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The quantum measurement problem as was formulated by von Neumann in 1933 can be solved by going beyond the operational quantum formalism. In our "prequantum model" quantum systems are symbolic representations of classical random fields. The…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
In this work we introduce the randomness which is truly quantum mechanical in nature arising as an act of measurement. For a composite classical system we have the joint entropy to quantify the randomness present in the total system and…
Quantum mechanical entanglement is a resource for quantum computation, quantum teleportation, and quantum cryptography. The ability to quantify this resource correctly has thus become of great interest to those working in the field of…
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…
Consider a discrete-time quantum walk on the $N$-cycle governed by the following condition: at every time step of the walk, the option persists, with probability $p$, of exercising a projective measurement on the coin degree of freedom. For…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
We generalize recent work of Massar and Popescu dealing with the amount of classical data that is produced by a quantum measurement on a quantum state ensemble. In the previous work it was shown how spurious randomness generally contained…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
A variant of the von Neumann-Wigner Interpretation is proposed. It does not make use of the familiar language of wave functions and observers. Instead it pictures the state of the physical world as a vector in a Fock space and, therefore…
The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more…
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…
In this work, the definition of the density operator on quantum states in Hilbert spaces and some of its aspects relevant in thermodynamics and information-theoretical entropy calculations are given. In this framework, a physical model…
We study the measurement process by treating classical detectors entirely quantum mechanically. As a generic model we use a point-contact detector coupled to an electron in a quantum dot and tunneling into the continuum. Transition to the…
Lenz and Stollmann recently proved the existence of the integrated density of states in the sense of uniform convergence of the distributions for certain operators with aperiodic order. The goal of this paper is to establish a relation…
For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…
The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of measuring the von Neumann entropy, $S(\rho)$, and R\'enyi entropy, $S_\alpha(\rho)$ of an…
The quantum measurement problem, understanding why a unique outcome is obtained in each individual experiment, is tackled by solving models. After an introduction we review the many dynamical models proposed over the years. A flexible and…
Von Neumann in 1932 was the first to outline the possible non existence of dispersion free ensembles in quantum mechanics, and he used also such basic evidence to give a preliminary proof on incompatibility between quantum mechanics and…
It is accepted that among the ways through which a quantum phenomenon decoheres and becomes a classical one is what is termed in the literature the Zeno effect. This effect, named after the ancient Greek philosopher Zeno of Elea (born about…