Foundations of Physics 44 (2):192-212 (2014)
AbstractUsing 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
Added to PP
Historical graph of 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.
Similar books and articles
Limited Holism and Real-Vector-Space Quantum Theory.Lucien Hardy & William K. Wootters - 2012 - Foundations of Physics 42 (3):454-473.
Three Slit Experiments and the Structure of Quantum Theory.Cozmin Ududec, Howard Barnum & Joseph Emerson - 2011 - Foundations of Physics 41 (3):396-405.
Ensemble Steering, Weak Self-Duality, and the Structure of Probabilistic Theories.Howard Barnum, Carl Philipp Gaebler & Alexander Wilce - 2013 - Foundations of Physics 43 (12):1411-1427.
A Representation of Quantum Measurement in Nonassociative Algebras.Gerd Niestegge - 2009 - Foundations of Physics 39 (2):120-136.
A Representation of Quantum Measurement in Order-Unit Spaces.Gerd Niestegge - 2008 - Foundations of Physics 38 (9):783-795.
An Approach to Quantum Mechanics Via Conditional Probabilities.Gerd Niestegge - 2008 - Foundations of Physics 38 (3):241-256.
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.
Information Invariance and Quantum Probabilities.Časlav Brukner & Anton Zeilinger - 2009 - Foundations of Physics 39 (7):677-689.
“Local Realism”, Bell’s Theorem and Quantum “Locally Realistic” Inequalities.Elena R. Loubenets - 2005 - Foundations of Physics 35 (12):2051-2072.
Particle Creation as the Quantum Condition for Probabilistic Events to Occur.Nicholas Maxwell - 1994 - Physics Letters A 187 (2 May 1994):351-355.
Isolation and Information Flow in Quantum Dynamics.Benjamin Schumacher & Michael D. Westmoreland - 2012 - Foundations of Physics 42 (7):926-931.
Can Entanglement Be Destroyed by Any Local Operation in Relativistic Quantum Field Theory?Giovanni Valente - 2010 - Philosophy of Science 77 (5):1029-1041.