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Quantum theory from simple physical principles for single systems

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If you have a question about this talk, please contact William Matthews.

We describe simple physically and informationally meaningful principles that give rise to the quantum description of finite-dimensional systems terms of density matrices and positive operator-valued measures.

The first three principles characterize finite dimensional formally real Jordan-algebraic systems: real, complex, and quaternionic quantum theory, plus systems whose state spaces are balls, and one exceptional case. The principles are (1) a generalized spectral decomposition, (2) a high degree of symmetry, and (3) that there is no irreducible three (or more) path interference. We’ll explore the physical implications of the principles, individually and in various combinations.

Complex quantum theory then follows from “local tomography”: that the state of a composite system be determinable from the statistics (including correlations) of local observables. But one may obtain quantum theory without considering composite systems, by requiring (4) “energy observability”: the generators of reversible dynamics are observables.

Dropping (3) might allow systems enjoying many properties of quantum physics, but exhibiting higher-order interference; we’ll discuss properties of such theories, in particular whether they support good notions of entropy and a reasonable statistical mechanics, and whether they are possible candidates for new physics encompassing quantum theory as a limiting case.

Time permitting, the possibility and properties of composites of systems satisfying (1-3) (Jordan-algebraic systems) will be discussed.

This talk is part of the CQIF Seminar series.

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