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To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…
A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16,…
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…
We introduce the notion of "separation of conditions" meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…
We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum and definite…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
Non Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non Gaussianity of quantum states, based on the…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
Theories involving localized collapse allow the possibility that classical information could be obtained about quantum states without using POVMS and without allowing superluminal signalling. We can model this by extending quantum theory to…
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…
Quantum measurements are described as instantaneous projections in textbooks. They can be stretched out in time using weak measurements, whereby one can observe the evolution of a quantum state as it heads towards one of the eigenstates of…
Quantum measurements are crucial to observe the properties of a quantum system, which however unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system while being subject to a…
Although quantum mechanics is a mature theory, fundamental problems discussed during its time of foundation have remained with us to this day. These problems are centered on the problematic relation between the quantum and classical worlds.…
The possibility to test quantum measurement theories is discussed in the more phenomenological framework of the quantum nondemolition theory. A simple test of the hypothesis of the state vector collapse is proposed by looking for deviations…
We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice…
Maximum likelihood estimation is applied to the determination of an unknown quantum measurement. The measuring apparatus performs measurements on many different quantum states and the positive operator-valued measures governing the…