Papers

We investigate domain-wall physics in a non-Hermitian Su-Schrieffer-Heeger model featuring the non-Hermitian skin effect and its higher-dimensional extensions, focusing on analytical eigenstate solutions under open boundary conditions. By gluing two Su-Schrieffer-Heeger chains with inverted coupling ratios together, we identify two distinct interface geometries, and derive closed-form quantization conditions for the complex wave number and wave functions using symmetry-based ansatzes. Besides conventional skin modes and topological zero modes, the domain walls generate additional localized states at finite energy that detach from the bulk open-boundary-condition continuum. We validate the analytical results by exact diagonalization, and further generalize the interface construction to a two-dimensional Lieb lattice, where competing nonreciprocities produce tunable funneling regimes towards codimension-one and codimension-two interfaces.

Loading multiple quantum states in parallel into a quantum machine learning (QML) model can unlock learning tasks where key information resides in the relations between states rather than in individual states. We introduce an adaptive relational learning framework for such multi-instance quantum data that accesses pairwise and higher-order relations. Our model combines global measurements via SWAP or CYCLE tests for evaluating an $n$-state Bargmann invariant with shallow trainable transformations applied locally to each input state. We demonstrate the approach for continuous-variable (CV) photonic systems, which naturally provide access to quantum data and necessary computing operations. We solve tasks involving hidden relationship detection, geometric phase classification, and sensing in the presence of an unknown shared nuisance interaction. We benchmark the adaptive model against a non-adaptive “measure-first” approach based on continuous-variable classical shadows, and show that the cost of shadow estimation grows rapidly with $n$, while our model avoids this dependence. Already for $n=2$, we achieve perfect test accuracy $A=1.0$ with $500$ inference shots, improving average test accuracy over the shadow-based method by $\Delta A=0.15$ while using $100$ times fewer shots per data point. Our work opens routes to sensing and quantum-data applications where adaptive photonic QML can access relational features that are costly to recover with non-adaptive, measure-first models.

Quantum imaginarity, as a critical resource metric for quantifying intrinsic nonreal coherence encoded in quantum states, exhibits nontrivial evolutionary behaviors in curved spacetime backgrounds. This work focuses on bipartite Dirac field reduced states in the quantum atmosphere of a static Schwarzschild black hole, aiming to explore the modulation of three mainstream imaginarity measures by Hawking thermal radiation. We reveal that the relative-entropy imaginarity, the geometric imaginarity and robustness of imaginarity, the fully accessible state presents a valley-shaped radial profile with a local minimum inside the quantum atmosphere, while the cross-coupling and fully inaccessible states follow opposite peak-shaped trends. Further analysis demonstrates that the Hartle-Hawking constant significantly strengthens the redistribution effect of imaginarity across both regions, whereas an increase in the event horizon radius weakens such redistribution and flattens the extremum features. These findings offer a new perspective for decoding the information structure of black hole quantum atmospheres and the intrinsic quantum nature of Hawking radiation.

Exceptional points are topological defects of complex band structures that are stable against weak perturbations, yet in two-band systems with bounded non-Hermitian couplings they are ultimately removed by a sufficiently strong Hermitian field. Here we demonstrate a striking exception in a two-dimensional subwavelength atomic array. Along a continuous square-to-triangular deformation at fixed magnetic field, the bulk passes between line-gapped topological regions with \textcolor{black}{band Chern numbers \( (C_1,C_2)=(2,-2) \)} through a gapless exceptional region. Within a finite interval of lattice deformation, increasing the magnetic field merely drives the exceptional points toward the light cone because of the singular radiative dipolar couplings. We further show that skin localization toward open boundaries responds non-monotonically to the same field. An intermediate field drives a bipolar skin localization, with bulk modes from different spectral branches accumulating at opposite boundaries, whereas stronger fields suppress boundary localization. Our results establish the interplay of lattice geometry, light-cone singularity, and Hermitian magnetic field as a route to engineering Chern and exceptional topology beyond the conventional strong-field limit.

