Papers

Full quantum network nonlocality (FQNN) describes a scenario where all sources in a network are nonlocal. Existing criteria of FQNN can only be verified in star networks by violating a single Bell-like inequality. Here we propose a method that certifies FQNN in general quantum networks using only a single Bell-like inequality. We show that the topological obstacle to one-shot detection can be overcome by expanding the original network with a carefully chosen number of auxiliary local sources and parties. The correlations of the enlarged network are then tested with a single inequality; a violation implies that all original sources must be nonlocal. Our approach provides an efficient, experimentally friendly way to verify FQNN in any network topology.

We investigate the steady-state phase transition in a one-dimensional hybrid contact process. We implement the single-site and cluster mean-field approximations based on the effective fields and present all the possible steady states of the system. We show the existence of the stable absorbing and active phases, and the bistable region in the long-time limit. The saddle-node bifurcation is observed at the boundary between the absorbing phase and the bistable region, suggesting a discontinuous phase transition. While the absorbing to active phase transition is continuous. To characterize the nonclassical scaling behavior of the continuous phase transition, we extract the true critical points and exponents by means of the coherent anomaly method.

Two-photon blockade (TPB) besides the conventional one-photon blockade can control the photon at the level of individual quanta in the input-output measurements of light-matter coupling systems. Apart from conventional TPB (C-TPB) with opened cascade decay channel, unconventional TPB (U-TPB) with closed cascade decay channel may open novel avenues for manipulation of TPB. However, currently found U-TPB in linear coupling is limited in a narrow coupling window and the blockade strength is weak, which would hinder its applications. In the present work we propose to enhance the U-TPB by the Stark nonlinear coupling. Indeed, the introduction of the Stark nonlinear coupling to the linear coupling enables tuning of both cascade energy level and the anharmonicity which play key roles in the formation of TPBs. By investigating photon correlation functions and extracting phase diagrams in dissipation, we demonstrate that our scheme not only dramatically broadens the window of U-TPB to cover the entire strong-coupling regime but also deepens the blockading degree of the U-TPB by two orders. The cascade decay rates, state populations and the anharmonicity, are examined to identify and track the U-TPB and C-TPB. In the overview of phase diagrams we also reveal a broad U-TPB in ultrastrong couplings, with a crossover to the C-TPB. Since the Stark nonlinear coupling is realizable and tailorable, our proposal may pave a practical way for manipulation of the TPB.

We study pure disjoint $(r,\delta)$-quantum locally recoverable codes (qLRCs) without assuming a stabilizer structure. We formulate local Knill–Laflamme conditions for recovery from up to $\delta-1$ erasures within a recovery block, and introduce blockwise Shor–Laflamme and unitary weight enumerators that capture how error weight is distributed across recovery sets. We establish several properties of these enumerators and use them to derive a Singleton-like bound that strengthens the known bound for disjoint $(r,\delta)$-qLRCs under a purity assumption, as well as a linear-programming upper bound on the code dimension. These results provide a non-stabilizer, weight-enumerator-based approach to the study of pure disjoint $(r,\delta)$-qLRCs.

Understanding how fermionic exchange and Coulomb repulsion jointly shape two-electron correlations is essential for identifying genuine quantum signatures in multi-electron interference experiments. To address this interplay, we investigate Hanbury Brown and Twiss interference of two electrons generated by two independent needle-tip emitters within a full quantum-mechanical framework. In the absence of Coulomb interaction, the approach reproduces the results previously obtained within a quantum path formalism. For Coulomb-interacting electrons, we predict characteristic features absent in a semiclassical description: a pronounced Coulomb-dominated suppression region as well as Coulomb-induced phase offsets and fringe shifts. At the same time, outside of the Coulomb-dominated region, the spatial oscillation frequency is essentially governed by fermionic exchange symmetry. Our results establish quantitative parameter regimes for disentangling Coulomb interaction from fermionic exchange symmetry in such experiments.

