Papers

Stable bound states living on a discrete one-dimensional N-point lattice are assumed generated by a certain two-parametric PT symmetric potential $V=V(A,B)$. At any $N$, the coordinates $A=A^{(EP)}$ and $B=B^{(EP)}$ of the Kato's exceptional point (marking the phase-transition instant of the loss of stability) are defined, exactly, via roots of a certain elementary quartic polynomial.

Strong dynamical symmetries provide an algebraic description of persistent oscillations in open quantum systems governed by the Lindblad equation. For finite-dimensional systems with a full-rank stationary state, such symmetries are necessary and sufficient for non-decaying oscillatory modes to appear in the Liouvillian's spectrum. These modes can be directly constructed by acting on stationary states with the identified symmetry operators. Here we establish an asymptotic counterpart of this algebra for collective spins. Taking a single spin $S$ in a magnetic field, subject to dissipation through linear jump operators, we identify the exact conditions on the field and dissipative couplings under which non-decaying oscillatory modes emerge as $S \rightarrow \infty$. We then write down a simple, closed form for the corresponding `symmetry' operator which can be applied to the steady state to construct these modes, which are eigenvectors of the Liouvillian, with imaginary eigenvalues, up to $O(1/S)$ corrections. A second operator, an emergent conserved quantity, completes the algebra, and its slow relaxation determines how quantum noise selects the stationary state. The construction can be directly extended to a pair of interacting spins sharing a common reservoir, with the resulting quantum algebra making the entanglement during a quench analytically accessible.

Since ancient Greek times, geometry has been a method by which humans can make inferences, by the use of similar triangles, about the world far beyond their immediate senses. Similarity plays an equally important role in quantum measurement, except that instead of triangles, the similarity is between the infinitesimal generators of rotation, canonical transformation, or some other virtual symmetry. For many quantum optical measurements of a single mode, these generators produce Kraus operators that are contained within a twelve-dimensional Lie group: the Instrumental Weyl-Heisenberg group manifold ($\mathrm{IWH}^{\textbf{12}}$). In particular, $\mathrm{IWH}^{\textbf{12}}$ is general enough to include all diffusively generated 'dyne measurements. In this paper, $\mathrm{IWH}^{\textbf{12}}$ will be used to develop two more general classes of 'dyne measurement: one that interpolates between diffusive homodyne and diffusive heterodyne (“slomodyne”) and one that adds to 'dyne measurements adaptive squeezing and displacement. Our analysis uses an approach known as the Instrument Manifold Program (IMP). In particular, a Harish-Chandra-like decomposition of $\mathrm{IWH}^{\textbf{12}}$ is used to calculate the vielbein transformation from a right-invariant basis to the corresponding coordinate basis, allowing us to universally and autonomously navigate $\mathrm{IWH}^{\textbf{12}}$ and locate the Kraus-operator of whatever selective process is being considered as it evolves in time according to the measurement record.

Bell's theorem is popularly stated as the inconsistency of quantum theory with local realism. Realism is here formalized by the ontological models framework, where elements of reality are points of a measurable space and probabilities obey the Kolmogorov axioms. In the Bell scenario, locally causal ontological models posit a common cause supporting a global valuation, a joint assignment of outcomes to all measurements at once, across incompatible contexts. Within this notion of realism, Bell's theorem makes any realist explanation of the quantum predictions conspiratorial: any mechanism, whether superluminal, superdeterministic, or retrocausal, must be finely tuned so as never to manifest operationally. We redefine realism through a new ontological framework that generalizes the standard one. The elements of reality, which we call records, are no longer points but relational parts of a point-free generalization of a topological space (sublocales of a locale). A record shared by two incompatible contexts establishes the sameness of a measurement across them, without such pairwise identities composing into a global valuation, and the common cause is then a web of such records. Within this framework, Bell's no-go theorem becomes a go theorem: local causality, restated for records, is no longer at odds with the quantum statistics. This is possible because modularity, the inclusion-exclusion law of classical probability, fails across incompatible contexts, so that the probability theory generalizes Kolmogorov's. We exhibit explicit models reproducing several quantum strategies, including the optimal CHSH violation. More broadly, locally causal models of this kind attain every Bell-CHSH value up to the algebraic maximum. A realist explanation of the quantum predictions need not be conspiratorial; every causal influence posited by these models is reflected in the operational predictions.

