相关论文: Finite-Precision Quantum Mechanics

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the Past Hypothesis) to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to…

I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…

In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…

For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…

We reconsider the problem of the interpretation of the Quantum Theory (QT) in the perspective of the entire universe and of Bphr idea that the classical language is the language of our experience and QT acquires a meaning only with a…

We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…

A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this…

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of…

Entanglement is generally considered necessary for achieving the Heisenberg limit in quantum metrology. We construct analogues of Dicke and GHZ states on a single $N+1$ dimensional qudit that achieve precision equivalent to symmetrically…

A conceptual difficulty in the foundations of quantum mechanics is the quantum measurement problem (QMP), essentially concerned with the apparent non-unitarity of the measurement process and the classicality of macroscopic systems. In an…

Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined…

The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…

Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits to the precision of measurement. Conventional measurement techniques typically fail to reach these limits. Conventional bounds to the precision of measurements…

What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a…

Quantum mechanics started out as a theory to describe the smallest scales of energy in Nature. After a hundred years of development it is now routinely employed to describe, among others, quantum computers with thousands of qubits. This…

The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…

In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…

The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…

Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…

On the basis of our recent model of a one-dimensional (1D) completed scattering we argue that Leggett's principles of macroscopic realism must and can be extended onto the level of single electrons and atoms. These principles need three…