Thomas Galley

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The postulates of quantum mechanics can be divided into two parts: the
dynamical part which defines the pure states, their dynamics and
composition rule and the probabilistic part which defines the structure
of measurements and the probability rule. In this talk I will show that
the dynamical part of quantum theory fully determines the probabilistic
part, within the operational framework.

First I will show that for single systems there are infinitely many
probabilistic structures compatible with the dynamical structure, and
that these can be put into correspondence with certain representations
of the unitary group. Following this I will outline the operational
conditions which arise when considering multiple systems, and how they
constrain the possible probabilistic structures. I will then outline how
the condition of associativity (of systems) singles out the measurement
postulates of quantum mechanics amongst all possible alternatives.

In a final part I will discuss how this result relates to existing work,
such as Gleason’s theorem and Zurek’s derivation of the Born rule from
envariance.

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Perimeter Institute for Theoretical Physics
Seminar room 0.02, THP new building
Contact: Mateus Araújo