Quantum theory based on real numbers cannot be experimentally falsified

In the realm of quantum theory, the question of whether complex numbers are essential for experimental results has long been debated. Real Quantum Theory (RQT) offers an alternative approach by replacing complex amplitudes with real ones while maintaining the standard composition rule. RQT successfully reproduces single-party and bipartite Bell correlations observed in Quantum Theory (QT). However, concerns have been raised about its lack of local tomography and potential divergence in broader local experiments. A study by Renou et al. suggested that a bilocal network experiment could disprove RQT without affecting QT, casting doubt on the empirical equivalence of the two theories. A new analysis challenges this conclusion by highlighting an untestable assumption underlying the previous findings. The distinction between product-state independence and operational independence plays a crucial role in understanding the correlation structures predicted by both theories. By imposing operational constraints on source independence, it is demonstrated that every finite network correlation achievable in QT can also be achieved in RQT under similar measurement locality conditions. This equivalence extends to multipartite protocols involving channels and measurements with specified locality structures, reinforcing the idea that as long as no violations of QT are observed, RQT cannot be experimentally falsified. These results not only restore the empirical indistinguishability of QT and RQT but also shed light on their differing interpretations of correlation structures within the same observed world. The findings challenge previous assumptions about the experimental distinguishability of quantum theories based on real numbers and highlight the importance of considering operational constraints when evaluating theoretical frameworks in quantum physics.

Introduction: Quantum theory is a fundamental framework in physics that has been extensively studied and tested over the years. However, there has been ongoing debate about whether complex numbers are essential for experimental results in quantum theory. Real Quantum Theory (RQT) offers an alternative approach by replacing complex amplitudes with real ones while maintaining the standard composition rule.

Understanding RQT: Real Quantum Theory (RQT) is a theoretical framework that proposes to replace complex numbers with real numbers in quantum theory while still preserving its standard composition rule. This means that instead of using complex amplitudes to describe quantum states, RQT uses real-valued probabilities. The idea behind this approach is to simplify the mathematical formalism of quantum mechanics and potentially provide a more intuitive understanding of its underlying principles.

Empirical Equivalence of QT and RQT: One crucial aspect of evaluating any scientific theory is its empirical equivalence – whether it can reproduce all experimental observations made by another well-established theory. In this case, the question arises: can RQT replicate all single-party and bipartite Bell correlations observed in Quantum Theory (QT)? The answer seems to be yes, as demonstrated by previous studies.

This raised concerns about whether RQT could truly be considered an alternative to QT or if it was just a simplified version lacking important features.

Operational Independence vs Product-State Independence: To understand why these doubts were raised about the empirical equivalence between QT and RQT, we must first look at two types of independence assumptions – operational independence and product-state independence.

Operational independence refers to the assumption that measurements performed on one part of a system do not affect the outcomes of measurements on another part, even if they are entangled. On the other hand, product-state independence assumes that the state of a composite system is independent of its subsystems' states.

However, this assumption was later challenged by a new analysis that highlighted its untestable nature.

The Importance of Operational Constraints: The new analysis showed that imposing operational constraints on source independence can lead to different conclusions about the correlation structures predicted by QT and RQT. In simpler terms, when considering experimental setups where measurements are performed with specified locality conditions, both theories predict similar results.

This finding not only restores the empirical indistinguishability between QT and RQT but also sheds light on their differing interpretations of correlation structures within the same observed world. It highlights how crucial it is to consider operational constraints when evaluating theoretical frameworks in quantum physics.

Implications for Experimental Distinguishability: One significant implication of these findings is that as long as no violations of QT are observed in experiments, RQT cannot be experimentally falsified. This challenges previous assumptions about the experimental distinguishability of quantum theories based on real numbers and emphasizes the importance of considering operational constraints when evaluating them.

Conclusion: In conclusion, this research paper provides valuable insights into the ongoing debate about whether complex numbers are essential for experimental results in quantum theory. By highlighting an untestable assumption underlying previous findings and emphasizing the importance of considering operational constraints, it restores the empirical equivalence between Quantum Theory (QT) and Real Quantum Theory (RQT). These results have implications for our understanding of correlation structures in quantum physics and highlight potential limitations in distinguishing between different theoretical frameworks based solely on experimental data.