QLunch: Quantum framework from simple physical principles for single systems – University of Copenhagen

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QMath > Events > Quantum Lunch > w16 Howard Barnum

QLunch: Quantum framework from simple physical principles for single systems

Speaker: Howard Barnum, University of Copenhagen and University of New Mexico 

Title: Quantum framework from simple physical principles for single systems

Abstract:
The "general probabilistic theories" (GPT) framework models systems by a compact convex state space, and a convex set of probability-valued affine functionals on that space.  I give a mathematical characterization, in this setting, of the quantum framework for describing systems in terms of density matrices and POVMs. The principles are (1) a purely convexity-theoretic generalization of the spectral decomposition, (2) a high degree of symmetry (transitivity of the automorphism group of the theory on "spectral frames"), (3) that there is no irreducible three (or more) path interference, and (4) the generators of reversible dynamics are observables.

I'll discuss the physical and mathematical implications of various combinations of these and related principles, including open questions, especially at the intersection of representation theory and convexity.

Joint work with Markus Mueller and Cozmin Ududec.