Quantum Entanglement Rules Refined, Removing Key Assumptions About Measurement Settings

Scientists have long sought to refine our understanding of nonlocality and the foundations of quantum mechanics. A new study by G. Bacciagaluppi, R. Hermens, and G. Leegwater challenges a key assumption underpinning Bell’s theorem, Measurement Independence, the idea that measurement settings are independent of hidden variables. The researchers demonstrate that violations of this assumption, similar to violations of locality, could in principle allow for signalling, making them experimentally testable. By imposing the constraint of no-signalling, they derive a version of Bell’s theorem that circumvents the need for Measurement Independence, offering a potentially more robust framework for exploring the limits of quantum theory and its implications for ‘experimental metaphysics’. This work represents a significant step towards disentangling the various assumptions required for Bell-type tests of quantum nonlocality.

For decades, Bell’s theorem has been invoked to demonstrate the counterintuitive nature of quantum entanglement, relying on assumptions such as the independence of measurement settings from hidden variables.

This work demonstrates that violations of this Measurement Independence assumption, the idea that the choice of what to measure doesn’t influence the underlying state of a quantum system, can, under specific conditions, be linked to a form of communication that, while not practically achievable, is not fundamentally prohibited by physics. The study establishes that certain breaches of Measurement Independence share characteristics with violations of locality caused by faster-than-light action, suggesting they too could be, in principle, detectable.

By imposing a ‘no-signalling’ constraint, a principle rooted in relativity that prevents information from travelling faster than light, the researchers derive a modified version of Bell’s theorem that circumvents the need for Measurement Independence altogether. The team’s analysis reveals that relaxing the Measurement Independence assumption necessitates careful consideration of potential signalling mechanisms.

They formulate conditions under which such signalling would become operational, allowing for the empirical testing of these violations. The ‘Schulman model’ , a specific theoretical framework challenging standard interpretations of quantum mechanics, serves as a concrete example illustrating the implications of this extended theorem.

Ultimately, this research offers a new perspective on ‘experimental metaphysics’, the intersection of empirical testing and foundational questions in physics. The findings not only deepen our theoretical understanding of entanglement but also suggest new avenues for probing the fundamental limits of information transfer and the nature of physical reality itself.

Detecting violations of Measurement Independence through a signalling protocol

A rigorous examination of Measurement Independence forms the basis of this work, addressing a crucial assumption within Bell’s theorem derivations. To establish this link, the research constructs an explicit signalling protocol designed to reveal violations of Measurement Independence.

This protocol considers a standard Bell experiment involving entangled pairs of spin-1/2 particles prepared by Charlie, with Alice and Bob independently choosing from measurement settings denoted as I, I′, J, and J′. The study defines statistical distributions, σ IJ ρ (λ), to represent the hidden variables λ influencing the outcomes of these measurements, and calculates expectation values ⟨AB⟩ IJ λ to quantify correlations.

Crucially, the methodology moves beyond simply identifying potential violations of Measurement Independence; it details how these violations could manifest operationally as detectable signals. The innovative aspect of this approach lies in formulating conditions under which ‘signalling in principle’ would become observable, even acknowledging that such signals might traverse spacetime in a non-standard, zig-zag manner consistent with relativistic constraints.

By carefully defining the statistical relationships between hidden variables, measurement choices, and outcomes, the research aims to extend Bell’s theorem to encompass models that permit violations of Measurement Independence. This work establishes a connection between violations of measurement independence and the possibility of signalling, demonstrating that such violations are, in principle, testable.

The research centres on distributions of hidden variables that explicitly depend on both measurement contexts and preparation contexts, extending beyond the standard assumption of independence. Crucially, the study introduces an ‘equiprobability theorem’ which states that if a hidden variables model reproduces the probabilities of a maximally entangled state while satisfying locality and measurement independence, then individual hidden variables λ predict equiprobable measurement results.

The equiprobability theorem is demonstrated through analysis of chains of coplanar spin measurements, revealing that deviations from perfect correlations along the chain directly impact the probability of specific spin outcomes. Specifically, Theorem 0’ establishes that if correlations along a chain of 2n coplanar spin directions deviate from perfect (anti)correlation by a bounded amount δ, the marginal probability deviates from equiprobability by at most 2nδ.

This theorem is robust to small deviations in the spin directions considered. Furthermore, the study proves that a failure of equiprobability at the operational level necessitates a failure of either locality or measurement independence. By considering maximally entangled states, the researchers show that as the number of links in the coplanar chain approaches infinity, the deviation from equiprobability diminishes, confirming the link between signalling, measurement independence, and the underlying hidden variable distributions. This work provides a framework for analysing hidden variable models and identifying conditions under which signalling becomes possible, even in scenarios adhering to the principle of locality.

The Bigger Picture

Scientists have long grappled with the foundations of quantum mechanics, specifically the implications of Bell’s theorem and the persistent challenge of reconciling quantum predictions with our intuitive understanding of locality and independence. This work doesn’t offer a simple resolution, but a crucial refinement of the terms of the debate.

By meticulously dissecting the assumptions underpinning Bell’s inequalities, researchers demonstrate that violations aren’t necessarily proof of spooky action at a distance, but could instead signal a failure of ‘measurement independence’ , the idea that measurement settings are unrelated to hidden variables. The significance lies in shifting the focus from simply detecting non-locality to diagnosing its source.

For decades, experiments have sought to disprove local realism, and this research suggests a parallel path: testing whether the assumptions about measurement independence hold true. This is not merely a philosophical exercise. If measurement independence is routinely violated, it opens the door to a different class of hidden variable theories, ones previously dismissed as untestable.

However, establishing that a violation of measurement independence is genuinely signalling, and not some subtler correlation, remains a formidable task. The ‘Schulman model’ serves as a useful illustration, but real-world systems are far more complex. Moreover, the practical implications of superdeterministic models, where everything is predetermined, are still hotly debated.

Future work will likely concentrate on developing more robust tests for signalling, and exploring the boundaries between genuine non-locality and seemingly non-local correlations arising from hidden dependencies. The quest to understand quantum reality, it seems, is becoming less about finding what is impossible, and more about precisely defining what is permissible.