Dynamical decoupling protocols provide a versatile toolbox for robust control of quantum systems, suppressing noise that would otherwise limit their performance. This tutorial aims to provide an intuitive interpretation of these protocols. Written from an experimentalist's perspective, we use the Bloch sphere picture to visualise quantum dynamics for a range of sequences. Here each dynamical decoupling operation can be viewed as an "effective field vector", whilst the phase and population of the two-level system is encoded into a "Bloch vector". The two-level dynamics are calculated by the cross product between these two vectors, such that the quantum state represented by the Bloch vector rotates around the effective field vector. Several prominent control schemes are simulated using this picture, starting with a Rabi oscillation, followed by the Ramsey sequence and a selection of pulsed and continuous dynamical decoupling techniques. These sequences are engineered to preserve control of the quantum system for as long as possible, with their efficacy often quantified by a coherence time. We clarify the definition of the longitudinal $T_1$, transverse $T_2$ and inhomogeneous $T_2^*$ coherence times, which are used across the literature. Each simulation has an accompanying animation to illustrate the protocol's two-level dynamics on the Bloch sphere. The custom simulation and Bloch sphere plotting scripts are also provided in an open access repository to allow the reader to reproduce, modify, and explore these results. Dynamical decoupling sequences have established themselves as an invaluable tool across the entire quantum technologies remit; by providing an open framework alongside this tutorial, we aim to make these protocols more accessible to new researchers discovering this thriving field.

In this work, we study $(r,t,x)$ quantum locally recoverable codes (qLRCs) with locality $r$, $t$ recovery sets per qudit, and intersection parameter $x$. We first show that, assuming the underlying classical codes have dual minimum distance at least two, a CSS code is an $(r,t,x)$-qLRC if and only if the underlying classical codes are $(r,t,x)$ classical LRCs (cLRCs) with common recovery sets. We then use subset-inclusion matrices to construct families of binary dual-containing $(r,t,x)$-cLRCs, which yield binary $(r,t,x)$-qLRCs via the CSS construction. For CSS $(r,t,x)$-qLRCs, we derive upper bounds on the dimension and rate, minimum-distance bounds in the pure case, and a Singleton-like dimension bound in the exact case. Finally, we show that these families attain high rates and nontrivial minimum distances.

The formation of Fabry Perot and guided wave self hybridized exciton polaritons in two dimensional materials results in long range exciton energy transfer and strong exciton exciton interactions. Here, we demonstrate that the coupling strength between photonic modes and excitons is significantly boosted by embedding the active excitonic layer in a metal clad WS2 waveguide. The photonic modes in this waveguide exhibit modified dispersion properties for both Fabry Perot type and guided wave exciton polaritons compared to pure WS2 flakes, and show an increased couplingr strength. Our results provide a robust approach for controlling exciton photon interactions and their coupling strength in hybrid heterostructures.

Optomechanical systems offer a promising platform for observing dynamical signatures of quantum gravity through precision measurements of quantum harmonic oscillator dynamics. However, most existing analyses consider only the linear radiation-pressure interaction while neglecting higher-order optomechanical couplings and laser phase noise. These neglected contributions can be comparable in magnitude to the predicted quantum-gravity corrections and may therefore introduce spurious signals or mask the genuine physical effect. Here we reanalyze two experimentally realized platforms, a Fabry-Perot optomechanical system and a membrane-in-the-middle optomechanical system, by incorporating the complete nonlinear dynamics and realistic laser phase noise. Using measured device parameters, we derive revised protocols for generalized uncertainty principle tests and establish practical sensitivity bounds. Our results demonstrate that previous idealized estimates significantly overestimate the achievable resolution, underscoring the necessity of including higher-order interactions and implementing effective laser phase noise suppression in realistic assessments of optomechanical quantum gravity tests.

Quantum software patterns provide high-level abstractions for building quantum programs, but there is still little empirical evidence on how they are adopted in practice. In prior work, we extended an existing quantum-pattern atlas into a 61-pattern catalog, created a knowledge base that links framework components to those patterns, and built a tool that mines pattern implementations from open-source code. We applied this tool on 80 projects and find that all 23 patterns occur in practice. In this work, we extend the tool with two additional matching channels and a vocabulary expansion step, and execute a quantitative evaluation of its accuracy on Qrisp, a framework not present in the knowledge base, reaching a micro-F1 of 0.712 against 0.449 without the expansion step. We then construct composition graphs that record calls among the high-level framework components associated with patterns and store them in a graph database. We use these graphs to examine how pattern implementations are assembled inside each framework, why patterns co-occur, and how much of a pattern's detection count comes from components called directly by developers rather than introduced through internal framework calls. We release qpa, an open-source mining pipeline, together with the knowledge base, which maps 286 framework components across five sources to the pattern catalog, maintained with the support of an LLM ensemble that classifies newly extracted components, and the resulting pattern usage dataset, to support reproducible studies on the adoption and evolution of quantum patterns.

