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The concept of quantum phase space offers a view on quantum mechanics, which is different from the standard Hilbert space approach, but which more closely resembles the classical phase space. Due to the properties of quantum mechanics there…
We introduce a new density for the representation of quantum states on phase space. It is constructed as a weighted difference of two smooth probability densities using the Husimi function and first-order Hermite spectrograms. In contrast…
We examine the moment-reconstruction performance of both the homodyne and heterodyne (double-homodyne) measurement schemes for arbitrary quantum states and introduce moment estimators that optimize the respective schemes for any given data.…
We study the problem of estimating a function of many parameters acquired by sensors that are distributed in space, e.g., the spatial gradient of a field. We restrict ourselves to a setting where the distributed sensors are probed with…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
The Husimi distribution is proposed for a phase space analysis of quantum phase transitions in the two-dimensional $U(3)$ vibron model for $N$-size molecules. We show that the inverse participation ratio and Wehrl's entropy of the Husimi…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
The full characterization of quantum states of light is a central task in quantum optics and information science. Double homodyne detection provides a powerful method for the direct measurement of the Husimi Q quasi-probability…
In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…
This paper contributes to the emerging viewpoint that governing equations for dynamic state estimation, conditioned on the history of noisy measurements, can be viewed as gradient flow on the manifold of joint probability density functions…
We illustrate the use of the statistical method of moments for determining the position and momentum distributions of a quantum object from the statistics of a single measurement. The method is used for three different, though related,…
Local parametric statistics of zeros of Husimi representations of quantum eigenstates are introduced. It is conjectured that for a classically fully chaotic systems one should use the model of parametric statistics of complex roots of…
In this study, we compare the Wigner function $W$, its modulus, and the Husimi distribution $H$ in a one-dimensional quantum system exhibiting a transition from a single-well to a double-well configuration, using the quasi-exactly solvable…
In this essay, we discuss the notion of optimal transport on geodesic measure spaces and the associated (2-)Wasserstein distance. We then examine displacement convexity of the entropy functional on the space of probability measures. In…
The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian manifolds and generalizes the notion of hyperplanes. As several…
We formulate a model of a quantum particle continuously monitored by detectors measuring simultaneously its position and momentum. We implement the postulate of wavefunction collapse by assuming that upon detection the particle is found in…
We show that there exist informationally incomplete phase space observables such that the Cartesian margins are informationally equivalent with position and momentum. This shows that it is possible to reconstruct the position and momentum…
We undertake a thorough investigation into the phenomenology of quantum eigenstates, in the three-particle FPUT model. Employing different Husimi functions, our study focuses on both the $\alpha$-type, which is canonically equivalent to the…
For the filtering of peaks in periodic signals, we specify polynomial filters that are optimally localized in space. The space localization of functions having an expansion in terms of orthogonal polynomials is thereby measured by a…