Related papers: Bures and Statistical Distance for Squeezed Therma…
We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than…
In this work, we propose a theory of temperature estimation of quantum systems, which is applicable in the regime of non-negligible prior temperature uncertainty and limited measurement data. In this regime the problem of establishing a…
An explicit parameterization for the state space of an $n$-level density matrix is given. The parameterization is based on the canonical coset decomposition of unitary matrices. We also compute, explicitly, the Bures metric tensor over the…
We propose a novel method to constrain the spatial extent of dust around galaxies through the measurement of dust temperature. Our method combines the dust emission of galaxies from far-infrared (FIR) image stacking analysis and the quasar…
Statistical modeling often involves identifying an optimal estimate to some underlying probability distribution known to satisfy some given constraints. I show here that choosing as estimate the centroid, or center of mass, of the set…
Continuous variable quantum states of light are used in quantum information protocols and quantum metrology and known to degrade with loss and added noise. We were able to show the distribution of bright polarization squeezed quantum states…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
We study the problem of joint estimation of real squeezing and amplitude of the radiation field, deriving the measurement that maximizes the probability density of detecting the true value of the unknown parameters. More generally, we…
The thermodynamic geometry formalism is applied to strongly interacting matter to estimate the deconfinement temperature. The curved thermodynamic metric for Quantum Chromodynamics (QCD) is evaluated on the basis of lattice data, whereas…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact…
We describe the statistical mechanics of a new method to produce very cold atoms or molecules. The method results from trapping a gas in a potential well, and sweeping through the well a semi-permeable barrier, one that allows particles to…
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…
We derive the stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model…
Temperature-accelerated sliced sampling (TASS) is a well-established enhanced sampling method that facilitates exhaustive exploration of high-dimensional collective variable (CV) space through directed sampling employing a combination of…
We extend the speed limit of a distance between two states evolving by different generators for quantum systems [K. Suzuki and K. Takahashi, Phys. Rev. Res. 2, 032016(R) (2020)] to the classical stochastic processes described by the master…
Gilbert proposed an algorithm for bounding the distance between a given point and a convex set. In this article we apply the Gilbert's algorithm to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of…
An analysis of the different approaches used within the van Hove BCS model for the high temperature superconductors has been done. How far the employment of an asymptotic expression for the density of states underestimates the thermodynamic…
We consider the problem of statistical inference for the S distribution and introduce new minimum distance estimators for the four parameters of the S distribution using Kolmogorov-Smirnov, Cramer-von Mises and related distance metrics.…