Related papers: Superposition, transition probabilities and primit…
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…
Transition Probability (fidelity) for pairs of density operators can be defined as "functor" in the hierarchy of "all" quantum systems and also within any quantum system. The introduction of "amplitudes" for density operators allows for a…
Quantum superposition says that any physical system simultaneously exists in all of its possible states, the number of which is exponential in the number of entities composing the system. The strength of presence of each possible state in…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that…
We present a new interpretation of the terms superposition, entanglement, and measurement that appear in quantum mechanics. We hypothesize that the structure of the wave function for a quantum system at the sub-Planck scale has a…
The debate on the nature of quantum probabilities in relation to Quantum Non Locality has elevated Quantum Mechanics to the level of an "Operational Epistemic Theory". In such context the quantum superposition principle has an extraneous…
We develop a general framework for the construction of probabilities for the time of arrival in quantum systems. The time of arrival is identified with the time instant when a transition in the detector's degrees of freedom takes place.…
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…
In modern physics only relative quantities are considered to have physical significance. For example, position assigned to a system depends on the choice of coordinates, and only relative distances between different systems have physical…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
The questions we raise in this letter are as follows: What is the most general representation of a quantum state at a single point in time? Can we adapt the current formalisms to situations where the order of quantum operations is…
The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time and most advanced results are due to Alfsen and Shultz. Here we…
This paper provides a systematic study of the operational idea that a quantum ``state'' is only defined up to what can be distinguished by a chosen family of observables. Concretely, any von Neumann algebra of observables $\mathscr{M}$…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…