Abstract Non-compact symmetries such as SU(1,1) govern amplification and squeezing, yet have not been directly identified in macroscopic spin ensembles. Here we apply a symmetry-based analytical framework to previously published magnetic-resonance data acquired from proton spin ensembles in the living human brain. By reanalyzing the detected signal within this framework, we identify a non-compact SU(1,1) pair sector of the full SU(4) spin algebra whose generators carry double-quantum coherence order, and exclude compact SU(2) exchange pathways as an explanation of the observed dynamics. Although the SU(1,1) pair coherence resides in the double-quantum sector, the 45°–gradient–45° readout block converts it into a detectable signal through a specific coherence-transfer pathway. We argue that the primary significance of the detected signal is as a witness of entry into a deep metric regime in which purely singlemode compression is no longer sufficient and cross-mode squeezing-like structure becomes necessary. In this sense, the signal functions first as a metric-regime witness and, more specifically, as a witness of non-compact pair-sector multiple-quantum coherence and squeezing. We then show that any strictly bipartite evaluation is obstructed in the high-temperature bulk-NMR setting, and that the appropriate entanglement framework is instead a macroscopic multiple-quantum-coherence witness. The observed signal features are consistent with metric-driven SU(1,1) pair dynamics, while definitive certification of many-body entanglement remains conditional on pathway-corrected calibration of the transfer coefficient and on evaluation of the corresponding separable MQC bound.
Abstract Non-compact symmetries such as SU(1,1) govern amplification and squeezing, yet have not been directly identified in macroscopic spin ensembles. Here we apply a symmetry-based analytical framework to previously published magnetic-resonance data acquired from proton spin ensembles in the living human brain. By reanalyzing the detected signal within this framework, we identify a non-compact SU(1,1) pair sector of the full SU(4) spin algebra whose generators carry double-quantum coherence order, and exclude compact SU(2) exchange pathways as an explanation of the observed dynamics. Although the SU(1,1) pair coherence resides in the double-quantum sector, the 45°–gradient–45° readout block converts it into a detectable signal through a specific coherence-transfer pathway. We argue that the primary significance of the detected signal is as a witness of entry into a deep metric regime in which purely singlemode compression is no longer sufficient and cross-mode squeezing-like structure becomes necessary. In this sense, the signal functions first as a metric-regime witness and, more specifically, as a witness of non-compact pair-sector multiple-quantum coherence and squeezing. We then show that any strictly bipartite evaluation is obstructed in the high-temperature bulk-NMR setting, and that the appropriate entanglement framework is instead a macroscopic multiple-quantum-coherence witness. The observed signal features are consistent with metric-driven SU(1,1) pair dynamics, while definitive certification of many-body entanglement remains conditional on pathway-corrected calibration of the transfer coefficient and on evaluation of the corresponding separable MQC bound.
• Published on bioRxiv, successfully observed multiple-quantum coherence (MQC) and SU(1,1) pair dynamics in proton spin ensembles of the living human brain. • Mathematically proved that the observed signal is not a classical SU(2) exchange model, but a non-compact SU(1,1) symmetry squeezing phenomenon based on double-quantum (DQ) coherence. • Overcame the thermodynamic obstruction of high-temperature biological environments at body temperature and presented a framework that strongly supports the possible existence of macroscopic many-body entanglement inside the brain. [Quantum Biology Society] The hypothesis that the living human brain could fundamentally operate like a giant quantum computer has long been a hot potato in the scientific community. This is because conventional physics dictates that quantum coherence collapses instantaneously in a warm and wet biological environment (about 310 K). However, a recent study has sent shockwaves through the academic world by discovering clear signal-level evidence of macroscopic quantum entanglement and multiple-quantum coherence (MQC) in the proton spin ensembles inside the human brain. An innovative paper titled "Signal-Level Witnessing of SU(1,1) Pair Dynamics in Brain Proton Spin Ensembles" was published on the preprint repository bioRxiv. Authored solely by independent researcher Christian Kerskens, this paper ruled out existing classical exchange pathways and analyzed the quantum dynamics of the brain from a new perspective. ■ SU(1,1) Quantum Squeezing Phenomenon Beyond Classical SU(2) Exchange In conventional nuclear magnetic resonance (NMR) or magnetic resonance imaging (MRI) theory, spin dynamics within dipolar-coupled ensembles of biological tissues have mainly been explained by the compact symmetry SU(2) exchange