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Questions tagged [contextuality]

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How are Gleason's and Kochen-Specker's theorems related?

If, on the one hand, I were to paraphrase Gleason's theorem, it would loosely state that if one can assign a truth value $p_k$ to each basis vector $\vec{u}_k$ such that $\sum_k p_k = 1$, then that ...
0 votes
0 answers

Are functions of commuting measurement operators equivalent to the same functions on the outcomes of those operators?

I.e., is it the case that for all states $\hat{\rho}$, we have that $F(\hat{A}_i, \hat{A}_j, \hat{A}_k, \hat{\rho}) \equiv F(a^{(l)}_i, a^{(m)}_j, a^{(n)}_k)$, where $a^{(l)}_i, a^{(m)}_j$ and $a^{(n)}...
1 vote
1 answer

Is degeneracy of eigenvalues required for the Kochen-Specker theorem?

I'm wondering why the operators for the Kochen-Specker theorem are 3-dimensional while they only produce two eigenvalues $\{0,1\}$. Is this degeneracy always needed regardless of the dimensionality of ...
1 vote
1 answer

What does it mean for two compatible observables to be a "coarse-graining" of a third?

In reading about quantum contextuality, I've encountered the statement that if [A,B] = 0, then there exists another observable C such that the spectral projections of A and B are a coarse-graining ...
6 votes
2 answers

Is Pilot Wave Theory contextual? How?

The Kochen Specker theorem says that hidden variable theories must be contextual. I'm not seeing anything in the definition of Bohmian mechanics that makes the hidden variable variable assignments ...
8 votes
2 answers

What is contextuality?

I have been trying to get and idea of contextuality in quantum mechanics for a while but I still do not get it. Reading Wikipedia lead on quantum contextuality, Quantum contextuality is a feature of ...