Related papers: Another quantum version of Sanov theorem
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
Here we continue with the ideas expressed in "On the strangeness of quantum mechanics" aiming to demonstrate more concretely how this philosophical outlook might be used as a key for resolving the measurement problem. We will address in…
Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate…
Quantum mechanics has irked physicists ever since its conception more than 100 years ago. While some of the misgivings, such as it being unintuitive, are merely aesthetic, quantum mechanics has one serious shortcoming: it lacks a physical…
Although quantum coherence is a basic trait of quantum mechanics, the presence of coherences in the quantum description of a certain phenomenon does not rule out the possibility to give an alternative description of the same phenomenon in…
We propose the principle, the law of statistical balance for basic physical observables, which specifies quantum statistical theory among all other statistical theories of measurements. It seems that this principle might play in quantum…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory which removes this indeterminism, as suspected…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
Quantum key distribution, which allows two distant parties to share an unconditionally secure cryptographic key, promises to play an important role in the future of communication. For this reason such technique has attracted many…
We use spin coherent states to compare classical and quantum evolution of a simple paradigmatic, discrete-time quantum dynamical system exhibiting chaotic behavior in the classical limit. The spin coherent states are employed to define a…
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation…
Doubts are raised concerning the usual interpretation of the alleged failure, by quantum mechanics, of the distributive law of classical logic. The difficulty raised by incompatible sets of observables is overcome within an epistemic…
The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analysed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be…
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,…
Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic…