Related papers: Quantum Measurement as Marginalization and Nested …
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
The measurement problem in quantum mechanics originates in the inability of the Schr\"odinger equation to predict definite outcomes of measurements. This is due to the lack of objectivity of the eigenstates of the measuring apparatus. Such…
Quantum measurement is a fundamental concept in the field of quantum mechanics. The action of quantum measurement, leading the superposition state of the measured quantum system into a definite output state, not only reconciles…
In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of…
The so-called quantum measurement problems are solved from a new perspective. One of the main observations is that the basic entities of our world are {\it particles}, elementary or composite. It follows that each elementary process, hence…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown,…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
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 overcome one of Bell's objections to `quantum measurement' by generalizing the definition to include systems outside the laboratory. According to this definition a {\sl generalized quantum measurement} takes place when the value of a…
In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from non-stabilizer operations within the…
One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
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.…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…
We implement Feynman's suggestion that the only missing notion needed for the puzzle of Quantum Measurement is the statistical mechanics of amplifying apparatus. We define a thermodynamic limit of quantum amplifiers which is a classically…