By consuming multiple copies of an unknown qubit state, one can modify its purity while preserving the direction of its Bloch vector. We determine the maximum linear rate at which qubit states of different purities can be interconverted, allowing a nonzero error, quantified, for instance, by the trace distance, provided that it vanishes in the limit of infinitely many copies. Interestingly, the optimal conversion rate is determined by the two eigenvalues of the complex right-logarithmic-derivative (RLD) Fisher information matrix associated with $\mathrm{SU}(2)$ rotations of the qubit state. When the output qubits have higher purity, corresponding to concentration, the optimal rate is given by the ratio of the maximum eigenvalues of the input and output RLD matrices. In contrast, when the output qubits have lower purity, corresponding to dilution, the optimal rate is given by the ratio of their minimum eigenvalues. Remarkably, both concentration and dilution can be implemented using SWAP tests as the only nontrivial two-qubit measurement primitive, together with ancillary qubits initially prepared in maximally mixed states, without requiring any additional two-qubit gates. Our work thus provides a novel operational interpretation of the full complex RLD Fisher information matrix. Crucially, its antisymmetric, purely imaginary part encodes geometric information beyond the statistical distance between density operators and plays an essential role in determining the optimal state-conversion rates.

The generalised quantum Stein's lemma is a key result in quantum hypothesis testing, and connects this fundamental primitive of quantum information processing with quantum resource manipulation, a task that is central for technological applications. Prior works have proved this statement in the idealised setting of independent and identically distributed (i.i.d.) sequences of quantum states, and recent extensions consider also sources that are 'close' to i.i.d., according to the strict notion put forth by Mazzola, Sutter, and Renner. For several applications, however, one would need to consider yet more general sources. We establish a version of the generalised quantum Stein's lemma that is conceptually much simpler and general, as it applies to any source that is asymptotically close to an i.i.d. state with respect to the normalised quantum Wasserstein distance of order 1. As an immediate consequence, we solve the Stein exponent of a scenario where the null hypothesis is arbitrarily varying, expressing it in terms of i.i.d. Stein exponents corresponding to arbitrary states in the convex hull of the null hypothesis base set.

A system between a preparation and a post-selection has had no agreed state since 1964. With positivity as the criterion, a post-selection admits an interval of orderings around the symmetric one exactly when the subspace it forbids is spanned by eigenvectors of a full-rank filtered state. Otherwise it certifies contextuality, testable on a qubit. The averaged filtered state carries the entanglement spectrum of the record, so the smallest forbidden subspaces a symmetry allows are even-dimensional in the Haldane class and odd in the trivial one. That parity is the record's topological class.

We present an open source Python package, ConteXtuAlity, for computing various quantities related to contextuality. This package features an interface to the sheaf-theoretic framework for contextuality, providing an implementation of measurement scenarios and empirical models as well as linear programs to compute the contextual fraction and the signalling fraction. In this work, we demonstrate the package's features and give examples of its use. We also provide benchmarks, demonstrating how performances scale with the size of measurement scenarios. The package is designed for both experienced theorists and newcomers to the field of contextuality alike, with an emphasis on flexibility and extensibility.

Standards bodies report cryptographic security as a single number of bits, but this value depends on the adversary cost model used to price time, memory, and quantum resources. Different conventions can therefore produce different rankings of cryptographic schemes. GAUGE represents security as a function over admissible cost models, called a security profile. Comparisons then become comparisons between profiles, and ranking reversals become an explicit structural property rather than a measurement error. We formalize price functionals over a cone of adversary cost models, show that security profiles are piecewise-linear and concave, and prove a rating trilemma: when two profiles cross, no rating can simultaneously be faithful to underlying costs, total over comparable pairs, and independent of the chosen cost model. We provide a polynomial-time linear-programming procedure that certifies whether the ranking of two schemes is robust, reverses under admissible models, or is genuinely incomparable. We extend GAUGE with a two-layer risk measure combining stochastic cryptanalytic decay with uncertainty over the appropriate cost model. We evaluate the framework on NIST post-quantum standards, classical anchors, and a 25-year chronology of cryptanalytic breaks. The analysis certifies a ranking reversal for ML-KEM-512 versus AES-128 from a 4-5% shift in memory pricing, and measures a lattice-sieving cost drift of 9.79 bits per year over eight years. A hybrid X25519 + ML-KEM-768 handshake reduces combined-break probability twenty-fold at a 2.3 kilobyte cost. The artifact reproduces all tables and figures in under seven seconds. GAUGE provides an explicit and auditable framework for reporting cryptographic security under competing cost models.