We develop an analytical theory of anomalous transport in a noninteracting Anderson model with heavy-tailed hopping amplitudes. The broad distribution of hopping amplitudes gives rise to an extended intermediate-time regime with a subdiffusive effective exponent, despite the absence of interactions or genuine many-body effects. By solving the transport equations analytically, we derive the time dependence of the mean-square displacement and identify a continuous crossover from an intermediate anomalous regime to asymptotically diffusive transport. As the localization transition is approached, the spatial extent of the subdiffusive window diverges parametrically, while the crossover to conventional diffusion remains finite in units of $\Gamma_0^{-1}$. This produces an increasingly broad anomalous transport regime in space that can closely resemble Griffiths-type transport observed near the many-body localization transition. Our results demonstrate that rare hopping processes alone provide a microscopic single-particle mechanism for robust transport anomalies, establishing an analytical benchmark for distinguishing interaction-induced effects from disorder-driven dynamics.

Although considered a niche technique, muon spectroscopy provides a unique and complementary insight into a range of different materials from hard condensed matter to biological samples and everything in between. In matter, the muon has a mass of $\frac{1}{9}~m_p$ or $207~m_e$, and is a local probe of quantum states that can provide a focus on the bulk properties of materials. While often interpreted in a classical framework, the muon is itself a quantum particle and it is increasingly common for researchers to take account of this when thinking about muon spectroscopy experiments. In this perspective, we focus on the power of using this quantum treatment of muon spectroscopy, which is a key future direction for the technique.

Free electrons, driven by rapid advances in photon-induced near-field electron microscopy, have emerged as a promising platform for quantum information processing, including quantum computing and quantum sensing. However, conventional measurements that rely on the electron energy loss spectrum (EELS) are inherently destructive to electron qubits, thereby constraining their applicability. In this Letter, we propose a scheme that performs projection measurement on the electron comb basis, where high measurement precision can be achieved with bright squeezed vacuum states and strong PINEM couplings. Notably, this approach is not only nondestructive to electron qubits but also maximally incompatible with energy measurements, enabling alternative quantum information applications, such as quantum error mitigation and Einstein-Podolsky-Rosen steering detection. Our findings open an avenue towards a systematic understanding of quantum free electrons and towards the development of nondestructive free electron quantum information tasks.

For the often encountered problem of the Poisson equation, this work presents a quantum algorithm solving it based on the quantum Fourier transform (QFT) for periodic boundary conditions as well as free field conditions, where the latter is realized via the Hockney method. Besides the QFT and an initialization procedure for amplitude encoding, the algorithm just uses a procedure for multiplying the state vector by a diagonal matrix w.r.t. amplitude encoding. For the latter, two alternative implementations are considered here. The first variant is a version of the LCU method and the second is a sequence of multi-controlled rotation gates that represents a factoring of the multiplied values into absolute values and complex phase factors. The functionality of the algorithm is verified via comparing the results obtained from state vector simulations for one- and two-dimensional test examples with their analytical solutions. For the considered test examples, it is found that the success probability for obtaining the desired ancilla qubit subspace in the LCU version is a factor of around two higher than that for the sequence of multi-controlled rotation gates. However, the LCU version requires a number of ancilla qubits up to the number of qubits that is set to store the discretized source term of the Poisson equation in amplitude encoding, whereas the sequence of multi-controlled rotation gates demands only one ancilla qubit. Computations of the success probabilities for both variants furthermore indicate that the success probability converges for a specific problem with increasing resolution. Concerning the required computational resources for the quantum algorithm, the conclusion is drawn that while the QFT is a more efficient procedure than its classical counterpart, the current implementations of the other necessary steps in the algorithm diminish the efficiency w.r.t. the runtime.

