We introduce Q of Fisher-Escolà, a novel statistical distribution designed to test whether conscious experience varies when quantum entanglement effects are considered.

By solving the integral of the Quantum Fisher Information Function, we obtain stable measurements of system susceptibility to quantum decoherence.

Mitigating quantum decoherence ensures that the transition of information beyond the quantum domain remains unaffected, preserving coherence.

We present the Fisher-Escolà paradox, a decoherence-related variation that may inspire future mathematical applications of quantum mechanics to consciousness.

The empirical applicability of Q of Fisher-Escolà extends to entangled qubit states, enabling structured exposure and systematic stimulus contingencies in implicit learning.

We provide theoretical tables detailing integrals for P(QTheoretical≥QObserved) at various significance levels, facilitating future research.

Our work includes statistical decision rules for hypothesis testing and biostatistical guidelines for extending quantum principles beyond their conventional domain.

Quantum theories have long sought to explain conscious experience, yet their biggest challenge is not conceptual but methodological. A critical gap remains: the lack of statistical tools capable of empirically testing these theories against objective reality. This study introduces and formalizes the Q of Fisher-Escolà distribution, the first statistical model to integrate quantum and classical probabilities, enabling robust inferential analysis in neuroscience and consciousness studies. We examined 150 density matrices of entangled states in a 10-qubit quantum system using IBM’s quantum supercomputers. Through maximum likelihood estimation, we mathematically confirmed that QFisher-Escolà ∼ beta(a, b, loc, scale). As a key contribution, a novel analytical solution to the Quantum Fisher Information (QFI) integral was derived, improving decoherence stability. Additionally, 10⁵ Monte Carlo simulations allowed us to establish critical thresholds for α = 0.05, 0.01, 0.001, and 0.0001, while assessing Type I and II error rates. Type I errors appeared in 2–5 % of right-tailed tests at α = 0.05 but approached zero as α decreased. Type II errors occurred in left-tailed tests (1–4 % at α = 0.05) but also diminished with stricter significance levels. In two-tailed tests, both error types remained below 3 %, highlighting the distribution’s robustness. The Q of Fisher-Escolà distribution pioneers a statistical framework for modeling quantum-classical interactions in consciousness research. It enables hypothesis testing and predicting subjective experiences, with applications in neuroscience and computational automation. Supported by mathematical proofs and empirical validation, this model advances the integration of quantum probability into neuroscience.

Quantum consciousness

Quantum Fisher Information

Hypothesis testing

Q Fisher-Escolà Distribution

Quantum entanglement

© 2025 The Authors. Published by Elsevier B.V. on behalf of Research Network of Computational and Structural Biotechnology.