Contextuality of quantum fluctuations characterized by conditional weak values of entangled states

Abstract

The quantum fluctuations of a physical property can be observed in the measurement statistics of any measurement that is at least partially sensitive to that physical property. Quantum theory indicates that the effective distribution of values taken by the physical property depends on the specific measurement context based on which these values are determined and weak values have been identified as the contextual values describing this dependence of quantum fluctuations on the measurement context. Here, the relation between classical statistics and quantum contextuality is explored by considering systems entangled with a quantum reference. The quantum fluctuations of the system can then be steered by precise projective measurements of the reference, resulting in different contextual values of the quantum fluctuations depending on the effective state preparation context determined by the measurement of the reference. The results show that mixed state statistics are consistent with a wide range of potential contexts, indicating that the precise definition of a context requires maximal quantum coherence in both state preparation and measurement.

9 pages, no figures, extended explanation of the contextuality of quantum fluctuations. Final version for publication on Phys. Rev. A

References in corpus (7)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Anomalous Weak Values Are Proofs of Contextuality
• Strange Weak Values
• Pre- and post-selection, weak values, and contextuality
• Uncertainty limits for quantum metrology obtained from the statistics of weak measurements
• How quantum paradoxes originate from the non-classical statistics of physical properties related to each other by half-periodic transformations
• What does the operator algebra of quantum statistics tell us about the objective causes of observable effects?

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• Quantum uncertainty as classical uncertainty of real-deterministic variables constructed from complex weak values and a global random variable
• Uncertainty limits of the information exchange between a quantum system and an external meter
• Experimental investigation of the relation between measurement uncertainties and non-local quantum correlations