Weak measurements, non-classicality and negative probability

TL;DR

This paper links nonclassical quantum features, negative pseudo probabilities, and anomalous weak values, showing how weak measurements can directly measure nonclassicality and offering new testing methods.

Contribution

It establishes a direct connection between nonclassicality tests, negative pseudo probabilities, and weak values, providing a novel approach to measure quantum features.

Findings

Pseudo-probabilities can be directly measured as anomalous weak values.

Negative pseudo probabilities are linked to nonclassical quantum features.

A quantum game based on violation of classical probability rules is proposed.

Abstract

This paper establishes a direct, robust and intimate connection between (i) non classicality tests for various quantum features, e.g., non-Boolean logic, quantum coherence, nonlocality, quantum entanglement, quantum discord; (ii) negative probability, and (iii) anomalous weak values. It has been shown [Adhikary et al. Eur. Phys. J. D, 74(68):68, 2020] that nonexistence of a classical joint probability scheme gives rise to sufficiency conditions for nonlocality, a nonclassical feature not restricted to quantum mechanics. The conditions for nonclassical features of quantum mechanics are obtained by employing pseudo probabilities, which are expectation values of the parent pseudo projections. The crux of the paper is that the pseudo-probabilities, which can take negative values, can be directly measured as anomalous weak values. We expect that this opens up new avenues for testing nonclassicality via weak measurements, and also gives deeper insight into negative pseudo probabilities which become measurable. A quantum game, based on violation of classical probability rule is also proposed that can be played by employing weak measurements.