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A Falsifiable Leggett--Garg Test of the Three-Layer Quantum Brain Hypothesis: Quantum Non-Demolition Probes and Brain--Reservoir Information Channels

Hikaru Wakaura, Taiki Tanimae

Published May 6, 2026• 0 citations
Publisher

Abstract

Abstract The three-layer quantum brain (3LQB) hypothesis proposes that biological tissue computes by exploiting nuclear-spin memories, radical-pair processors and spin-selective readouts. To convert this hypothesis from speculation to testable physics we (i)~derive a sharp falsifiable prediction--Leggett--Garg violation $K\!\ge\!1$ requires $\geff/\omega_{\mathrm{Larmor}}\le 0.5$, and (ii)~build a quantitative catalogue of probes able to confirm or refute it without disturbing the quantum information. Eleven quantum non-demolition (QND) detection schemes and ten brain--organic-quantum-computer information-exchange channels are evaluated with adaptive Lindblad-complete Monte-Carlo ($N=2{,}000$ trajectories, bootstrap 95\,\% CIs) calibrated against 31~primary-literature parameters (28~within $\frac{1}{2}$--$2\times$, zero outliers). Petz-map covariant recovery raises the back-action-only fidelity of weak EDMR from $0.701\,[0.687,0.714]$ to $0.777\,[0.759,0.793]$ (CIs non-overlapping). A clean-qubit Leggett--Garg sweep reaches $K=1.46\,[1.35,1.59]$ for $\gdec/\omega\le 0.16$ and collapses to $K=0.16\,[0.00,0.31]$ for $\gdec/\omega\ge 1.6$. Tissue and skull attenuation analysis (Gabriel 1996) shows that L-band EPR loses 60\,\% of signal at 3~cm depth whereas NV-nanodiamond and OPM-MEG suffer only $\le 0.5\,\%$ attenuation. Power analysis identifies five schemes (ZULF-NMR, OPM-MEG, MARY, hyperpolarised \textsuperscript{13}C MRI, isotope-behavioural) capable of decisive 3LQB discrimination at $\alpha=0.05$, $1-\beta=0.80$ with $N\!\le\!10^3$ subjects. The hypothesis is therefore experimentally testable using existing technology, and engineered organic substrates (PTM-COF, $\kappa$-(BEDT-TTF)$_2$X) provide ready-made positive controls.

