Quantum formalism for classical statistics

P. Quaas, K. Voß, P. Ziesche

K. Bruce Winterbon

C. Wetterich

Abstract Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being “classical” or “quantum” ceases to be a basic conceptual difference. The dynamics differs, however, between quantum and classical particles. We describe position, motion and correlations of a quantum particle in terms of observables in a classical statistical ensemble. On the other side, we also construct explicitly the quantum formalism with wave function and Hamiltonian for classical particles. For a suitable time evolution of the classical probabilities and a suitable choice of observables all features of a quantum particle in a potential can be derived from classical statistics, including interference and tunneling. Besides conceptual advances, the treatment of classical and quantum particles in a common formalism could lead to interesting cross‐fertilization between classical statistics and quantum physics.

Robert W. Spekkens

A significant part of quantum theory can be obtained by postulating a single conceptual innovation relative to classical theories, namely, that agents face a fundamental restriction on what they can know about the physical state of any system. This talk will consider a particular sort of statistical restriction wherein only classical variables with vanishing Poisson bracket can be known simultaneously. When this principle is applied to a classical statistical theory of three-level systems (trits), the resulting theory is found to be operationally equivalent to the stabilizer formalism for qutrits. Applied to a classical theory of harmonic oscillators, it yields quantum mechanics restricted to quadrature eigenstates and observables. Finally, applied to a classical statistical theory of bits, it yields a theory that is almost equivalent to (but interestingly different from) the stabilizer formalism for qubits. I will discuss the significance of these results for the project of deriving the formalism of quantum theory from physical principles.

Klavs Hansen

M Reginatto, M J W Hall

We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a general description of the measurement of a quantum system by a classical apparatus without running into inconsistencies. An example of classical and quantum particles interacting gravitationally is also given.