Entanglement in indistinguishable particle systems can be characterized by the impossibility of unambiguously attributing a complete set of physical properties to the individual constituent particles. In this work, we introduce a geometric quantifier of the incompatibility of such simultaneous property attribution for pure states of $N$ indistinguishable bosons. Using the Majorana stellar representation, any symmetric multi-qubit state can be expressed as the symmetrization of constituent single-particle states, allowing the associated single-particle properties to be directly linked with the corresponding Majorana stars. This establishes a direct connection between the geometry of the Majorana representation on the Bloch sphere and the entanglement criterion based on the attribution of single-particle properties in systems of identical two-level bosons. We then generalize this geometric approach to higher-dimensional bosons, extending the quantifier from qubits to qudits, while retaining a geometric interpretation of property-attribution incompatibility in terms of Fubini-Study angles.

When a classical Brownian particle is subjected to a temperature gradient it can undergo thermophoresis, i.e., the particle gets transported towards the colder regions of the environment, which bears relevant consequences to nonequilibrium self-organization. Here, we investigate how the quantum Brownian motion is affected by a temperature gradient. We employ a recently proposed generalized system-plus-reservoir model, where one assumes a continuum field of thermal baths. As our main result, we obtain the quantum influence functional, within the Feynmann-Vernon path integral approach. To test convergence, we derive an effective Langevin equation for the center of mass of the quantum wavepacket, and show that it coincides with the classical Langevin equation at high temperatures. Both the fully quantum (low temperatures) and the semiclassical (high temperature) limits show signatures of quantum thermophoresis in the quantum Brownian motion, a so far unexplored effect.

Stabilizer states constitute an important class of quantum states that can be generated from computational-basis states using Pauli operators and Clifford gates. Although they may exhibit substantial multipartite entanglement, quantum circuits restricted to stabilizer operations can be efficiently simulated classically and therefore cannot, by themselves, provide a quantum computational advantage. Such an advantage requires non-stabilizer resources, commonly referred to as quantum magic. In this paper, we investigate the non-stabilizerness of quantum states arising in a class of spin Hamiltonians by computing their stabilizer Rényi entropies. Using real-space renormalization-group techniques, we obtain a closed-form expression valid in the low-energy, large-distance regime. We analyze how quantum magic evolves under coarse-graining and explore its behavior across different parameter regimes and quantum phases.

We investigate the quantum Mpemba effect in a graphene nanotorus qubit and show that its strength depends strongly on how the initial state is prepared. We compare two protocols that share the same final Hamiltonian, thermal bath, and Markovian Liouvillian: bare Gibbs preparation, in which the coherent drive is switched on only at the final quench, and driven steady-state preparation, in which the initial states are stationary states of the driven dynamics. Using the distance to the final stationary state and an integrated Mpemba parameter, we find broad regions of strong anomalous relaxation for bare Gibbs preparation, with $M_B$ approaching unity, whereas the driven steady-state protocol almost completely suppresses the effect. A Liouvillian-mode analysis reveals the mechanism: the bare Gibbs protocol typically yields a smaller hot-state weight in the slow active sector than the cold state, $R_s<1$, while the driven steady-state protocol predominantly gives $R_s>1$. Since the final Liouvillian spectrum is identical for both protocols at corresponding parameter points, the contrast originates from preparation-dependent modal weights rather than from changes in the decay-rate hierarchy. These results identify state preparation as a control parameter for anomalous quantum relaxation in a curved graphene qubit.