Crystal anisotropy provides a powerful route for realizing direction-dependent transport in solid-state systems. While its influence on electronic transport is well established, the role of anisotropy in magnon spin transport in van der Waals magnets is largely unexplored. Here, in a nonlocal geometry, utilizing the monoclinic van der Waals antiferromagnet CrPS$_4$, we observe pronounced anisotropy in both electrically and in thermally excited magnon spin transport. Electrically generated magnons exhibit a magnon spin conductivity at least 2.2 times larger and a spin diffusion length at least 2.7 times longer for transport along the crystallographic-b axis compared to the crystallographic-a axis, where $\lambda_m^{a} \sim$ 211 nm and $\lambda_m^{b} \geq$ 575 nm. In comparison, at 8T, we find the nonlocal second-harmonic resistance associated with thermally excited magnons to be $\sim$7 times larger along the crystallographic-b axis at 25K. We further show that a magnon spin diffusion length cannot be reliably extracted from the nonlocal second-harmonic resistance, owing to the extended temperature profile within CrPS$_4$. Likewise, we show that the anisotropy in the spin Seebeck coefficients cannot be reliably estimated from the thermally excited magnon spin transport alone, as it is intertwined with the anisotropic heat conductivity of CrPS$_4$. Utilizing the electrically generated magnon spin transport, we demonstrate that intrinsic crystalline anisotropy serves as an effective control parameter for tuning magnon spin transport, opening new avenues for magnonic device engineering.

This paper develops a resource-bounded framework for evaluating practical controllability in open quantum systems using a trained graybox response model. Rather than treating controllability as a binary property of an idealised Hamiltonian model, the proposed approach evaluates the best-achievable process fidelity over a finite, hardware-realisable pulse family under explicit control constraints. The graybox model retains the known coherent dynamics while learning control-dependent open-system distortions from pulse-response data. The resulting surrogate predictions are used to reconstruct the implemented processes and compare them with Haar-random target gates. Practical controllability is then characterised through the distribution of best-achievable infidelities and an area-based summary metric. The framework is demonstrated for a driven qubit under closed-system, classical-noise, and combined quantum-plus-classical-noise dynamics, with pulse amplitude and inverse Gaussian width used as the control-resource coordinates. The results show how finite control resources and open-system noise jointly constrain the gate performance attainable by the chosen pulse family.

In systems with infinitely many degrees of freedom, fundamental results from quantum information theory can fail. An important example is the uniqueness of purifications: Even when two subsystems, described by commuting von Neumann algebras $A$ and $B$, are tomographically complete, purifications of a state on $A$ need not be related by unitaries in $B$. It was recently shown that this occurs precisely when Haag duality fails, i.e., when the commutant $B'$ is strictly larger than $A$. This raises the question of which fundamental entanglement properties survive in such a setting. We show that, for a pure global state, the ability to steer any ensemble decomposition of the marginal state on $A$ by measurements on $B$ is equivalent to the existence of a state-preserving conditional expectation from $B'$ onto $A$. This establishes a direct connection between quantum steering and subfactor theory. The key observation is that steering is equivalent to the existence of extensions of ensemble decompositions from $A$ to $B'$. Working with general Jordan algebras, we prove that unital positive maps have state-preserving left inverses if and only if ensemble decompositions can be lifted. For the inclusion $A\hookrightarrow B'$, a left inverse is precisely a conditional expectation, yielding the characterization above.

Two alternative approaches for studying Helium-like atomic ions in non-relativistic quantum mechanics are proposed: (I) a numerical approach, based on the Lagrange-mesh method which can easily reach up to 14-15 significant digits in the energy spectrum for any nuclear charge $Z$ with modest CPU time in single processor mode and (II) a highly-accurate, few-parametric interpolation formula for the energies vs. $Z$. The interpolation formula of general nature is proposed, it can be applied to the energies of any excited state of the helium-like sequence. It is based on matching the $1/Z$-expansion at large $Z$ and the Puiseux expansion with integer and half-integer powers around the so-called second critical charge $Z_B$, introduced by F and D Stillinger (1969, 1974), confirmed by the present authors in 2019 for the ground state $1^1 S$, then revisited here, and extended to the excited states in the present work. For example for the first two spin-singlet $1^1 S$, $2^1 S$ and the first two spin-triplet $2^3 S$, $3^3 S$ states this interpolation formula with nine free parameters can reach an accuracy of 10-14 significant digits (s.d.) in the energies for any physically-relevant nuclear charge $Z$, giving absolute accuracy at large $Z$. Many results are obtained for the first time.