Quantum state texture (QST) is a recently proposed quantum resource that characterizes the nonuniformity of a density matrix in a given computational basis. In the resource theory of QST, the Fourier states f_k are maximally resourceful states, attaining the maximum QST measure. We study the QST behavior of three maximally resourceful states in a two-mode Dirac field under Hawking radiation from a Schwarzschild black hole, using a fidelity-based measure. We consider three cases: only mode B undergoes radiation, only mode A undergoes radiation, and both modes undergo radiation simultaneously. Our results show that for single-mode radiation, if the mode unaffected by radiation is orthogonal to the single-mode textureless state, the QST of the overall output state remains maximal and is independent of the Hawking temperature; we call this phenomenon orthogonality protection. When both modes undergo radiation simultaneously, orthogonality protection vanishes, and the QST of all three Fourier states decreases with increasing Hawking temperature. Notably, the QST measure of f_3 under two-mode radiation is higher than that under only mode B radiation, indicating that QST can be redistributed among modes: QST gained by one mode under radiation can partially compensate for QST lost by the other. We further provide a general resource-theoretic explanation of orthogonality protection, showing that this phenomenon is independent of the specific form of the QST measure. These results reveal how QST degrades under Hawking radiation and provide a new perspective on the redistribution of quantum resources in black hole backgrounds.

Hexagonal boron nitride (hBN) is a promising material platform for quantum technologies, enabling both the realization of nanophotonic devices and the hosting of point defects that act as high-quality single-photon emitters (SPEs). Among these defects, B centers, which reproducibly emit at 436 nm, can be generated individually at predefined positions using electron beam irradiation, a crucial capability for top-down quantum photonics. Yet, the spatial accuracy of emitter creation strongly conditions the potential applications. Here, we generate arrays of individual B centers in a scanning electron microscope (SEM) with in-situ cathodoluminescence (CL) monitoring. We characterize the sources of random deviations from the target positions to identify the limitations to their deterministic positioning. In particular, we measure the distance between the electron beam and the emitter at the moment the emitter is created based on CL mapping. This approach provides a direct estimation of the spatial extent of the beam-emitter interaction. We find this contribution to be the main constraint to the emitter fabrication accuracy, yielding a standard deviation of 27 nm. Additional contributions, primarily from the finite density of UV-emitting carbon dimer precursors, increase the overall positional standard deviation to 40 nm. Our results highlight the possible improvements to the B center creation technique to reach sub-10 nm accuracy.

As quantum hardware enters the fault-tolerant regime, algorithms are beginning to be executed on encoded qubits, yet scalable certification of how well they run remains an open problem. Here we introduce magic-free certification, a certification protocol for universal fault-tolerant circuits that consumes no magic, the resource that generally places them beyond efficient classical simulation and is by far the most expensive element of a fault-tolerant computation. The protocol is code- and decoder-agnostic, runs interleaved with the target circuit on the same device, and has a sample complexity that grows linearly with the number of logical qubits and non-Clifford gates while remaining decoupled from the logical error rate itself. Given a predefined error tolerance $p_L^*$, the protocol determines at a chosen confidence level whether the device executes the target circuit at a logical error rate below $p_L^*$. The method relies on trap circuits, copies of the target with every magic state replaced by a stabilizer state, whose outcomes are deterministic and which, being indistinguishable from the target to stochastic Pauli noise, fail at the same rate. We illustrate the protocol in Steane-code simulations of a magic state injection gadget and a quantum Fourier transform.

A central goal of quantum machine learning is to identify applications in which small quantum circuits can improve task performance while remaining executable on real hardware. We investigate deepfake (synthetic) speech detection, a largely unexplored application in this area, where reliable confidence scores are as important as discrimination performance because deployment decisions are made at fixed thresholds and overconfident errors can be costly. We introduce QBFF, which routes a compressed speech representation through a small 8-qubit variational circuit (VQC) used as a drop-in bottleneck, with a matched classical bottleneck as the control. The quantum circuit yields better-calibrated confidence in most matched comparisons, including out-of-distribution evaluation, though the downstream deployment-cost benefit is model-dependent. We then run the same circuit on a real IBM quantum processor. To our knowledge, this is the first anti-spoofing pipeline to run on a QPU; hardware execution demonstrates feasibility, with lower subset EER and $C_{llr}$ but higher mean actDCF than the matched classical reference. Together, these results show that hardware-executable quantum bottlenecks can improve score reliability, with gains that vary by evaluation setting.