pathway. SU(2) symmetry creates a classical form of dynamics where spins oscillate and exchange with each other in an energy-constrained environment. However, unusual magnetic resonance data previously acquired from the living human brain exhibited features that directly contradict this SU(2) model. Phenomena that cannot be explained by classical exchange appeared, such as signals occurring immediately without an evolution delay, or refocusing occurring at the sum rather than the difference of the two frequencies. The author of this study, Christian Kerskens, presented a new analytical framework suggesting that these anomalous signals originate from a non-compact SU(1,1) pair sector. SU(1,1) symmetry is mainly dealt with in quantum optics and is the dynamics governing the exponential amplification and quantum squeezing of signals. This is the first time this symmetry has been directly observed in a macroscopic spin ensemble. ■ The Readout Pathway Uncovering Hidden Double-Quantum (DQ) Coherence The most significant characteristic of SU(1,1) pair operators is that they possess a double-quantum (DQ) coherence order rather than zero-quantum (ZQ). In principle, typical detectors cannot directly read these multiple-quantum states. However, the researcher mathematically proved that the unique 45°-gradient-45° pulse readout block used in the experiment provides a specific coherence-transfer pathway that converts this hidden DQ pair coherence into a detectable signal. In other words, he revealed that a specific wave we read as a brain MRI signal was actually the result of an entangled double-quantum state among brain protons. ■ Quantum Proof Overcoming the 'Thermodynamic Obstruction' of 310 K Biological Temperature Another crucial achievement of this study is that it bypassed the pseudopure-state obstruction, a chronic limitation of room-temperature bulk NMR environments. In the high-temperature brain environment, thermodynamic noise is dominant, so an entangled state can never be proven with a bipartite entanglement evaluation formula that isolates and looks at only two spins. The researcher redefined the observed signal not simply as a signal of two isolated spins, but as a collective multiple-quantum coherence (MQC) signal of the entire massive spin ensemble. The observed signal acts as a powerful quantum witness indicating that the macroscopic proton pool of the brain has exceeded the pure single-mode compression limit and entered a complex cross-mode entangled structure. This paper is evaluated as having an enormous impact on the convergence of brain science and quantum biology, as it demonstrated with a rigorous physical framework the possibility that the living human brain possesses a macroscopic quantum state with countless proton spins entangled with each other through SU(1,1) dynamics.
A companion paperestablishes a thermodynamic SU(1,1) witness criterion for non-classical spin-sector correlations in double-quantum (DQ) NMR signals. The present paper takes that criterion as input and addresses the mediator question that it raises but does not resolve: given a validated DQ witness, what class of physical mediator could have produced the witnessed correlations? We do not rederive the witness criterion. We classify a chain of mediator constraints. First, a shared classical stochastic process entering only through local Hamiltonians on two spin sub-pools induces a random-unitary LOCC map and is separability-preserving. Under the witness assumption and this specific coupling form, this textbook classical mediator class is therefore insufficient. We are explicit that the bound applies to local stochastic mediators of the stated form and does not, on its own, exclude bilinear classical fields, non-Markovian classical environments with memory, or dynamical classical fields that develop correlations. Second, we construct a minimal continuous-variable mediator capable of producing the DQ channel. Through explicit second-order elimination, a Gaussian covariance mediator with anomalous two-mode correlations generates effective pair-creation and pair-annihilation terms in the spin sector. Within this model class, the Bures--Wasserstein metric is the canonical covariance transport geometry, and the Williamson admissibility condition supplies the quantum boundary. A logarithmic barrier enforcing the symplectic-eigenvalue floor, as used in the variational BW programme \citep{PaperLagrangian}, generates a divergent local-mode rigidity at the admissibility boundary that blocks radial compression and selects the active non-passive tangent sector, which in the two-mode case carries an su(1,1) algebra. Third, we discuss living brain tissue as the motivating biological realization: the spin system acts as the readout, the structured tissue substrate is the candidate mediator, and cardiovascular--CSF dynamics provide a physiological gate controlling mediator access. We explicitly address the standard decoherence objection by reframing what is meant by ``quantum'' in the framework: the framework's claim is at the level of admissible covariance geometry, not at the level of protected microscopic spin entanglement.
