Local Tomography and the Jordan Structure of Quantum Theory

Foundations of Physics 44 (2):192-212 (2014)

Abstract

Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection rules is the only non-signaling probabilistic theory in which (i) individual systems are Jordan algebras (equivalently, their cones of unnormalized states are homogeneous and self-dual), (ii) composites are locally tomographic (meaning that states are determined by the joint probabilities they assign to measurement outcomes on the component systems) and (iii) at least one system has the structure of a qubit. Using this result, we also characterize finite dimensional quantum theory among probabilistic theories having the structure of a dagger-monoidal category

Download options

PhilArchive



    Upload a copy of this work     Papers currently archived: 72,879

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2014-02-16

Downloads
32 (#361,400)

6 months
1 (#386,001)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Quantum Quandaries: A Category-Theoretic Perspective.J. C. Baez - 2006 - In Dean Rickles, Steven French & Juha T. Saatsi (eds.), The Structural Foundations of Quantum Gravity. Clarendon Press.

Add more references

Similar books and articles

Formalism and Interpretation in Quantum Theory.Alexander Wilce - 2010 - Foundations of Physics 40 (4):434-462.
Bell’s Correlations and Spin Systems.Martin Bohata & Jan Hamhalter - 2010 - Foundations of Physics 40 (8):1065-1075.