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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 2: "Condensed Metaphysics" II: Specific Models

AGPhil 2.4: Hauptvortrag

Montag, 26. März 2012, 17:15–18:00, E 020

Decoherence and the Emergence of a Joint Distribution — •Stephan Hartmann — TiLPS, Tilburg University, Tilburg, The Nethrlands

Bell states and other entangled states exhibit correlations that cannot be accounted for by a non-contextual local hidden-variable model. Various authors have shown that the non-existence of a non-contextual local hidden variables model entails that there is no joint probability distribution over random variables that represent the observables in question. The converse is also true. If there is no joint probability distribution, then there is no non-contextual local hidden variables model. Starting from the observation that entangled quantum states, in the absence of any stabilizing fields, will decay under the influence of decoherence, we investigate the decay of a GHZ state under the influence of decoherence in a Markovian Master equation model. Using necessary and sufficient conditions for the existence of a joint probability distribution derived by de Barros and Suppes we then show that a joint probability distribution emerges after about 20% of the half time of the decay. Interestingly, at this time the system is still highly entangled, although a classical model can account for the correlations in it. Next, we study the physics before the emergence of a joint distribution. It turns out that the correlations of Bell states and GHZ states can be accounted for in terms of upper probability distributions, which are well known from the theory of uncertain reasoning. We will show that upper probabilities are also useful in quantum theory and explicitly construct upper distributions for the cases at hand. This talk is based on joint work with Patrick Suppes (Stanford).