The Uhlmann fidelity ${\rm F}(\rho_0,\rho_1) = {\rm tr}|\sqrt{\rho_0}\sqrt{\rho_1}|$ is one of the most fundamental quantities in quantum information theory for quantifying the closeness between two quantum states. Estimating the Uhlmann fidelity to within additive error $\varepsilon$ requires a number of copies of the states, or queries to their state-preparation circuits, that depends at least linearly on the smaller of the ranks of $\rho_0$ and $\rho_1$. Consequently, this rank dependence disappears when either state is pure, in which case the query and sample complexities depend only polynomially on $1/\varepsilon$. However, the known optimal estimator for ${\rm F}(\rho,|\psi\rangle\!\langle\psi|)$ due to Fang and Wang (ESA 2025) requires prior knowledge of which state is pure. In this work, we remove this mathematically unnecessary prior-knowledge requirement and establish an optimal estimator for ${\rm F}(\rho, |\psi\rangle\!\langle\psi|)$ under the sole promise that one of the two states is pure, without knowing which one. Our estimator is obtained by specializing the refined algorithmic Uhlmann transform of Utsumi, Nakata, Wang, and Takagi (2025) to the case where one state is pure. In this setting, the Uhlmann fidelity can be recovered as follows: apply a unitary dilation of ${\rm tr}_{\sf A}(|\psi_0\rangle\!\langle\psi_1|)$ (or its inverse) to the reference register $\sf R$ of the purification $|\psi_1\rangle$ (or $|\psi_0\rangle$) on the registers $\sf A$ and $\sf R$, estimate the corresponding square-root amplitude in each case, and take the maximum of the resulting two estimates.

Computational electromagnetics plays a central role in many industrial applications but often requires substantial computational resources, particularly when fine spatial discretizations are needed. While classical approaches remain the standard, quantum computing offers the potential to accelerate large-scale simulations by encoding them with a limited number of qubits. Here, we investigate the performance and resource scaling of the Harrow-Hassidim-Lloyd (HHL) and Quantum Singular Value Transformation (QSVT) algorithms for solving linear systems generated by the finite-difference time-domain (FDTD) method, a widely adopted numerical scheme for discretizing Maxwell's equations. We benchmark their performance across representative industrial use cases, including radar propagation, lens simulations, and beamforming processes. Our results demonstrate the validity of the approaches, achieving state infidelities smaller than $2\cdot 10^{-3}$ with success probabilities greater than $10^{-3}$, compatible with practical quantum state sampling. Overall, we observe that the QSVT method consistently delivers higher accuracy. We further observe that the condition number of the linear matrix, a key factor governing the performance of quantum solvers, saturates as the number of spatial lattice points increases. This implies that the spatial grid can be scaled to realistic industrial dimensions without increasing the HHL or QSVT circuit depth due to ill-conditioned matrices.

Understanding how complex connectivity emerges in networks is a fundamental challenge in classical and quantum science. In classical random networks, complex subgraphs typically require relatively high connection probabilities, whereas quantum random network theory predicts that such structures can arise at a single, lower threshold through entanglement and local operations. Here, using an integrated silicon photonic chip, we experimentally realize a quantum subgraph predicted by quantum random network theory in a four-node quantum random network. Our integrated platform exploits probabilistic photon-pair sources and coherent control of path modes to prepare a structured quantum subgraph through local transformations and postselection, operating in a threshold regime that differs from classical random networks. We verify that the subgraph state exhibits genuine high-dimensional multipartite entanglement across the nodes, providing experimental evidence that quantum entanglement enables connectivity structures beyond classical accessibility.

In this paper, we investigate zero transfer on mixed graphs. Zero transfer is a quantum walk phenomenon in which the transition amplitude between two vertices is identically zero for all times, so that no quantum state transfer occurs between them. Using the Hermitian adjacency matrix, we derive necessary and sufficient conditions for zero transfer in mixed graphs. We then specialize these criteria to oriented circulant graphs, obtaining nonexistence results for prime order, structural restrictions for even order, and exhaustive computational classifications for small orders.

