Related papers: Finite-Precision Quantum Mechanics
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
We argue that a clear view on quantum mechanics is obtained by considering that the unicity of the macroscopic world is a fundamental postulate of physics, rather than an issue that must be mathematically justified or demonstrated. This…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability continual case. Quantum theory of time continuous measurements and quantum prediction…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
The list of basic axioms of quantum mechanics as it was formulated by von Neumann includes only the mathematical formalism of the Hilbert space and its statistical interpretation. We point out that such an approach is too general to be…
The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as $1/N^2$ with the number of particles involved---substantially surpassing the $1/N$-scaling characteristic to…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
In this letter, we provide evidence for a classical sector of states in the Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of states whose the minimum bound of position -momentum uncertainty (equivalent to an…
One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory.…
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…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
We develop a novel approach to Quantum Mechanics that we call Curved Quantum Mechanics. We introduce an infinite-dimensional K\"ahler manifold ${\cal M}$, that we call the state manifold, such that the cotangent space $T_z^*{\cal M}$ is a…