogonality breaking signal is exclusively due to the sample dichroism is an advantageous feature for the precise decoupled characterization of such an anisotropic parameter in samples showing several simultaneous effects.

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Section: A Stochastic Depolarization Model Of An Ensemble Of Random L...mentioning

confidence: 99%

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus

Ortega-Quijano¹,

Fade²,

Roche³

et al. 2016

J. Opt. Soc. Am. A

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“…The alternative way is to take an average. For that matter, we define the first trigonometric moment about the mean direction [40] as…”

Section: B Circular Statisticsmentioning

confidence: 99%

Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates

Cruz

Catarina

Gautier

et al. 2020

Quantum Sci. Technol.

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We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

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“…Because the range of possible values is finite, the uniform distribution p max (φ) = 1/(2π) with S(p max ) = ln(2π) is an admissible reference distribution with maximum entropy when no additional information is given. Another interesting reference distribution is the von Mises distribution [53] p max (φ) = e κ cos(φ−µ) 2πI 0 (κ) ,…”

Section: Example Of Angle and Angular Momentummentioning

confidence: 99%

Relative entropic uncertainty relation

Floerchinger,

Haas,

Hoeber

2020

Preprint

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Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This new type of entropic uncertainty relation can be applied directly to observables with either discrete or continuous spectra. We find that a sum of relative entropies is bounded from above in a non-trivial way, which we illustrate with some examples.

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Directional Distributions

Cited by 6 publications

References 70 publications

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus

Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates

Relative entropic uncertainty relation

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