Characterizing Contextuality via Rank Separation with Applications to Cloning

Abstract: Quantum contextuality is a key nonclassical feature essential for understanding advantages in quantum computation and communication. We introduce a new framework to study contextuality based solely on information processing statistics. This simple and intuitive perspective leads to a powerful criterion denoted as rank separation for identifying contextuality in various quantum scenarios. We showcase the power of this technique through several applications, including a new derivation of Hardy's quantum excess-baggage theorem, and a simplified proof of contextuality for minimum error quantum state discrimination. Finally, we show as a prominent example that quantum contextuality provides the resource in optimal phase-covariant and universal cloning schemes, hence establishing it as a fundamental source of nonclassicality in all known optimal quantum cloning scenarios.