We study a system of two quadratically-coupled harmonic oscillators, prepared respectively in the ground state and in a coherent state. This toy model can describe for instance the dynamics of one mode of a quantum field evolving in a harmonically-oscillating classical background. In such situations, it is well-known that, depending on the background oscillation amplitude and coupling strength, the system may exhibit parametric resonance. Using the Feynman-Vernon influence functional, we analyze the interplay between parametric resonance and quantum entanglement by perturbatively computing the purity of the mixed state resulting from tracing over one of the oscillators. We find a runaway behavior of the quantum entanglement between the two oscillators, as well as a rapid breakdown of the validity of perturbation theory, in regions of parametric instability. This provides a quantitative confirmation of various statements in the literature and is highly relevant to questions pertaining to the validity of the semiclassical approximation in coupled quantum-classical systems.

Randomized quantum algorithms for the estimation of expectation values of molecular observables offer a promising route to early fault-tolerant quantum advantage by trading circuit depth for an increased number of samples. However, this begs the question whether the resulting measurement overhead remains feasible for industrially relevant molecular systems. In this work, we benchmark the randomized sampling algorithm of Wang et al. [1] through numerical simulations on a hydrogen molecule and resource estimates for various active spaces of the cytochrome P450, an industry-relevant system in the pharmaceutical industry. Our numerical simulations reveal that the analytical error bounds significantly overestimate the actual sampling error, whereas the analytical bound on the required imaginary evolution time is comparatively tight, exceeding a direct DMRG estimate by roughly 44% for the active space where the comparison is feasible. The measurement overhead nevertheless remains prohibitively high: even for the smallest active spaces, the expectation-value estimation alone requires around 1010 samples, scaling to beyond 1015 for the largest active spaces considered. These results suggest that substantial improvements in measurement strategies or algorithmic scaling are necessary before randomized early-fault-tolerant algorithms become competitive for industrial quantum chemistry applications.

We propose Pathfinder-BP, a recursive decoder for topological quantum codes that combines belief propagation with controlled bit-flipping. An initial BP pass identifies and permanently fixes high-confidence errors. Upon convergence failure, the decoder recursively explores alternative error patterns by tentatively flipping low-confidence variables. On surface codes, Pathfinder-BP achieves a noise threshold and logical error rate comparable to minimum-weight perfect matching (MWPM). A crucial advantage of Pathfinder-BP is its highly parallelizable structure, which yields a worst-case decoding latency quasi-linear in the code distance, making it a suitable candidate for low-latency hardware implementation.

An isolated quantum system evolves reversibly, yet a small subsystem can lose nearly all information about its initial state. Conserved quantities may retain some of this information, depending on how strongly they overlap with local observables. Here we consider a subsystem in an arbitrary initial state coupled to a maximally mixed bath. We show that the worst-input mean-square equilibration error, maximised over window origins, is bounded from above and below by the mean square of a complete local autocorrelation, with the stationary part subtracted. A correlation record over a finite interval therefore controls the equilibration error in every interval of the same length. The result allows arbitrary degeneracies of energies and gaps. We apply it to two static Hamiltonian families. For fixed spin subsystems in the one-particle sector of a bounded-range periodic clock, fixed-accuracy thermalisation is guaranteed on windows that grow only slightly faster than linearly with system size, despite exponentially small positive energies. A random commuting model with logarithmic interaction range retains an extensive set of conserved observables. Its expected mean-square error is bounded by a finite-size term and an inverse-time term. The inverse-time dependence is unavoidable because of the initial transient. These examples show how local relaxation can coexist with exact conservation laws and a finely spaced spectrum.

We construct representations of the symmetry algebra and derive the exact spectrum of a three-dimensional oscillator with two spin-$\tfrac12$ degrees of freedom. The Hamiltonian and its first-order scalar and pseudo-scalar integrals were obtained in earlier classifications. Here we determine their action on the complete spectral basis. At fixed total angular momentum, a quadratic algebra acts on the three triplet orbital channels and admits a three-dimensional deformed-oscillator representation, while an overlapping two-state exchange algebra joins the middle triplet to the singlet. These finite modules determine angular–spin multiplicities but do not quantize the radial energy. A separate positive-discrete-series $su(1,1)$ representation of the common radial Hamiltonian generates the energy sequence. We give the finite matrices, Casimir and structure functions, normalized eigenfunctions, radial ladder actions, the exceptional $j=0$ sector, complete energy-shell multiplicities, and the effect of particle interchange.

