Higher order interference versus quantum theory

Higher order interference versus quantum theory

Seminar author:Howard Barnum

Event date and time:07/07/2016 02:30:pm

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We (Ududec, Barnum, and Emerson) adapt Rafael Sorkin’s hierarchy of
orders of interference in physical theories to the framework of
“general probabilistic theories”, defining a notion of k-path
interference experiment and of k-th order coherence in such theories
and showing that k-th order interference in such an experiment is
equivalent to k-th order coherence between faces of the state spaces
associated with paths in the experiment. We also show that
Jordan-algebraic theories have at most second-order interference (the
first nontrivial level, and the one exhibited by quantum theory).
Barnum, Mueller and Ududec used the absence of 3rd order interference
(the first non-quantum order) as one of four postulates characterizing
the finite-dimensional complex quantum state and effect spaces: (1)
abstract spectrality (2) strong symmetry (3) no higher-order
interference and (4) energy observability. I will explain this result
and discuss whether or not all four are needed for a reasonable
thermodynamics. With a slight strengthening of (1), to unique
spectrality, and a significant weakening of (2), to the conjunction of
(a) projectivity (an abstraction of certain aspects of the quantum
projection postulate (L¸ders’ version)) and (b) symmetry of transition
probabilities under exchange of states with the unique finegrained
effects they make certain, we have the property, important in quantum
thermodynamics, that the outcome probabilities for any fine-grained
measurement are majorized by the spectrum of a state, and hence that
measurement-probability-based generalizations of classical
entropy-like functions are given by the classical function applied to
the spectrum.

This is joint work with Cozmin Ududec and Joe Emerson (interference
and coherence), Markus Mueller and Cozmin Ududec (characterization of
quantum formalism) and with Jonathan Barrett, Marius Krumm, and Markus
Mueller (thermodynamics).