DOI
10.21203/rs.3.rs-9586245/v1

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Abstract We numerically study whether a coherence-preserving recovery (CPR) map modulates the stop-signal-cancellation window of a biophysical Lindblad model: a d ⁣= ⁣4d\!=\!4d=4 $\Pnuc$ nuclear-spin sector (Layer~1) and d ⁣= ⁣8d\!=\!8d=8 radical-pair interface (Layer~2) coupled to classical neurotransmitter electrochemistry (Layer~3) on a coarse-grained \textit{Drosophila}-like graph (64--320 nodes, classical inter-node coupling). Eight radical-pair proteins span a 23-fold range of nuclear $\Ttwo$ (1.81.81.8--40.840.840.8~ms). We find: (i)~preserved off-diagonal coherence breaks Buridan's symmetry while high-decoherence controls cannot, but \emph{any} non-maximally-mixed dynamics suffices; (ii)~CPR shifts the point of no return by $\DPoNR = 6.9$--$8.5\tu$ (≈2\approx 2≈2--333~ms), extending the simulated cancellation window 6--7-fold; (iii)~within d ⁣= ⁣4d\!=\!4d=4 the readout saturates for any CPR-mixing η ⁣≥ ⁣0.01\eta\!\ge\!0.01η≥0.01---a model artifact; (iv)~multi-seed statistics (15 ⁣× ⁣10015\!\times\!10015×100 trials) confirm veto-rate doubling (d ⁣= ⁣4.44d\!=\!4.44d=4.44, p ⁣< ⁣10−6p\!<\!10^{-6}p<10−6); (v)~$\DPoNR$ scales with $\log_{10}\Ttwo(\Pnuc)$ (Pearson r ⁣= ⁣0.85r\!=\!0.85r=0.85, permutation p ⁣= ⁣0.012p\!=\!0.012p=0.012). A reservoir-layer-substitution test shows the macroscopic statistics depend on decoherence rate and CPR strength, not on the unitary details of the quantum layers. The results are best read as a sensitivity analysis of how a non-CPTP coherence-preserving channel, embedded in a biophysical Lindblad model, modulates a behavioural timing readout; we make no metaphysical claims, and CPR is heuristic with no fault-tolerance threshold theorem (Sec.~\ref{sec:cpr}).
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Recent efforts to identify quantum-like signatures in brain and cognition have explored Bell-type tests, temporal inequalities, and Schrödinger-inspired models. We propose a Leggett--Garg (LG) test of collective neuronal excitation--inhibition (E--I) dynamics. Two reference configurations, ∣E⟩\ket{E}∣E⟩ and ∣I⟩\ket{I}∣I⟩, span an effective two-state space governed by $H_S=\heffΩσ_x/2$. Spatial separation of the E and I complexes need not preclude coherent superposition: when they constitute distinct subsystems, the corresponding collective alternatives can form an entangled state. The proposal tests temporal correlations, not Bell nonlocality. Complementary feedforward detectors couple selectively to E or I, with ideal negative results enabling non-invasive inference of the opposite configuration. We give a four-output-cell realization of the required projectors and detector interactions. Ideal sequential measurements yield K3(τ)=2cos⁡(Ωτ)−cos⁡(2Ωτ)K_3(τ)=2\cos(Ωτ)-\cos(2Ωτ)K3​(τ)=2cos(Ωτ)−cos(2Ωτ), reaching 3/23/23/2. We also derive the four-time result K4max⁡=22K_4^{\max}=2\sqrt{2}K4max​=22​ and explain its structural CHSH correspondence through Choi--Jamiołkowski duality. Detector efficiency, false positives, imperfect null results, timing uncertainty, and measurement disturbance are incorporated into a realistic extension. We conclude by identifying the experimental challenges of preparing, controlling, and selectively measuring collective E--I states in neuronal circuits.
This paper introduces the Entangled Neuro-Quantum Architecture (ENQuA), a hypothetical framework for a network of human brains interfaced with a central quantum computer. Building upon the 2025–2026 experimental validation of robust quantum phenomena in biological systems—including room-temperature protein-based qubits and confirmed superradiance in tryptophan networks—we propose a hybrid network topology. The ENQuA leverages microtubules as local quantum processors and superradiant tryptophan networks as ultra-fast "quantum buses" for inter-neural signaling. The interface utilizes non-invasive Motif DOT XCS technology and Nitrogen-Vacancy (NV) center sensors to bridge biological and synthetic quantum states. We address decoherence through the "3-Layer Quantum Brain Hypothesis," combining long-lived nuclear-spin memory with radical-pair reservoirs and motional-narrowing stabilization. The architecture’s capabilities include unified conscious experience and hybrid neuromorphic-quantum computation. Finally, we analyze the 2026 UNESCO mandate for Quantum Neurorights. This work synthesizes the latest breakthroughs in quantum biology, neuromorphic engineering, and neuroethics to propose a scientifically grounded vision for the future of collective cognition.
Abstract Organisms continually commit to actions and occasionally cancel them before they occur. Whether quantum coherence could shape such decisions is debated, and the proposed radical-pair substrate in the brain has been read optimistically: biological noise was treated as a computational resource, coherence times as milliseconds, and error-corrected coherence as preserved deliberation. However, each of these readings is, on inspection, the opposite of what a careful open-systems analysis gives. Here we study the three-layer radical-pair hypothesis under a single revised theory anchored on cryptochrome, importing two established physics tools—open-system quantum error correction and the drift-to-bound theory of decisions—into the living-decision problem. We show that at biological rates the radical-pair channel is entanglement-breaking, that motional narrowing (protein tumbling acting as natural dynamical decoupling) is what restores a correctable regime, and that decoherence-free encoding with concatenation then reaches fidelity F = 0.996. Used as a reservoir, the system gives no advantage for static classification but a temporal-prediction error that tracks quantum resources (rQFI = −0.52). Strikingly, when the reservoir drives a decision, error correction does not enlarge the window in which the action can be vetoed; by preserving the decision signal it reaches the motor threshold sooner and advances the point of no return toward the action, a result we reproduce as a fidelity rescue on IBM superconducting hardware (an analog of the mechanism, not of the biology). We distill this into the principle of error-correction–advanced commitment: a more coherent decision is faster and less revisable, not freer—sharpening, rather than resolving, the question of quantum agency.