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LFCS Seminar: Thomas Streicher

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Computability in Quantum Theory

  • LFCS Seminar
When May 24, 2012
from 02:00 PM to 03:00 PM
Where IF 2.33
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The usual foundation of Quantum Theory a la von Neumann is based on traditional functional analysis, Hilbert spaces and self adjoint operators. Weihrauch's TTE (Type Two Effectivity) provides a convenient setting for studying computability in functional analysis. In our talk we study notions of computability for a more algebraic foundation of Quantum Theory. Quantum ``propositions'' are identified with closed subspaces of Hilbert space which organize into the so-called Hilbert lattice. States are [0,1]-valued measures on the Hilbert lattice and observables are measures on the reals taking values in the Hilbert lattice. In our lecture we show that these mathematical objects also fall into the realm of TTE. For this purpose it is convenient to show that all objects live within the topological domain theory developed by Schröder and Simpson because this is an abstract characterization of those spaces for which TTE works.
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