Related papers: Relating the Bures measure to the Cauchy two-matri…
We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures induced by…
We consider the random Hermitian matrix model of dimension $2n$, with external source, defined by the probability density function \begin{equation*} \frac{1}{Z_{2n}} \lvert \det(M) \rvert^{\alpha} e^{-2n\mathrm{Tr} (V(M) - AM)}, \quad V(x)…
It is known that there are infinitely many distinguishability metrics for mixed quantum states. This freedom, in turn, leads to metric-dependent interpretations of physically meaningful geometric quantities such as complexity and volume of…
Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two…
Embedded random matrix ensembles with $k$-body interactions are well established to be appropriate for many quantum systems. For these ensemble the two point correlation function is not yet derived though these ensembles are introduced 50…
Given some observable H of a finite-dimensional quantum system, we investigate the typical properties of random quantum state vectors that have a fixed expectation value with respect to H. Under some some conditions on the spectrum, we…
The aim of this paper is to show that fermion and boson random point processes naturally appear from representations of CAR and CCR which correspond to gauge invariant generalized free states (also called quasi-free states). We consider…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of…
The prevalence of algorithmic bias in Machine Learning (ML)-driven approaches has inspired growing research on measuring and mitigating bias in the ML domain. Accordingly, prior research studied how to measure fairness in regression which…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
Linearizing the Heisenberg equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of a real symplectic Lie algebra. The presence of disorder in the…
The density matrix of a two-level system (spin, atom) is usually determined by measuring the three non-commuting components of the Pauli vector. This density matrix can also be obtained via the measurement data of two commuting variables,…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
We study dynamics of the measurement process in quantum dot systems, where a particular state out of coherent superposition is observed. The ballistic point-contact placed near one of the dots is taken as a noninvasive detector. We…
The apparent random outcome of a quantum measurement is conjectured to be fundamentally determined by the microscopic state of the macroscopic measurement apparatus. The apparatus state thus plays the role of a hidden variable which, in…
We study the Wasserstein metric to measure distances between molecules represented by the atom index dependent adjacency "Coulomb" matrix, used in kernel ridge regression based supervised learning. Resulting quantum machine learning models…
Characterization of quantum systems from experimental data is a central problem in quantum science and technology. But which measurements should be used to gather data in the first place? While optimal measurement choices can be worked out…
The measurement process in quantum mechanics is usually described by the von Neumann projection postulate, which forms a basic constituent of the laws of quantum mechanics. Since this postulate requires the outside observer of the system,…