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Christian Kerskens

Publications and source records attributed to Christian Kerskens.

8 recordsLinked to original sources
arXiv2026

Gaussian Purification Quotients and Fixed Nielsen Penalties

Information distance and circuit complexity are both obtained by minimizing lengths, but they minimize over different objects. We make this distinction explicit for faithful one-mode Gaussian states. First, invariant-form uniqueness implies that no positive-definite quadratic gate cost can be invariant under the full adjoint action of the noncompact symplectic group; a positive Cartan majorant necessarily introduces additional reference data. The Uhlmann purification quotient realizes the Bures metric, and the radial covariance direction requires a system-ancilla coupling because system-only Gaussian unitaries preserve the Williamson eigenvalue. We then minimize fixed right-invariant quadratic norms on the minimal two-mode Gaussian gate algebra \(\mathfrak{sp}(4,\mathbb R)\). For the unweighted Frobenius norm, the quotient coefficients for radial and traceless covariance tangents are $G_0=[\hbar^2(u-1)]^{-1}$ and $G_2=[\hbar^2(3u-1)]^{-1}$, where $u=(2ν/\hbar)^2$. Their ratio does not equal the Bures ratio. The radial coefficient, however, reproduces the Bures value exactly at every $u$; the mismatch is confined to the traceless sector. More generally, a constant block-diagonal two-weight schedule gives $G_0/G_2=1+2(β/α)u/(u-1)$; matching Bures throughout the isotropic family would require the state-dependent relation $β/α=1/u$. At the Bures-Fisher determinant crossing \(u=φ\), pointwise matching is possible only by inserting $β/α=φ^{-1}$. Thus the Bures purification quotient is an exact state-geometric cost, but it is neither an unweighted symplectic gate cost nor a member of this fixed two-weight Nielsen family. The existence of a more general fixed positive gate norm realizing the quotient remains open.

quant-ph↗
arXiv2026

The Killing Form and Petz Uniqueness of Gaussian Bures Geometry

For centered bosonic Gaussian states, the covariance pullback of the Bures cometric differs from the lift-normalized classical covariance Fisher--Rao cometric by a state-independent bilinear form. Under the canonical identification of symmetric covariance covectors with $\mathfrak{sp}(2N,\mathbb{R})$, this form is the trace form and hence a fixed multiple of the Killing form. We prove that, within the normalized symmetric Petz family, Bures is uniquely selected by requiring such an additive state-independent symplectic correction. We determine the full Williamson-frame spectrum and show that a boundary stratum with $m$ pure modes has an $m^2$-dimensional cometric kernel isomorphic to $\mathfrak u(m)$, while the pure Gaussian orbit remains nondegenerate. For radial one-mode estimation, ideal heterodyne detection accesses the exact fraction $(ν-\hbar/2)/(ν+\hbar/2)$ of the SLD quantum Fisher information. Its vanishing boundary limit reflects finite heterodyne information relative to a divergent radial quantum Fisher information, not zero measurement information. Finally, a minimal Schur realization fixes the auxiliary inertia and identifies the second Schur complement as the true covariant vertical block.

quant-ph↗
arXiv2026

The Global Geometry of the Gaussian Bures Manifold: Admissible Domain, Spectral Boundary, and Asymptotic Classicality

We construct the covariance-sector Bures geometry of centered bosonic Gaussian states from the Gaussian symmetric-logarithmic-derivative equation and determine its quantum-admissible domain. At the Williamson uncertainty floor, the boundary geometry is anisotropic: spectrum-changing radial coefficients diverge, whereas squeezing and rotation directions along the pure Gaussian orbit remain finite. Dually, the covariance cometric acquires an exact \(m^2\)-dimensional kernel when \(m\) modes become pure, yet the boundary remains at finite radial Bures distance. We derive the potential \[ Φ=-\tfrac12\sum_k\log(ν_k^2-\tfrac14), \] which generates fixed-frame covariance dilation and equals \(βF\) on fixed-Hamiltonian thermal families. At large symplectic eigenvalue, the relative quantum correction is \(O(\hbar^2/ν^2)\), recovering covariance Fisher--Rao geometry. This intrinsic classical regime differs from the pure-state boundary, where classical statistics require a specified measurement channel. As a secondary comparison, the normalized Bures, Fisher--Rao, and action-matched Bures--Wasserstein determinant densities possess an exact one-mode junction at \[ (x,η)=(\sqrtφ,\sqrtφ),\qquad x=2ν/\hbar. \] This junction is kinematic, and its branch interpretation is conditional. At a prescribed finite nonzero compression rate, the Bures action diverges while the Bures--Wasserstein cost remains finite; a bounded Bures budget instead enforces radial deceleration.

quant-ph↗
arXiv2026

Hamiltonian Lift of Bures--Wasserstein Covariance Dynamics with a Spectral Floor

Covariance dynamics on the positive-definite cone are commonly described by gradient flows, which encode dissipative relaxation but obscure the underlying phase-space structure. We construct a finite-dimensional Hamiltonian lift of covariance dynamics on Sym$^+_n$ equipped with the Bures--Wasserstein metric. The natural mechanical Lagrangian yields canonical momentum $Π=\tfrac12 L_Σ[\dotΣ]$, where $L_Σ$ is the Lyapunov operator, and explicit Hamiltonian $\mathcal{H}(Σ,Π) = 2{\rm tr}(ΠΣΠ)+V(Σ)$. Adding Rayleigh dissipation recovers the Bures--Wasserstein gradient flow in the overdamped limit. For a spectral-floor and trace-control potential, the quadratic fluctuation Hamiltonian around the isotropic equilibrium separates trace and traceless modes; the baseline stiffness diverges as $(s-ν)^{-2}$ as the equilibrium covariance approaches the floor. The construction identifies a conservative parent system for constrained Bures--Wasserstein covariance relaxation and fixes the local stiffness scale induced by the spectral floor.

quant-ph↗
arXiv2026

A Thermodynamic SU(1,1) Witness Framework for Double-Quantum NMR Signals in Neural Tissue

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 \(\mathcal{O}(10^{-2})\) 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 \(T_2^*\)) is empirically verified.

quant-ph↗
arXiv2026

Evidence for Bures--Wasserstein Boundary Dynamics in the Living Human Brain

When substrate-constrained covariance flow on the Bures--Wasserstein manifold reaches the Williamson boundary, single-mode compression saturates and further admissible covariance evolution is forced into the cross-mode complement. This paper derives how that substrate boundary transition becomes experimentally visible in an embedded spin probe in the living human brain. We formulate a boundary-conditioned transfer theorem: when the substrate enters the deep boundary regime in a coupled mode, the boundary-selected cross-mode continuation of substrate covariance flow enters the reduced spin dynamics as a nonzero inter-spin correlation block. The spin probe does not inherit the substrate boundary as a state; it detects the boundary indirectly through the transferred cross-mode sector of the reduced dynamics. To leading order, this transfer is selective: it acts through an additive cross-diffusion channel while leaving conventional single-mode NMR observables such as \(T_1\), \(T_2\), linewidths, and the ordinary single-quantum response dominated by the thermal background. Projecting the induced spin cross-mode structure into the two-spin algebra, we argue that the experimentally relevant dominant recipient is the double-quantum SU(1,1) pair sector rather than the compact zero-quantum SU(2) exchange sector. We then derive the coherence-transfer pathway through which this double-quantum pair coherence is converted into a detectable signal by the \(45^\circ\)--gradient--\(45^\circ\) readout block.

q-bio.NC↗
arXiv2022

Experimental evidence of non-classical brain functions

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.

physics.gen-ph↗