Group-IV color centers, such as the silicon-vacancy (SiV) defect, are highly promising for solid-state quantum technologies. However, nanodiamonds typically exhibit significant lattice strain and structural disorder, which degrade their optical properties and hinder the resolution of the fine spectral structure at cryogenic temperatures. High-pressure high-temperature (HPHT) annealing offers a potential route to relax internal strain, although the phase stability of diamond at the nanoscale under such conditions remains poorly constrained. Here, we investigate the structural evolution of nanodiamonds during HPHT annealing using a Paris-Edinburgh press coupled with in situ synchrotron X-ray diffraction at SOLEIL. A dedicated sample assembly combining nanodiamonds - NaCl - Pt enabled accurate pressure-temperature calibration and real-time monitoring of phase transformations. The diffraction data reveal that the onset of diamond-to-graphite transition occurs at approximately 1800 K at 2 GPa and 2120 K at 4 GPa under the applied HPHT heating protocol. These experimentally determined graphitization onsets define a practical pressure-temperature processing window for HPHT annealing of nanodiamonds while avoiding detectable graphitization and provide a calibrated framework for reliable off-beam annealing treatments that avoid graphitization. Photoluminescence measurements on samples annealed below the graphitization threshold show improved optical response, with partial resolution of the SiV fine structure at 12 K. These optical measurements suggest a relationship between nanoscale phase stability and the optical response of individual SiV-containing nanodiamonds following HPHT annealing. The experimentally established HPHT processing window provides a practical framework for the controlled processing of quantum nanodiamonds while avoiding graphitization.

GKP states enable fault-tolerant CV quantum computation, but their generation remains experimentally challenging due to their highly non-Gaussian and infinite-energy ideal structure. In this work, we present a realistic and scalable protocol for generating finite-energy resource states, specifically the qunaught state, using Schrodinger cat states generated in a strongly coupled quantum dot-cavity system. Our scheme combines deterministic squeezed cat-state generation, cat-breeding protocols, and homodyne measurements. Using numerical simulations, we analyze the role of various parameters of the quantum dot-cavity system in the generation of practical qunaught states. Furthermore, we quantify the trade-off between the fidelity and generation probability of these states and exploit the fact that accepting a structured set of homodyne outcomes can significantly enhance the overall success rate. The proposed approach is compatible with integrated photonics and telecom wavelengths, offering a promising route toward scalable CV quantum information processing.

In fault-tolerant quantum computing, fast and accurate decoding is crucial. Snowflake is a decoder for the surface code that runs in a streaming fashion. In this paper, we implement Snowflake on commercial FPGAs and validate them at room and cryogenic temperatures. Our results demonstrate high decoding throughput for small code distances that, when extrapolated, remains within acceptable limits for larger distances. Further, we incorporate the calculation of certain decoder confidence scores with negligible overhead both in terms of latency and physical resource utilisation. We note that implementing a large-scale system would require either a large FPGA beyond today's technology or clusters of FPGAs connected via a high-speed bus. Thus, we discuss an alternative architecture that exploits the locality of Snowflake by processing 2D slices of the 3D decoding window and offloading segments of the 3D structure to a high-speed memory.

Exact cylindrical solutions of the free Dirac equation provide natural single-particle modes for a broad class of axially symmetric relativistic fermion systems, including electron vortices, twisted-particle scattering, rotating matter, and cylindrical field quantization, but are commonly formulated in different internal bases. We derive the general regular positive-energy cylindrical solution at fixed energy, transverse and longitudinal momenta, and total angular momentum, and show how the commonly used spin-polarized, separation, helicity, and transverse-helicity modes are embedded in the resulting two-dimensional solution space. A conserved transverse operator resolves the residual doublet into two symmetry-defined branches. Their parameter-dependent eigenspaces admit a gauge-invariant quantum-geometric characterization, with opposite Berry curvatures, a common quantum metric, and saturation of the two-level metric–curvature relation. We further derive symmetry constraints on branch conversion and the corresponding reduced two-state dynamics. The resulting framework connects mode classification, symmetry resolution, quantum geometry, and dynamics across distinct cylindrical Dirac settings.

