Related papers: Projection hypothesis in the setting for the quant…

Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…

In this paper, we attempt to establish quantum measurement theory in the Heisenberg picture. First, we review foundations of quantum measurement theory, that is usually based on the Schr\"{o}dinger picture. The concept of instrument is…

A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…

We argue that in contrast to the classical physics, the measurements in the quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and all relevant…

The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of…

We describe in a qualitative way a possible picture of the Measurement Process in Quantum Mechanics, which takes into account: 1. the finite and non zero time duration T of the interaction between the observed system and the microscopic…

A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…

The topic of measurement in relativistic quantum field theory is addressed in this article. Some of the long standing problems of this subject are highlighted, including the incompatibility of an instantaneous ``collapse of the…

The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…

The measurement process of observables in a quantum system comes out to be an unsovable problem which started in the early times of the development of the theory. In the present note we consider the measured system part of an open system…

Recently, three experiments have been proposed in order to show that the standard and Bohmian quantum mechanics can have different predictions at the individual level of particles. However, these thought experiments have encountered some…

Classical and quantum statistical mechanics are cast here in the language of projective geometry to provide a unified geometrical framework for statistical physics. After reviewing the Hilbert space formulation of classical statistical…

We study an electrostatic qubit monitored by a point-contact detector. Projecting an entire qubit-detector wave function on the detector eigenstates we determine the precision limit for the qubit measurements, allowed by quantum mechanics.…

The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…

Symmetric informationally complete measurements are both important building blocks in many quantum information protocols and the seminal example of a generalised, non-orthogonal, quantum measurement. In higher-dimensional systems, these…

Every measurement determines a single value as its outcome, and yet quantum mechanics predicts it only probabilistically. The Kochen-Specker theorem and Bell's inequality are often considered to reject a realist view but favor a skeptical…

One of the main postulates of quantum mechanics is that measurements destroy quantum coherence (wave function collapse). Recently it was discovered that in a many-body system dilute local measurements still preserve some coherence across…

We show that, contrarily to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of "observable". Nonorthogonal repeatability, however, occurs…

The projection postulate has been used to predict a slow-down of the time evolution of the state of a system under rapidly repeated measurements, and ultimately a freezing of the state. To test this so-called quantum Zeno effect an…

The problem of estimating a parameter of a quantum system through a series of measurements performed sequentially on a quantum probe is analyzed in the general setting where the underlying statistics is explicitly non-i.i.d. We present a…