Abstract
In this paper, we show how the framework of information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon a few elementary features of quantum phenomena, such as complementarity and global gauge invariance. When appropriately formulated within an information-geometric framework, and combined with a novel information-theoretic principle, these features lead to the abstract quantum formalism for finite-dimensional quantum systems, and the result of Wigner’s theorem. By means of a correspondence principle, several correspondence rules of quantum theory, such as the canonical commutation relationships, are also systematically derived. The derivation suggests that information geometry is directly or indirectly responsible for many of the central structural features of the quantum formalism, such as the importance of square roots of probability and the occurrence of sinusoidal functions of phases in a pure quantum state. Global gauge invariance is shown to play a crucial role in the emergence of the formalism in its complex form.
- Received 19 May 2008
- Publisher error corrected 1 December 2008
DOI:https://doi.org/10.1103/PhysRevA.78.052120
©2008 American Physical Society
Corrections
1 December 2008