How many distinguishable labels can a biological oscillator carry? Proposals invoking collective vibrational modes, endogenous electromagnetic fields, microtubule excitations and oscillatory phase codes are each debated on grounds particular to themselves, with no shared standard for comparison. We show that spectral distinguishability alone bounds the number of labels by the quality factor, M <= Q = 2 pi nu tau. This follows from the relation between linewidth and coherence time, so it is independent of substrate, of mechanism, and of any position on quantum effects in biology, and it can be evaluated from two published quantities. Applied to a recently proposed 30 GHz intracolumnar microwave field in cortex, it gives Q = 0.19: the linewidth exceeds the carrier five-fold. The obvious rescue, that a driven emitter can be spectrally narrower than its gain medium, requires a resonant cavity, and the model's own geometry forbids one. An independent bound on metabolic power is exceeded by five to nine orders of magnitude. Six further criteria follow from the same standpoint, including a two-sided persistence window requiring a label to be both readable and rewritable. Screening eleven carriers, only the low-frequency neural rhythms pass. High-frequency molecular carriers are eliminated by brevity, not by the fragility the debate has assumed.

A nonzero commutator proves that two orderings differ as operators, but it does not ensure that a physical state can reveal the difference. We ask when non-Abelian ordering information becomes dynamically invisible. For Hermitian operators $B$ and $C$, we compare the evolutions generated by the opposite-order products $M=(B+iC)(B-iC)$ and $\widetilde M=(B-iC)(B+iC)$, and define their operational visibility from the minimum overlap of the output states over a normalized time window. This visibility bounds the difference produced by the two orderings in every observable on the chosen state. An exact one-qubit solution shows that the same fixed pair can be perfectly invisible in one state and visible in another. We then keep the ordered generators fixed and vary only the many-body ground state across a quantum phase transition. The same ordering difference is nearly invisible in one regime and clearly visible in the other. Moreover, states with identical leading quadratic decay can develop sharply different finite-time visibility because their first distinction appears at higher order. The effect persists across distinct operator pairs and coefficient perturbations. Thus dynamical Abelianization is a property of the state-dependent process, i.e., non-Abelian ordering information can become operationally inaccessible even though the underlying operators remain non-commuting.

Quantum metrology achieves Heisenberg-limited precision in single-parameter estimation, but its multiparameter extension is fundamentally constrained by both parameter-encoding and measurement incompatibility. Noncommuting signal generators may cause incompatible parameter-encoding, preventing the quantum Fisher information matrix from simultaneously achieving the Heisenberg scale for all parameters. Due to incompatible optimal measurements, the classical Fisher information matrix represents the practical attainable precision. Here, we introduce a multiparameter metrology framework based on indefinite evolution (IE), in which different control operations and signal reversal are placed in a coherent superposition. For a single-qubit probe with mutually orthogonal signal generators, IE enables compatible parameter encoding and optimal measurement without the signal reversal. For parallel generators, where only signal reversal realized by its generator is available, IE can achieve the same performance. We further extend this mechanism to noisy, many-body, and high-dimensional probes, and establish general conditions for achieving the simultaneous Heisenberg-limit. In contrast, definite evolution cannot achieve the same performance under compatible optimal measurements, even when signal reversal is available. Our results identify IE as an operational resource for overcoming multiparameter incompatibility and open a route toward attainable Heisenberg-limited sensing in interferometric platforms.

Universal approximation in reservoir computing is typically associated with a class of reservoirs. We show that universality can be associated with a single reservoir, considering a minimal setup of a single atom in front of a mirror. In its linear-transducer limit, our reservoir is a universal approximator of fading-memory maps under an operating class of checkable conditions, with a rate constant measured at the operating point. A given reservoir can reach arbitrary accuracy by changing measurement settings. The proof gives an explicit recipe: for a target accuracy, it specifies the required physical resources and resonator modes. Enlarging the number of accessible modes increases the matchable kernel span without reducing capability. Beyond the linear limit, the atom's saturation replaces high-order polynomial readouts, and the device operates on real-world tasks alongside classical baselines. Our results highlight an example of universality with a minimal quantum setup.