Minimal state-dependent proof of measurement contextuality for a qubit

Abstract

We show that three unsharp binary qubit measurements are enough to violate a generalized noncontextuality inequality, the LSW inequality, in a state-dependent manner. For the case of trine spin axes we calculate the optimal quantum violation of this inequality. Besides, we show that unsharp qubit measurements do not allow a state-independent violation of this inequality. We thus provide a minimal state-dependent proof of measurement contextuality requiring one qubit and three unsharp measurements. Our result rules out generalized noncontextual models of these measurements which were previously conjectured to exist. More importantly, this class of generalized noncontextual models includes the traditional Kochen-Specker (KS) noncontextual models as a proper subset, so our result rules out a larger class of models than those ruled out by a violation of the corresponding KS-inequality in this scenario.

9 pages, 3 figures

References in corpus (5)

• Hidden Variables and the Two Theorems of John Bell
• A simple test for hidden variables in spin-1 system
• Notes on Joint Measurability of Quantum Observables
• Entropic Test of Quantum Contextuality
• Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements

Cited by in corpus (21)

• Kochen-Specker Contextuality
• The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory
• Quantum realization of arbitrary joint measurability structures
• Aspects of the phenomenology of interference that are genuinely nonclassical
• Leggett-Garg macrorealism and the quantum nondisturbance conditions
• Recycling qubits for the generation of Bell nonlocality between independent sequential observers
• Experimental generalized contextuality with single-photon qubits
• Contextuality in entanglement-assisted one-shot classical communication
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Joint Measurability and Temporal Steering
• Fine's theorem, noncontextuality, and correlations in Specker's scenario
• Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
• Contextuality beyond the Kochen-Specker theorem
• Joint measurability structures realizable with qubit measurements: incompatibility via marginal surgery
• No-broadcasting characterizes operational contextuality
• Revealing quantum contextuality using a single measurement device
• A note on the joint measurability of POVMs and its implications for contextuality
• N term pairwise correlation inequalities, steering and joint measurability
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Exclusivity principle and unphysicality of Garg-Mermin correlation
• Margenau-Hill operator valued measures and joint measurability