Parametric interactions are foundational to superconducting quantum technologies, yet conventional microwave-driven pumping introduces parasitic Kerr nonlinearities and higher-order harmonics that limit device performance. Josephson Photonics (JP) avoids these parasitics by utilizing dc-biased junctions but has remained constrained by high phase noise and the absence of a stable phase reference. Here, we overcome this limitation by integrating a Josephson voltage standard (JVS) to establish a noise-tolerant phase reference, and demonstrate that this reference is coherently transferred to an inelastic Cooper-pair tunneling amplifier (ICTA) via the superconducting order parameter. The resulting low-phase-noise architecture yields a 14-dB enhancement in averaged gain and better quantum-limited noise performance. Critically, the phase reference enables the first observation of phase-sensitive gain and squeezing in a dc-biased amplifier. By reconciling clean, Kerr-free nonlinearities with phase-coherent drive, our architecture establishes a robust platform for high-purity parametric processes in superconducting circuits.

We present a claim-relative evidence/reference framework for hybrid quantum-classical workflow integrity. Observational indistinguishability yields structural blind regions, distinct from finite-batch statistical misses. Within the declared lattice, a trusted same-batch scalar $R_0$ suffices for conclusion integrity, aggregate $M_0$ for aggregate plus conclusion integrity, and item-aligned binding for item identity. In 3,600 label interventions, feature/prediction views realize exact label-path invariance; all 764 geometry-aligned aggregate-blind rows equal their paired-clean responses, giving zero attack-only increment. For statistical response, the geometry-aligned construction detects 343/2,700 conclusion-changing ($\tau \to 0^+$) label interventions with the conformal rule and 1,183/2,700 with the uncorrected union; the original frozen same-item geometry yields 11/2,617 and 43/2,617, respectively. The executed conformal clean false-action rates are 0.048–0.059 descriptively; its finite-sample guarantee requires exchangeability, which the overlapping-draw design violates. The cluster-preserving adaptive stress test (Gate A) reduces response versus matched controls in 25–40 of 40 environment/split cells while retaining conclusion changes. A bounded 165-design-cell ideal-statevector and finite-shot-emulation branch directly instantiates semantic, estimated and observed kernel transitions. The fixed equal-weight design estimates neither deployment prevalence nor QPU, provider or deployed-service assurance.

An accurate theoretical treatment of periodically driven quantum systems is crucial for various fields in the exact sciences, for instance Nuclear Magnetic Resonance (NMR) spectroscopy. Conventionally, either average Hamiltonian theory or Floquet theory is used to predict or describe experimental outcomes, such as the time evolution or the spectra yielding the information of the sample under study. A detailed analysis of the equivalence of these two approaches with an emphasis on applications in NMR will help to improve the theoretical understanding of NMR experiments. In this work, we identify the Floquet-Magnus expansion as essential to prove the mathematical equivalence of Floquet theory and average Hamiltonian theory. We advocate a calculation scheme which is less prone to algebraic mistakes because explicit integration is avoided. On this basis, we provide the first four orders of both theories. We further examine their applicability to some experiments in NMR. As examples, we investigate the Bloch-Siegert shift and dipolar coupled spin systems under magic-angle spinning. Based on our analysis, we recommend the use of the Floquet-Van Vleck approach including both the effective Hamiltonian and the kick operator. The consistent separation of secular and non-secular contributions appears to be especially advantageous for numerical robustness. Its accuracy is about three times better than the one provided by average Hamiltonian theory despite their formal equivalence. Our findings provide important insights into the theoretical background of Floquet theory and average Hamiltonian theory. This includes the extent of their algebraic and perturbative equivalence, with an emphasis on how these findings are of relevance in the analysis of solid-state NMR experiments.

