Ideal measurements yield the same outcome when repeated, even when other compatible measurements have been performed in between. Some predictions of quantum theory for ideal measurements cannot be explained under the assumption that ideal measurements reveal preexisting outcomes that are independent of the context (i.e., the set of compatible measurements that have been jointly measured), this is known as quantum contextuality or Kochen–Specker (KS) contextuality . Quantum contextuality is an intrinsic signature of nonclassicality as its classical simulation requires memory  and thermodynamical cost . Moreover, it has been proven that quantum contextuality is necessary for fault-tolerant quantum computation via magic state distillation and measurement-based quantum computation . Quantum contextuality also plays a fundamental role in some quantum key distribution protocols  and is crucial for understanding the underlying physics behind the limitation of quantum correlations . So far, quantum contextuality has been experimentally observed in trapped ions , photons , ensembles of molecular nuclear spins in the solid state , and superconducting systems .
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