Quantum random number generators are crucial for information security, yet existing implementations are hindered by bulky optics, device imperfections, and state alignment constraints. Here, using a compact metasurface platform, we achieve polarization-independent certified randomness by establishing a quantitative quantum graph framework. By mapping multi-channel nanophotonic responses onto graph vertices, we assign metasurface measurements an operational information-theoretic meaning, directly connecting weighted graph degrees to conditional min-entropy estimation. The resulting graph-certified measurements yield robust private randomness even under entanglement-based attacks without complex optics. Experimentally, we fabricate 4- and 6-channel dielectric metasurfaces to implement high-dimensional positive operator-valued measure graphs, successfully certifying randomness with heralded single photons and Poissonian light. By integrating complex quantum measurements into a single passive layer, our metasurface quantum graphs provide a scalable route for integrated quantum technologies.

We show that completely positive maps can be decomposed into sums of submaps which are close in completely bounded trace norm but as far apart as possible in terms of geometric channel fidelity. We then show that this kind of behavior extends to a large class of quantum channel divergences. We construct quantitative norm estimates for quantum channel divergences in terms of the Arveson-Radon-Nikodym theorem.

In this PhD thesis, we take an axiomatic approach to studying multivariate divergences, which are measures of the information content of a tuple of classical or quantum states. These divergences are studied in the context of large-sample and catalytic convertibility of tuples of states. This type of convertibility is characterized by the ordering of an axiomatically defined family of divergences. In this thesis, we identify this family of divergences explicitly for two scenarios, one classical and one quantum. In the classical setting, we show that the relevant divergences are certain generalizations of the bivariate Rényi divergences. Unlike previous studies, we do not require the distributions to have the same support, yielding interesting new divergences. In the quantum setting, we consider pairs of classical-quantum states with pure component states, and find that majorization is characterized by all $\alpha$-$z$ relative entropies for $\alpha<1$. This demonstrates the first operational interpretation of these relative entropies.

Genuine multipartite entanglement (GME) is a valuable resource for quantum technologies, but quantifying it in many-body systems can be demanding since measures defined through optimizations over bipartitions are often assumed to require large joint measurements and many measurement settings. We introduce the concepts of GME evaluation length and GME evaluation number, which capture, respectively, the largest subsystem that must be jointly measured and the number of distinct subsystems that need to be measured to evaluate multipartite entanglement measures defined via bipartition optimizations. Taking the genuine multipartite concurrence (GMC) as a canonical example, we show that, for $N$-qubit Haar-random pure states, the GMC can be evaluated using only $N$ single-qubit purity measurements. Thus, for typical many-body states, evaluating the GMC requires considering only the $N$ single-site bipartitions, rather than the exponentially many distinct bipartitions. We further corroborate this behavior numerically for physically accessible states generated by local random quantum circuits. Our results show that the practical cost of quantifying GME can be dramatically lower than suggested by its formal definition, establishing measurement complexity as a complementary operational lens for multipartite entanglement.

A one-dimensional waveguide is a crucial medium for transferring propagating quantum information between remote qubits, yet the photon-mediated interaction is typically fixed by the static device geometry, qubit parameters, and their couplings to the transmission line. Such an interaction can be engineered to be coherent or dissipative via virtual- or real-photon exchange, respectively, yet its effective strength remains fixed in either case. Here we demonstrate dynamical control over this interaction by applying Floquet engineering to two superconducting qubits coupled to a waveguide terminated by a capacitive mirror. By positioning one qubit at an antinode and the other qubit at a node or an antinode of the resonant standing wave, we realize a Hermitian or non-Hermitian coupling between the two qubits. A periodic flux drive of the qubit frequencies then enables on-demand control of the coherent energy splitting and the collective decay. Our results establish Floquet engineering as a route to dynamically reshape both coherent and dissipative photon-mediated interactions between remote quantum emitters.

