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How does quantum contextuality relate to realism?

Physics Asked on July 3, 2021

According to Spekkens contextuality can be defined as follows:

Suppose A, B and C are Hermitian operators such that A and B commute,
A and C commute, but B and C do not commute. Then the assumption of
noncontextuality is that the value predicted to occur in a measurement
of A does not depend on whether B or C was measured simultaneously.

Consider the following realistic scenarios

ABC x y
+++ + +
++- + -
+-+ - -
+-- - +
-++ - +
-+- - -
--+ + -
--- + +

where the first three columns represent the predetermined values of $A$, $B$, and $C$, and the last two represent the products $x = Acdot B$ and $y = Acdot C$. If the system is prepared determinstically such that $x = +$ and $y = -$, then we’re left with either $ABC = ++-$ or $ABC = –+$ as our pool of pre-determined (i.e. realistic) assignments.

Clearly, a measurement of $B = pm$ necessarily implies $A = pm$ whereas $C = pm$ necessarily implies $A = mp$. How is this realistic assignment of values not non-contextual?

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