TITLE: Is there an analogue of the Kochen-Specker property in quantum field theory?
QUESTION [6 upvotes]: Motivation
Entanglement and entanglement measures are traditionally defined in finite-dimensional systems. Nowadays there are very well-known definitions of entanglement measures in quantum field theories.
In finite-dimensional systems, one also has a notion of contextuality in the sense of the Kochen-Specker theorem. There are various recent work on "measures" of contextuality.
Note that one can give examples of systems that have the KS property but no entanglement.
Question
Is there an analogue of the Kochen-Specker property in quantum field theory?
Subquestion & first step:
Does it make sense to define and measure contextuality on an arbitrary square lattice?

REPLY [1 votes]: Contextuality is only partially related with entanglement. It concerns some  consequences of the fact that  observables exist which cannot be defined simultaneously. More precisely it is a property of every realistic  hidden variable theory which explains the same outcomes of measurements of a quantum theory. The Kochen Specker theorem is consequence of the Gleason theorem. The latter, to work,  needs nothing but a separable Hilbert space with dimension greater than two. Hence QFT is included straightforwardly.
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