The Tarski fixed-point problem asks for a fixed point of a monotone map on a $k$-dimensional grid lattice of width $n$ and has applications in game theory, economics, and verification. Substantial gaps remain between the known upper and lower bounds on its quantum query complexity. We prove two hardness bootstrapping theorems for quantum query lower bounds. Starting from a hard instance family whose instances have pair-wise incomparable unique fixed points, and a lower bound established by the nonnegative adversary method, we bootstrap this lower bound by (i) a factor of $\Omega(t)$ when the dimension is multiplied by $t$ and the width remains unchanged, and (ii) a factor of $\Omega(\log m)$ when the width is multiplied by $m$ and the dimension is doubled. Applying these theorems, we obtain three consequences: (i) an $\Omega(k\log^2 n)$ lower bound for $k\geq 4$, improving previously best-known classical and quantum lower bounds; (ii) for every fixed constant $\alpha>0$, there exists a constant $\delta(\alpha)>0$ such that $Q_\epsilon(\text{Tarski}(n,k))=\Omega(kn^{\delta(\alpha)})$ whenever $k>n^\alpha$, and in particular, an $\Omega(kn^{0.0072})$ lower bound for $k>n^{2/203}$, the first lower bound with simultaneous linear dependence on the dimension and polynomial dependence on the width; and (iii) a superpolynomial lower bound of $(k/\log k)^{\Omega(\log k)}$ for exponentially wide grids, where $n=2^{\Theta(k)}$. The last result rules out a route to polynomial-time algorithms for simple stochastic games and ARRIVAL through generic polynomial-query black-box Tarski solvers.

Deterministic preparation of bosonic resource states is a central task in continuous-variable quantum information processing and quantum metrology. Here we develop a measurement-based imaginary time evolution (MITE) protocol for preparing squeezed and non-Gaussian states. The protocol combines ancilla-mediated weak measurements of the Hamiltonian with a conditional phase rotation that suppresses excited state trapping and stabilizes convergence toward the ground state. The method is potentially applicable in hybrid discrete variable-continuous variable (DV-CV) platforms, where the qubit acts as the measurement readout. We demonstrate deterministic convergence over a broad range of parameters and show that the performance degradation near the stability boundary is governed by the shrinking Bogoliubov quasiparticle gap. The same framework also extends to non-Gaussian bosonic resource states, including Schrödinger cat states and excited states of the single-mode squeezing Hamiltonian, which display Wigner negativity. The squeezed states remain robust under bosonic loss over experimentally relevant regimes.

Quantum teleportation, a key building block for quantum technologies, enables distant parties, Alice and Bob, to transfer an unknown quantum state using entanglement, local operations, and classical communication. In this work, we propose a quantum teleportation protocol for single-photon time-frequency continuous variables, where time is the time of arrival at a detector. We detail the operational requirements of the protocol, notably the nonlinear interactions needed for the photon-photon time-frequency entangling gate. By explicitly treating the detector position as the reference frame for time of arrival, we show that, even with ideal classical and quantum channels, the input-output fidelity is not unity unless the receiving party can correct the detector-position mismatch. This results in a trade-off between teleportation fidelity and the temporal bandwidth of the input photon wavepacket. The protocol itself can be used for remote detector synchronization. In particular, we show that time-frequency cat and Gottesman-Kitaev-Preskill states provide an internal temporal ruler through fidelity revivals. We further derive the classical and best-copy fidelity thresholds for single-photon Gaussian wavepackets, finding that the relevant vacuum-equivalent shot noise is input-dependent, in contrast with quadrature-based continuous-variable quantum teleportation. Our proposal derives from a quantum theory of space-time events, whereafter we establish space as a reference for the time degree of freedom, thereby grounding our work in ongoing research on reference frames and superselection rules in quantum optics and quantum information. Beyond protocols harnessing time-frequency continuous variables of single photons, this work points toward remote synchronization in quantum communication architectures.

The spectral form factor (SFF), which is the Fourier transform of the two-point spectral correlation, is a fundamental diagnostics of quantum chaos. Nevertheless, its experimental detection in quantum many-body systems was less unexplored until recently. Here, we establish a relationship between the SFF with the quantum Fisher information (QFI) by means of quantum sensing protocols. Furthermore, when the eigenvalues and eigenstates of the disordered Hamiltonian are statistically independent, we prove that QFI is typical both in short and long timescales while numerics suggest that it is also typical at intermediate timescales, which ensures self-averaging of QFI. The self-averaging property renders the experimental measurement of QFI with our protocol less noisy in contrast with the direct measurement of SFF which is known to be non-self-averaging. Our results reveal an intriguing connection between quantum noise and the signatures of quantum chaos.

