Aleks Kissinger (Oxford, UK), Picturing Non-locality: Generalised Mermin Arguments in Categorical Quantum Mechanics


  • Feb. 20, 2012, 15:20 - 16:20


One might ask if the apparent non-locality of quantum mechanics is simply a side affect of local (i.e. classical) statistical correlations in physical quantities that we cannot measure directly. However, Bell's theorem showed that quantum mechanics produced statistical correlations that could not be explained with any local hidden variable model. In a remarkable thought experiment in 1990, Mermin strengthened result by picturing an experimental setup where not a single local hidden state could reproduce the predictions of quantum mechanics with non-zero probability. Whereas Bell's theorem relies on specific probabilities of outcomes to rule out locality, Mermin's only relies on possibilities.

While this argument is compelling, it only hints at the structural elements of quantum mechanics at play in the manifestation of non-locality. Perhaps the most crucial of these elements is the notion of complementary observables. These are physical quantities where maximal knowledge of one implies minimal knowledge of the other (c.f. position and momentum), and especially a particular kind of complementary observables which we call "strongly complementary observables". The features of strong complementarity can be totally represented in the abstract context of dagger-monoidal categories, and provides a vehicle for constructing a completely abstract version of the Mermin argument. Perhaps the most striking feature of this translation comes from the use of graphical language for monoidal categories, wherein conceptual notions like locality, measurement, and parity of outcomes are evident in the topology of string diagrams.