Chapter 6 is about “pseudo-telepathic” games and “contextuality,” the dependence of the outcome of a measurement of a quantum observable on the context defined by what other observables are measured in the procedure. The simplest example of a pseudo-telepathic game is the Greenberger–Horne–Zeilinger correlation, a tripartite correlation between Alice, Bob, and Clio. The Kochen–Specker theorem demonstrates that the observables of a quantum system more complex than a qubit cannot have definite, noncontextual, preexisting values before they are measured, not even for certain finite sets of observables. An inequality by Klyachko and colleagues is derived for any noncontextual assignment of values to five observables related in a certain way defined by the five edges of a pentagram, where each edge corresponds to a different observable or measurement context. The inequality is violated by appropriate measurements on a qutrit (a quantum system whose observables have three possible values) in a certain quantum state.
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