# An Information-theoretic Approach to Space Dimensionality and Quantum Theory

### APA

Müller, M. (2012). An Information-theoretic Approach to Space Dimensionality and Quantum Theory. Perimeter Institute. https://pirsa.org/12050020

### MLA

Müller, Markus. An Information-theoretic Approach to Space Dimensionality and Quantum Theory. Perimeter Institute, May. 01, 2012, https://pirsa.org/12050020

### BibTex

@misc{ pirsa_PIRSA:12050020, doi = {10.48660/12050020}, url = {https://pirsa.org/12050020}, author = {M{\"u}ller, Markus}, keywords = {Quantum Foundations}, language = {en}, title = {An Information-theoretic Approach to Space Dimensionality and Quantum Theory}, publisher = {Perimeter Institute}, year = {2012}, month = {may}, note = {PIRSA:12050020 see, \url{https://pirsa.org}} }

Institute for Quantum Optics and Quantum Information (IQOQI) - Vienna

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Abstract

It is sometimes pointed out as a curiosity that the state space of quantum theory and actual physical space seem related in a surprising way: not only is space three-dimensional and Euclidean, but so is the Bloch ball which describes quantum two-level systems. In the talk, I report on joint work with Lluis Masanes, where we show how this observation can be turned into a mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (dropping quantum theory and complex amplitudes altogether). Furthermore, suppose there are systems that in some sense behave as “binary units of direction information”, interacting via some continuous reversible time evolution. We prove that this uniquely determines d=3 and quantum theory, and that it allows observers to infer local spatial geometry from probability measurements.