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.
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?