An experimental test of noncontextuality without unwarranted idealizations (1505.06244v1)

Abstract: To make precise the sense in which nature fails to respect classical physics, one requires a formal notion of classicality. Ideally, such a notion should be defined operationally, so that it can be subjected to a direct experimental test, and it should be applicable in a wide variety of experimental scenarios, so that it can cover the breadth of phenomena that are thought to defy classical understanding. Bell's notion of local causality fulfills the first criterion but not the second. The notion of noncontextuality fulfills the second criterion, but it is a long-standing question whether it can be made to fulfill the first. Previous attempts to experimentally test noncontextuality have all presumed certain idealizations that do not hold in real experiments, namely, noiseless measurements and exact operational equivalences. We here show how to devise tests that are free of these idealizations. We also perform a photonic implementation of one such test that rules out noncontextual models with high confidence.

Summary of the Paper: An Experimental Test of Noncontextuality Without Unwarranted Idealizations

This paper presents a novel approach to testing the notion of noncontextuality in quantum mechanics, departing from prior methodologies that assumed idealizations not valid for realistic experiments. The authors address longstanding challenges by providing a more operational criterion for noncontextuality, avoiding typical idealizations such as noiseless measurements and exact operational equivalences. This paper operationalizes a precise notion of noncontextuality conducive to experimental validation across diverse quantum phenomena.

The central focus lies on refining the concept of noncontextuality, traditionally confined by Kochen-Specker-type constructions, into a broader, operational context. The refinement leverages preparation and measurement noncontextuality, requiring that operationally indistinguishable procedures (those producing identical statistics) are represented by identical ontological states. The experimental test revolved largely around revising two critical aspects: accommodating measurement noise and addressing the lack of strict operational equivalence amidst real-world experimental conditions.

The researchers have successfully devised a noncontextuality inequality expressed as $A \leq \frac{5}{6}$, where $A$ represents the average correlation between preparation and measurement outcomes. This bound is derived under the assumption of noncontextuality, and it accounts for realistic imperfections in experimental setup, marking a shift from unrealistic noiseless contexts to pragmatic noisy environments.

The experimental setup involved a photonic system wherein the authors implemented a sequence of measurements designed to realize this inequality. By employing quantum optical methods and rigorous statistical techniques, they observed $A = 0.99709 \pm 0.00007$, significantly surpassing the theoretical noncontextuality bound by over 2300 standard deviations. This empirical evidence contradicts noncontextual models at a high confidence level, underscoring the inherent contextual nature of quantum systems.

The paper progresses beyond previous experiments by placing minimal reliance on hypothesized idealizations or assumptions. Instead, the authors emphasize an operational, direct testing approach, autonomously bounding noncontextuality frameworks. Consequently, the results highlight tangible nonclassical effects that defy reproduction by ontologically noncontextual models.

Implications and Future Directions

The implications of this research are multifaceted, spanning both theoretical and practical realms. Theoretically, it broadens the understanding of quantum nonclassicality, providing a robust argument against noncontextual models encompassing a wider class of quantum phenomena. Practically, the methodologies developed for this experiment may enhance quantum technologies, where exploiting contextuality is pivotal for computational and cryptographical advantages.

Future work can extend this framework to complex systems where contextuality plays a crucial role. Moreover, the techniques used for isolating operational equivalences from noisy environments could be instrumental in refining quantum control and measurement in technology development.

In summary, this paper adeptly reframes the experimental investigatory scope of noncontextuality, yielding compelling empirical support amidst realistic settings. It crafts a significant precedent for future inquiries, proposing a practical and operational methodology to disentangle the foundational elements of quantum mechanics from classical intuitions.