Related papers: Special functions in quantum phase estimation
When two successive squeezing operations with the same phase are applied to a field mode, reliably estimating the amplitude of each is impossible because the output state depends solely on their sum. In this case, the quantum statistical…
This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…
We consider the single particle spectral function for a two-dimensional clean superconductor in a regime of strong critical thermal phase fluctuations. In the limit where the maximum of the superconducting gap is much smaller than the Fermi…
Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the…
We systematically discuss candidate wave functions for the ground state of the bilayer \nu = 1 as the distance between the layers is varied. Those that describe increased intralayer correlations at finite distance show a departure from the…
Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and…
Squeezed light enables quantum-enhanced phase estimation, with crucial applications in both fundamental physics and emerging technologies. To fully exploit the advantage provided by this approach, estimation protocols must remain optimal…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable…
Supersymmetric or Darboux transformations are used to construct local phase equivalent deep and shallow potentials for $\ell \neq 0$ partial waves. We associate the value of the orbital angular momentum with the asymptotic form of the…
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function that gives the right marginal probability functions if integrated over position or momentum. Here we depart from the definition of the…
Optical phase estimation is a vital measurement primitive that is used to perform accurate measurements of various physical quantities like length, velocity and displacements. The precision of such measurements can be largely enhanced by…
This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…
We extend the technique of using the Trapezoidal Rule for efficient evaluation of the Special Functions of Mathematical Physics given by integral representations. This technique was recently used for Bessel functions, and here we treat…