Abstract We numerically study whether a coherence-preserving recovery (CPR) map modulates the stop-signal-cancellation window of a biophysical Lindblad model: a $d\!=\!4$ $\Pnuc$ nuclear-spin sector (Layer~1) and $d\!=\!8$ 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 $\Ttwo$ ($1.8$--$40.8$~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 $\DPoNR = 6.9$--$8.5\tu$ ($\approx 2$--$3$~ms), extending the simulated cancellation window 6--7-fold; (iii)~within $d\!=\!4$ the readout saturates for any CPR-mixing $\eta\!\ge\!0.01$---a model artifact; (iv)~multi-seed statistics ($15\!\times\!100$ trials) confirm veto-rate doubling ($d\!=\!4.44$, $p\!<\!10^{-6}$); (v)~$\DPoNR$ scales with $\log_{10}\Ttwo(\Pnuc)$ (Pearson $r\!=\!0.85$, permutation $p\!=\!0.012$). 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}).
Abstract We numerically study whether a coherence-preserving recovery (CPR) map modulates the stop-signal-cancellation window of a biophysical Lindblad model: a d=4\Pnuc nuclear-spin sector (Layer1) and d=8 radical-pair interface (Layer2) 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 (1.8--40.8~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--3~ms), extending the simulated cancellation window 6--7-fold; (iii)within d=4 the readout saturates for any CPR-mixing η≥0.01---a model artifact; (iv)multi-seed statistics (15×100 trials) confirm veto-rate doubling (d=4.44, p<10−6); (v)\DPoNR scales with log10\Ttwo(\Pnuc) (Pearson r=0.85, permutation p=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}).
Abstract Whether quantum coherence plays a functional role in neural information processing remains contested, largely because biological environments are deemed too noisy for quantum states to sur- vive at relevant timescales. We construct a three-layer model—nuclear spin memory, radical pair interface, classical electrochemistry—and identify five quantum error correction (QEC) paradigms that map onto known biophysical mechanisms: decoherence-free subspaces (DFS) via 31P singlet states, dynamical decoupling (DD) via protein motional narrowing, purification QEC (PQEC) ex- ploiting enzymatic redundancy (∼104 copies/cell), gauging symmetry protection via radical-pair spin conservation, and catalytic coherence recovery (ICEC) at enzyme active sites. We parametrize the model for two molecular systems: monoamine oxidase A (MAO-A; γeff = 4.55, radical pair un- confirmed) and Drosophila cryptochrome (CRY; γeff = 3.25, radical pair experimentally confirmed, |J| < 1 MHz). We quantify each mechanism individually: DFS provides complete protection against collective dephasing (F = 1.000), DD yields a B−2 0 -dependent relaxation suppression (4.6×107-fold at Earth field vs X-band), and PQEC achieves near-unity fidelity using 64 of ∼104 available copies. We integrate gauging, PQEC, and covariant recovery into a unified three-layer stabilizer and benchmark it on pattern classification, time-series prediction, and quantum-coherent decision dynamics. For MAO-A, the stabilizer significantly outperforms standard covariant QEC in classification (accuracy 85.2% vs 80.0%, p = 0.017, Cohen’s d = 1.19) and coherence preservation (+40% at moderate noise), while for time-series prediction the improvement is not statistically significant (p = 0.79). CRY yields statistically equivalent stabilizer performance (MNIST 86.2% vs 85.2%, p = 0.67; spike median MSE 7.31 vs 7.65, Mann–Whitney p = 0.99), demonstrating that the QEC framework is robust across molecular substrates. CRY’s decisive advantages are experimental: a confirmed radical pair and immunity to homeostatic neurotransmitter buffering. Four falsifiable experiments are proposed.
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≥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 21--2×, 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 ≤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 α=0.05, 1−β=0.80 with N≤103 subjects. The hypothesis is therefore experimentally testable using existing technology, and engineered organic substrates (PTM-COF, κ-(BEDT-TTF)2X) provide ready-made positive controls.
Abstract Biological radical-pair systems operate at decoherence rates γeff = 3.25–4.55, far exceeding the entanglement-breaking threshold γc ≈ 0.3 (channel-model-dependent). Standard quantum error correction provably fails (Q1 = 0). We identify three escape routes: (i) motional narrowing from protein tumbling reduces γeff to 0.19–0.27 < γc; (ii) decoherence-free subspace encoding achieves F = 0.99 with 27 enzyme copies (assuming collective noise fraction fcoll ≥ 0.94); (iii) the Petz recovery map with a noisy nuclear-spin reference preserves concurrence C = 0.46 as an information-theoretic bound. Radical-pair quantum reservoir computing (QRC) performance degrades monotonically with noise and correlates with quantum resources (rQFI = −0.52); motional narrowing rescues QRC by 6×, though a classical echo-state network retains an advantage at current simulation scales. These results reframe the quantum brain hypothesis: not quantum computation, but quantum reservoir dynamics enhanced by biologically natural motional narrowing.
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.
This paper presents in details how the subjective time is constructed by the brain cortex via reading packets of information called "time labels", produced by the right basal ganglia that act as brain timekeeper. Psychophysiological experiments have measured the subjective "time quanta" to be 40 ms and show that consciousness operates beyond that scale - an important result having profound implications for the Q-mind theory. Although in most current mainstream biophysics research on cognitive processes, the brain is modelled as a neural network obeying classical physics, Penrose (1989, 1997) and others have argued that quantum mechanics may play an essential role, and that successful brain simulations can only be performed with a quantum computer. Tegmark (2000) showed that make-or-break issue for the quantum models of mind is whether the relevant degrees of freedom of the brain can be sufficiently isolated to retain their quantum coherence and tried to settle the issue with detailed calculations of the relevant decoherence rates. He concluded that the mind is classical rather than quantum system, however his reasoning is based on biological inconsistency. Here we present detailed exposition of molecular neurobiology and define the dynamical timescale of cognitive processes linked to consciousness to be 10-15 ps showing that macroscopic quantum coherent phenomena in brain are not ruled out, and even may provide insight in understanding life, information and consciousness.
Abstract Whether the electron--nuclear spin coherence behind radical-pair magnetoreception could also support biological \emph{computation} has been conjectured for decades but never made quantitative. We treat a cryptochrome-type radical pair as a reservoir computer, solving the radical-pair master equation with electronic decoherence and driving it as a real turnover does---by the birth of a spin-correlated pair whose singlet character encodes the input. Three results follow, none of them the expected one. The reservoir is \emph{readable by ordinary chemistry}: the nuclear polarisation the product carries away gives an out-of-sample information-processing capacity of 4.7 against its own memoryless floor of 2.0, with no spectroscopy. There is no quantum advantage: a classical network matched channel-for-channel exceeds the five-spin reservoir by 49--123%. And the memory horizon is set not by the microsecond pair lifetime but by the turnover interval, because the nuclear register survives recombination in the diamagnetic product---so the binding constraint is chemical rather than temporal, namely that the \emph{same} register be reused between turnovers. Predicting the register's relaxation instead of assuming it makes that constraint testable: at the geomagnetic field a proton on the intact protein relaxes in milliseconds, not seconds, capping the horizon below the neural band unless the register's dipolar vector reorients about two and a half times faster than the protein (τeff≲6~ns). What survives is a smaller claim on firmer ground: a criterion whose two constants can be measured in vitro, in place of one whose central relaxation time was never measured at all.