Quantum theory realises all joint measurability graphs
نویسندگان
چکیده
Joint measurability of sharp quantum observables is determined pairwise, and so can be captured in a graph. We prove the converse: any graph, whose vertices represent sharp observables, and whose edges represent joint measurability, is realised by quantum theory. This leads us to show that it is not always possible to use Neumark dilation to turn unsharp observables into sharp ones with the same joint measurability relations, highlighting a caveat in the “church of the larger Hilbert space”.
منابع مشابه
All joint measurability structures are quantum realizable
The general impossibility of jointly implementing arbitrary sets of measurements is a fundamental feature of quantum theory. Indeed, it is a key ingredient that enables a demonstration of the nonclassicality of quantum theory in proofs of Bell’s theorem [1] and the Kochen-Specker theorem [2]. A finite set of measurements is called jointly measurable or compatible if there exists a single measur...
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