Entanglement criteria based on variances or Fisher information are well developed for compact collective spin algebras, but their extension to non-compact dynamical sectors is less straightforward. In particular, double-quantum (DQ) observables associated with effective SU(1,1) structures can lead to formally unbounded classical fluctuation estimates unless additional physical constraints are imposed.
In this note, we develop a thermodynamic witness framework in which the classically accessible fluctuation sector is strictly bounded by finite-temperature detailed-balance conditions and motionally narrowed sequence-transfer limits. By analyzing the quantum dynamical semigroup of the spin-bath interaction, we demonstrate that spontaneous transient pair correlations generated by a stationary incoherent bath are contractively capped near an amplitude of 10−9. Furthermore, classical coherent sequence amplification is empirically bounded to O(10−2) in motionally narrowed tissue.
The resulting functional provides a concrete, theoretically derived bounding framework against which macroscopic DQ anomalies (e.g., fractional amplitudes on the order of 10% to 15%) can be rigorously classified as classically inexplicable, provided macro-scale structural stability (constant T2∗) is empirically verified.
Recent proposals in quantum gravity have suggested that unknown systems can mediate entanglement between two known quantum systems, if and only if the mediator itself is non-classical. This approach may be applicable to the brain, where speculations about quantum operations in consciousness and cognition have a long history. Proton spins of bulk water, which most likely interfere with any brain function, can act as the known quantum systems. If an unknown mediator exists, then NMR methods based on multiple quantum coherence (MQC) can act as entanglement witness. However, there are doubts that today’s NMR signals can contain quantum correlations in general, and specifically in the brain environment. Here, we used a witness protocol based on zero quantum coherence (ZQC) whereby we minimised the classical signals to circumvent the NMR detection limits for quantum correlation. For short repetitive periods, we found evoked signals in most parts of the brain, whereby the temporal appearance resembled heartbeat-evoked potentials (HEPs). We found that those signals had no correlates with any classical NMR contrast. Similar to HEPs, the evoked signal depended on conscious awareness. Consciousness-related or electrophysiological signals are unknown in NMR. Remarkably, these signals only appeared if the local properties of the magnetisation were reduced. Our findings suggest that we may have witnessed entanglement mediated by consciousness-related brain functions. Those brain functions must then operate non-classically, which would mean that consciousness is non-classical.
Nonclassicality Analysis and Entanglement Witnessing in Spin-1/2 NMR Systems
We investigate quantum features and non-classical nature of two-spin-1/2 NMR systems at thermal equilibrium under external magnetic fields. More specifically, using suitable quantifiers, we analyze quantum coherence, mixedness, and entanglement in NMR systems and examine their features within the system. We derive closed-form analytical expressions for the quantum elements and show how they depend on temperature and magnetic field strength. We demonstrate that at zero temperature, the system exhibits a quantum critical point, characterized by non-analytic behavior in the measures of coherence, and a sharp peak in mixedness. Moreover, we analyze the entanglement of the system using a suitable entanglement witness. This provides an experimentally friendly setting for testing entanglement in NMR systems. In other words, the witness links the entanglement in the system to quantum observables, making it directly provable in NMR experiments. We establish a connection between quantum information quantifiers and experimentally accessible NMR spectra of the system, enabling the quantification of entanglement, coherence, and mixedness through NMR signal processing.
We investigate quantum-state properties of thermal two-spin-1/2 NMR systems under external magnetic fields, with the goal of translating density-matrix-based quantum quantities into experimentally accessible NMR observables. In particular, we consider mixedness and witness-based entanglement as complementary probes of the thermal spin-state structure. Mixedness quantifies the departure of the NMR ensemble from a pure-state dominated regime and identifies field-dependent population redistribution, while the entanglement witness provides a practical test of nonclassical spin-spin entanglement without requiring full density-matrix reconstruction. Our framework links quantum-information quantities to NMR spectra, polarization observables, and spin-spin correlations, enabling the characterization of mixedness and witness-based entanglement through NMR signal analysis. We further examine the effect of noise and imperfections on the measurements. We also show how repeating the measurement improves the stability of the extracted signatures. These results provide insights for quantum-enhanced NMR, low-temperature spectroscopy, and emerging quantum sensing technologies where experimentally accessible signatures of mixedness and entanglement are needed.