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Oxford Quantum Talks Archive

Does knowing my lambda mean knowing my psi?

Terry Rudolph, Imperial College London
Categories, Logic and Foundations of Physics V, August 2009, Imperial College London

All known hidden variable theories that completely reproduce all quantum predictions share the feature that they add some information to the quantum state psi. That is, if one knew the "state of reality" given by the hidden variable(s) lambda, then one could infer the quantum state - the hidden variables are additional to the quantum state. However, for the case of a single 2-dimensional quantum system Kochen and Specker gave a model which does not have this feature. A natural question arises whether a similar model is possible for higher dimensional systems. At the time of writing this abstract I have no clue. I will talk about various constraints on such theories (in particular on how they manifest contextuality) and I'll present some examples of failed attempts to construct such models for a 3-dimensional system. The annoying thing about my failed attempts is that they can be expected to reproduce physical things like atomic spectra, and they only deviate from the quantum predictions for the Born rule by about a percent or so. However I have wasted enough time trying to get them to agree properly with quantum mechanics, and so my goal in this talk is to motivate someone smarter than me to prove that such a class of non-hidden, hidden variable theories cannot exist.

[video] [streaming video]