Quantum theory realises all joint measurability graphs

Abstract

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".

5 pages

References in corpus (6)

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Cited by in corpus (12)

• Kochen-Specker Contextuality
• Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
• Quantum realization of arbitrary joint measurability structures
• Necessary and sufficient condition for contextuality from incompatibility
• Multigraph approach to quantum non-locality
• Neither Contextuality nor Nonlocality Admits Catalysts
• Contextuality beyond the Kochen-Specker theorem
• Joint measurability structures realizable with qubit measurements: incompatibility via marginal surgery
• Emergence of Objectivity for Quantum Many-Body Systems
• The structure of ultrafine entanglement witnesses
• Joint measurability through Naimark's theorem
• Information leak and incompatibility of physical context: A modified approach