Label noise is prevalent in medical image datasets, arising from observer disagreement and ambiguous cases and deep networks memorize the mislabeled examples at the cost of generalization. Current solutions such as loss correction and sample selection add training complexity and generally assume the noise rate is known or estimable. This paper investigates whether robustness can be obtained architecturally, by routing a frozen backbone's features through a low-dimensional bounded bottleneck and classifying them with a head whose function class is intrinsically smooth. Variational quantum circuits with angle encoding and a linear cost function realise exactly such a class. Their use in medical imaging, however, has been limited by the small number of qubits available on noisy intermediate-scale devices, which typically restricts inputs to low-resolution grayscale images. We therefore couple a frozen ImageNet-pretrained ViT-B/16 backbone to a trainable linear bottleneck and an eight-qubit variational quantum circuit, allowing 224x224 RGB inputs to be processed. Under clean labels the model leads five of six MedMNISTv2 benchmarks against published hybrid quantum-classical models, with margins of 17.4 and 15.7 percentages on BloodMNIST and PathMNIST. The advantage emerges under corrupted labels. At symmetric noise rates of 30% and 50% the model outperforms many published quantum and noise-robust classical baselines on all six datasets without any explicit noise-handling component. Against a control that shares the backbone, bottleneck, parameter count and optimizer and replaces only the circuit with a ReLU layer, it retains 89.75% accuracy on PathMNIST at 50% noise where the control falls to 78.96%. Direct measurement of training dynamics shows that this advantage is not an inability to fit corrupted labels, which the circuit retains, but greater stability under prolonged training on them.

Predicting quantum-photonic circuit performance requires retaining source and device physics without making photon-counting calculations prohibitively expensive. Here we present PhoQuS, a framework that combines frequency-resolved source models, electromagnetic compact models and spatially correlated fabrication variation to simulate quantum photonic circuits. Covariance-Gram reduction after full-resolution Gaussian propagation lowers readout cost while retaining dominant spectral correlations. For continuous-variable state preparation, spectral reduction accelerates photon counting by 60.4-fold in an approximate Gottesman-Kitaev-Preskill circuit. Frequency-resolved modeling guides the use of cascaded squeezing with temporal walk-off compensation, yielding 0.99 fidelity to the single-mode circuit reference and 0.98 conditional purity in lossless simulations. For discrete-variable state preparation, simulations of three-photon Greenberger-Horne-Zeilinger circuits across a virtual wafer show that component robustness alone does not predict circuit fidelity, which depends jointly on source spectra, circuit architecture and control. PhoQuS connects device physics to protocol-level performance through a unified workflow that retains spectral detail while reducing readout cost.

We consider an orthogonal basis of $\mathbb C^2\otimes\mathbb C^2$ with three entangled states and one product state. This basis is not perfectly distinguishable by LOCC or even by separable measurements when a single copy of the unknown state is available. We show that with two copies no adaptive separable protocol, which measures the copies one at a time, distinguishes the basis perfectly. We then show that a collective separable measurement on the two copies does. Whether two copies suffice for LOCC remains open.

Quantum few-body systems exhibit a rich variety of phenomena that provide fundamental insights into universality. A paradigmatic example is the Efimov effect, in which an infinite tower of three-body bound states emerges with binding energies forming a geometric sequence. Motivated by advances in trapped-ion systems, recent theoretical work has predicted that the Efimov effect can arise in certain long-range quantum spin chains, where magnons exhibit a general dispersion $\epsilon_k=u|k|^z$ with $z\in(0.52,0.88)$ and interact through a contact potential. Nevertheless, whether Efimov universality persists in the presence of experimentally relevant long-range interactions between magnons remains unexplored. In this work, we address this issue by investigating the two- and three-magnon problems with a model interaction potential $V(x)=V_0/(1+|x|^\beta)$. Our results demonstrate that few-body universality persists for any $\beta>1$: In the two-magnon sector, the low-energy expansion of the scattering matrix near a two-body resonance agrees with the universal form predicted by contact-interaction theory. The three-magnon bound-state spectrum exhibits Efimov scaling, with a scaling factor consistent with the theory. We further highlight the experimental relevance of our model, which can be readily realized in trapped-ion systems. Our results pave the way for quantum simulations of universal few-body physics beyond the traditional paradigm of nonrelativistic particles.

