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The density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment.…
In this work we consider basic principles and problems of the standard quantum mechanical formalism. Especially we consider final measurement or detection procedure (collapse) as a quantum-classical continuous phase transition with…
We present a general methodology for addressing the infinite hierarchy problem that arises in measurement-induced dynamics of replicated quantum systems. Our approach introduces trace-preserving replica cutoffs using tomographic-like…
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 significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a…
We develop a comprehensive quantum estimation framework to quantify how precisely gravitationally induced decoherence can be inferred in optomechanical systems, using single-mode Gaussian probe states. Our approach combines a microscopic…
We present a novel perspective on gravity-induced wave function reduction using Bohmian trajectories. This study examines the quantum motion of both point particles and objects, identifying critical parameters for the transition from…
We propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced sophisticated…
Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical…
The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…
The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of…
The statistical tools needed to obtain a mass function from realistic collapse time estimates are presented. Collapse dynamics has been dealt with in paper I of this series by means of the powerful Lagrangian perturbation theory and the…
Continuous weak measurement allows localizing open quantum systems in state space, and tracing out their quantum trajectory as they evolve in time. Efficient quantum measurement schemes have previously enabled recording quantum trajectories…
Penrose has suggested that large fluctuations of the gravitational energy of quantum systems, resulting from fluctuations of its density in space, may induce a quantum collapse mechanism \cite{Penrose-1996}, but he did not propose a precise…
We present a generalization of continuous position measurements that accounts for a spatially inhomogeneous measurement strength. This describes many real measurement scenarios, in which the rate at which information is extracted about…
Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…
This paper summarizes several recent developments in the area of estimation and robust control of quantum systems and outlines several directions for future research. Quantum state tomography via linear regression estimation and adaptive…
We develop the general quantum stochastic approach to the description of quantum measurements continuous in time. The framework, that we introduce, encompasses the various particular models for continuous-time measurements condsidered…
Continuous measurement of quantum systems provides a standard route to quantum trajectories through the successive acquisition of information which further results in measurement back-action. In this work, we harness this back-action as a…
This article develops mathematical formalisms and provides numerical methods for studying the evolution of measures in nonsmooth dynamical systems using the continuity equation. The nonsmooth dynamical system is described by an evolution…