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In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical…
We consider a Boolean model $Z$ driven by a Poisson particle process $\eta$ on a metric space $\mathbb{Y}$. We study the random variable $\rho(Z)$, where $\rho$ is a (deterministic) measure on $\mathbb{Y}$. Due to the interaction of…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange…
Interpretations of quantum measurement theory have been plagued by two questions, one concerning the role of observer consciousness and the other the entanglement phenomenon arising from the superposition of quantum states. We emphasize…
The impossibility of theories with hidden variables as an alternative and replacement for quantum mechanics was discussed by J. von Neumann in 1932. His proof was criticized as being logically circular, by Grete Hermann soon after, and as…
In this paper we investigate the von Neumann entropy in the ground state of one-dimensional anyonic systems with the repulsive interaction. Based on the Bethe-ansatz method, the entanglement properties for the arbitrary statistical…
The well known Poisson Summation Formula is analysed from the perspective of the coherent state systems associated with the Heisenberg--Weyl group. In particular, it is shown that the Poisson summation formula may be viewed abstractly as a…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
Evolution of charged quantum fields under the action of constant nonuniform electric fields is studied. To this end we construct a special generating functional for density operators of the quantum fields with different initial conditions.…
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy…
This paper presents arguments purporting to show that von Neumann's description of the measurement process in quantum mechanics has a modern day version in the decoherence approach. We claim that this approach and the de Broglie-Bohm theory…
Entropy changes due to delocalization and decoherence effects should modify the predictions for the cosmological neutrino background (C$\nu$B) temperature when one treats neutrino flavors in the framework of composite quantum systems.…
Imposing restrictions on the Feynman paths of the monitored system has in the past been proposed as a universal model-free approach to continuous quantum measurements. Here we revisit this proposition, and demonstrate that a Gaussian…
In its original formulation, Heisenberg's uncertainty principle dealt with the relationship between the error of a quantum measurement and the thereby induced disturbance on the measured object. Meanwhile, Heisenberg's heuristic arguments…
Conventional wisdom holds that the von Neumann entropy corresponds to thermodynamic entropy, but Hemmo and Shenker (2006) have recently argued against this view by attacking von Neumann (1955) and his argument. I argue that Hemmo and…
Measurement quantum mechanics, the theory of a quantum system which undergoes a measurement process, is introduced by a loop of mathematical equivalencies connecting previously proposed approaches. The unique phenomenological parameter of…
A general Werner-type state is studied from two viewpoints: (i) an application of dynamical interaction of the objective system with its environment, represented by a unital positive operator-valued measure (POVM), which ensures increase of…
The Shannon entropy of a collection of random variables is subject to a number of constraints, the best-known examples being monotonicity and strong subadditivity. It remains an open question to decide which of these "laws of information…
Von Neumann obtained the formula for the entropy of a quantum state by assuming the validity of the second law of thermodynamics in a thought experiment involving semipermeable membranes and an ideal gas of quantum-labeled particles.…