Related papers: On the notion of a macroscopic quantum system
We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
It is assumed that the quantum state that may describe a macroscopic system at a given instant of time is one of the eigenstates of the reduced density matrix calculated from the wave function of the system plus its environment. This…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
Since the problem: "What is statistics?" is most fundamental in sceince, in order to solve this problem, there is every reason to believe that we have to start from the proposal of a worldview. Recently we proposed measurement theory (i.e.,…
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited,…
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Quantum theory implies, and empirical evidence confirms, that while particles $\textit{can}$ exhibit wave-like behavior in interferometric experiments, this behavior is so limited as $\textit{not}$ to allow for third- and higher-order…
Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the…
Experimental results presented in this paper supports the hypothesis on quantum-like statistical behaviour of cognitive systems (at least human beings). Our quantum-like approach gives the possibility to represent mental states by Hilbert…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating…