A short walk in quantum probability. (English) Zbl 1470.81011
Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2118, Article ID 20170226, 13 p. (2018).
Summary: This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas.
MSC:
| 81P05 | General and philosophical questions in quantum theory |
| 60F05 | Central limit and other weak theorems |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
Keywords:
quantum planar Brownian motion; quantum central limit theorem; quantum probability; mathematical physics; quantum physicsReferences:
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