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

TL;DR

This paper investigates how quantum fluctuations and their contextual values depend on measurement settings in entangled systems, revealing that maximal coherence is essential for defining measurement contexts.

Contribution

It introduces a framework linking quantum fluctuations, weak values, and measurement context in entangled states, emphasizing the role of quantum coherence.

Findings

Quantum fluctuations depend on measurement context.

Maximal coherence is necessary for defining precise contexts.

Mixed states allow for multiple potential measurement contexts.

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.