Does knowing my lambda mean knowing my psi?

          @misc{ pirsa_PIRSA:09090083,
            doi = {10.48660/09090083},
            url = {https://pirsa.org/09090083},
            author = {Rudolph, Terry},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Does knowing my lambda mean knowing my psi?},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {sep},
            note = {PIRSA:09090083 see, \url{https://pirsa.org}}
          }
          

Abstract

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 – the non-orthogonality of two quantum states is manifested as overlapping probability distributions on the hidden variables, and teh model could be termed “psi-epistemic”. 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. I will also discuss a very artificial tweaking of Bell’s original hidden variable model which renders it psi-epistemic for some (though not all) of the corresponding quantum states.