660 citations · 4.2k across the 53 of their papers we have counts for
53 papers
Self-duality and Jordan structure of quantum theory follow from homogeneity and pure transitivity
Howard Barnum, Cozmin Ududec, John van de Wetering
Quantum theory satisfies the mathematically powerful property of self-duality, meaning that its state and effect spaces are made isomorphic by an inner product. This is why both qu…
Strongly symmetric spectral convex bodies are Jordan algebra state spaces
Howard Barnum, Joachim Hilgert
We show that the strongly symmetric spectral convex compact sets are precisely the normalized state spaces of finite-dimensional simple Euclidean Jordan algebras and the simplices.…
Ruling out higher-order interference from purity principles
Howard Barnum, Ciarán M. Lee, Carlo Maria Scandolo +1
As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns for…
Oracles and query lower bounds in generalised probabilistic theories
Howard Barnum, Ciarán M. Lee, John H. Selby
We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computat…
Thermodynamics and the structure of quantum theory
Marius Krumm, Howard Barnum, Jonathan Barrett +1
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what mod…
Composites and Categories of Euclidean Jordan Algebras
Howard Barnum, Matthew A. Graydon, Alexander Wilce
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the…