Authentication in quantum-aware communication settings requires mechanisms that verify user legitimacy while also assessing whether the communication channel exhibits excessive disturbance. This paper presents QIAP, a stateful hybrid framework that combines classical commitment-based challenge-response authentication with BB84-based quantum-channel monitoring. QIAP uses a dual-branch verification structure inspired by rectilinear and diagonal basis selection. In the rectilinear branch, the prover opens a hash-based commitment and the verifier checks consistency with the registered round token. In the diagonal branch, the prover returns an HMAC tag bound to the verifier nonce, round identifier, and submitted commitment without disclosing the round-specific sub-secret. Under the stated hash, HMAC, freshness, secure-registration, protected-storage, and high-entropy-secret assumptions, QIAP provides computational resistance to the modeled wrong-secret and replay attempts and protects the long-term master secret from direct recovery. After successful authentication, the BB84 module estimates the quantum bit error rate (QBER) and aborts the session when the measured value reaches or exceeds the configured threshold. In the reported simulation, no successful authentication was observed among 1,000 tested wrong-secret attempts per branch. The baseline and full intercept-resend conditions produced mean QBER values of approximately 0.02 and 0.25, respectively. The classical authentication stage required approximately 0.6 ms, and the implemented authentication messages required approximately 113 bytes per round. These results indicate that QIAP can provide a lightweight hybrid framework for combining secret-based identity verification with QBER-based channel-disturbance assessment under the stated threat model.

Precise manipulation of qubits (spins) requires strong suppression of noise arising from couplings between qubits and their environment, as well as from driving field fluctuations. We propose a double-pulse sequence and an eighteen-pulse sequence to realize a single spin pi-rotation under off-resonance conditions (instead of conventional on-resonance or near-resonance conditions). It is proved that the latter sequence performs much better than the former in simultaneously suppressing both dephasing and driving field noise. As a proof of principle, we experimentally demonstrate, by implementing both sequences in an NMR spin system with a polarized initial spin state, that the off-resonance pi-rotation fidelity reaches as high as 0.9992 +/- 0.0008 for the double-pulse sequence and 0.9997 +/- 0.0006 for the eighteen-pulse sequence. In addition, the noise-tolerance range of the eighteen-pulse sequence is about 20 percent of the driving field strength, approximately three times wider than that of the double-pulse sequence. Besides its potential application in the NMR community, our proposal provides an alternative practical way to accurately control qubits by suppressing the coexisting transversal and longitudinal noises.

An exactly solvable lattice with periodic inverse-square singularities exhibits two physically distinct mechanisms of spectral-gap closure. The model arises from the generalized trigonometric Pöschl-Teller potential in the coupling range where both local solutions at each singularity are square-integrable. A transmitting, current-preserving self-adjoint matching condition connects neighboring cells and generates a nontrivial Bloch spectrum. For a generic lattice with two inequivalent singular sublattices, the spectrum contains two alternating families of gaps, and the band edges reproduce the scale-invariant spectra of the associated finite singular system. One gap family closes when the two sublattices become equivalent. In this symmetric limit, however, the primitive period halves, so the apparent band crossing results from Brillouin-zone folding. A different family closes at a critical but genuinely asymmetric configuration. Because the primitive period is preserved, adjacent bands then meet at the center of the original Brillouin zone in a genuine massless Dirac-like cone. Near either critical limit, a small finite gap acts as an effective Dirac mass: the dispersion remains quadratic near a band edge but crosses over to a massive Dirac-like form beyond that narrow region. The band curvatures define effective electron and hole masses. Exact Bloch eigenfunctions further reveal that isospectral lattices can display different single-particle probability densities. This model therefore provides an analytically controlled one-dimensional setting in which conventional quadratic carriers, massive Dirac-like band dispersions, and a tunable massless contact coexist within the same singular lattice.

We show that a common quantum-jump feedback protocol can permanently reverse the nonequilibrium free-energy ordering of two prescribed initial states while preserving their Gibbs equilibrium. The construction exploits collective compensation between monitored channels: their feedback corrections cancel at equilibrium but remain active during relaxation. This balance preserves free-energy monotonicity while allowing the relaxation modes to be reshaped. We prove that eliminating the complete slow-sector contribution of the initially higher-free-energy state, while retaining it for the comparison state, produces distinct asymptotic decay exponents. Their free-energy ratio then vanishes at long times, guaranteeing a permanent thermodynamic quantum Mpemba inversion under the same controlled dynamics. A thermal qutrit realizes the mechanism through coherence interference and exhibits distinct detection thresholds for spectral selection and exact slow-sector cancellation under feedback retuning.