From Information Geometry to Quantum Theory

@misc{citeulike:2814543, abstract = {In this paper, we show how information geometry, a geometry of discrete probability distributions, can be used as a framework for a derivation of the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely complementarity, global gauge invariance, and the simulability of measurements. When appropriately formulated within the information geometric framework and supplemented with a few additional plausible assumptions, these features lead to the finite-dimensional quantum formalism. The notion of complementarity is expressed by the assertion that the results of a measurement coarse-grain over the objectively-realized outcomes of the measurement. Using this idea, we obtain a formalism in which states are represented by unit vectors in a real Euclidean space, and physical transformations are represented by orthogonal transformations. A global gauge invariance condition allows this formalism to be rewritten in complex form, with physical transformations represented by unitary or antiunitary transformations. Finally, the assumption that any measurement can be simulated in terms of any given measurement flanked by suitable interactions yields the Born rule. The derivation allows many key features of the quantum formalism to be directly understood from an information geometric viewpoint.}, author = {Goyal, Philip }, citeulike-article-id = {2814543}, eprint = {0805.2770}, month = {May}, posted-at = {2008-05-20 01:18:20}, priority = {2}, title = {From Information Geometry to Quantum Theory}, url = {http://arxiv.org/abs/0805.2770}, year = {2008} }

TY - ELEC ID - citeulike:2814543 L3 - citeulike-article-id:2814543 TI - From Information Geometry to Quantum Theory N2 - In this paper, we show how information geometry, a geometry of discrete probability distributions, can be used as a framework for a derivation of the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely complementarity, global gauge invariance, and the simulability of measurements. When appropriately formulated within the information geometric framework and supplemented with a few additional plausible assumptions, these features lead to the finite-dimensional quantum formalism. The notion of complementarity is expressed by the assertion that the results of a measurement coarse-grain over the objectively-realized outcomes of the measurement. Using this idea, we obtain a formalism in which states are represented by unit vectors in a real Euclidean space, and physical transformations are represented by orthogonal transformations. A global gauge invariance condition allows this formalism to be rewritten in complex form, with physical transformations represented by unitary or antiunitary transformations. Finally, the assumption that any measurement can be simulated in terms of any given measurement flanked by suitable interactions yields the Born rule. The derivation allows many key features of the quantum formalism to be directly understood from an information geometric viewpoint. AU - Goyal, Philip PY - 2008/May/19/ UR - http://arxiv.org/abs/0805.2770 ER -