Thouless pumping is a celebrated topological effect that enables quantized particle transport and holds promise for applications in quantum technologies. However, the standard adiabatic pumping theory dictate that the Hamiltonian must be varied continuously and slowly throughout the whole pumping process. In this work, we show that Thouless pumping can be realized by using only discrete sampling of the Hamiltonian, removing the conventional constraint of continuous and slow change of control. Specifically, we select particular parameter points of the Hamiltonian for conventional continuous quantum adiabatic evolution, and then apply the Hamiltonian at these parameter points which induces a geodesic evolution for the pseudospin with a given quasimomentum. This realizes an adiabatic evolution for the Thouless pumping according to a necessary and sufficient condition for quantum adiabatic evolution.

Simulating nuclear magnetic resonance (NMR) spectra is a promising application of quantum simulation. Using Quantinuum's System Model H2, a trapped-ion quantum computer, we demonstrate an end-to-end, large-scale digital NMR simulation of a classically challenging benchmark molecule, 1,2-di-tert-butyl-diphosphane. We implement a hardware-efficient reduction of the nuclear-spin Hamiltonian, enabling Trotterized real-time evolution of an effective 21-spin model with tailored error suppression to reduce the effects of device noise. The reconstructed liquid-state proton NMR spectrum agrees with classical reference calculations and reproduces key spectroscopic features that previous quantum hardware demonstrations did not capture. Given the widespread use of NMR in chemical analysis and industrial research, these results advance digital quantum simulation of NMR spectra towards practical quantum utility.

This course on two-dimensional quantum gases, prepared for the São Paulo ICTP-SAIFR IVth School on Light and Cold Atoms, is organized into three lectures. The first introductory lecture addresses Bose-Einstein condensation in an ideal gas, the effect of interactions in the weakly interacting limit, Gross-Pitaevskii equation and its hydrodynamic formulation, as well as superfluidity. The second lecture is devoted to the main features of two-dimensional quantum gases: importance of the interactions, enhanced phase fluctuations and the emergence of a quasi long-range order, superfluidity through the Berezinskii-Kosterlitz-Thouless mechanism, scaling symmetry. The third lecture has taken the form of a seminar on fast rotating quasi two-dimensional Bose gases and thermal melting of the vortex lattice. The slides accompanying these notes can be found on the school website: https://www.ictp-saifr.org/slca2025/.

In order to solve practical problems on a quantum computer, it is necessary to use fault-tolerant quantum error correction schemes to overcome noise: the errors arising from imperfections in physical components. The Gottesman-Kitaev-Preskill (GKP) code aims at achieving this in a hardware efficient manner by encoding finite-dimensional logical subspaces in the Hilbert space of one or more continuous variable modes. In near term implementations, however, it is not feasible to eliminate errors entirely, so it is natural to also employ alternative error mitigation techniques together with error correction. In this work, we study a quantum error mitigation method known as probabilistic error cancellation in the context of the GKP code. We compare Steane-type and teleportation-based GKP error correction, and calculate the sampling overheads associated with the technique for square and hexagonal GKP codes. We employ the stabilizer subsystem decomposition for GKP codes to obtain an effective logical channel for noisy operations that is used to express the ideal one of a target logical unitary. We consider noise from finite squeezing on the data and the two ancilla modes, needed for error correction, and examine the relationship between the sampling overhead and the noise for different decoding methods. Our results are calculated for single- and two-qubit GKP Clifford gates and one round of error correction, and show the nontrivial combination of error correction and mitigation in continuous variable codes.

Muon-spin rotation/relaxation is one of the most powerful microscopic probes for understanding magnetic order, spin dynamics, superconductivity, and complex magnetic phases in emerging quantum materials. Quantitative interpretation depends critically on the accurate identification of the muon stopping site, a problem traditionally addressed using density functional theory-based structural relaxation. However, conventional DFT approaches are computationally demanding, time-consuming, and require extensive calculations. Here, we develop MEOWN (Muon Engine for Optimized Weighted Networks), a machine-learning-based, physics-informed computational framework that combines a Polarizable Unperturbed Electrostatic Potential (P-UEP) model with machine-learning-guided optimization and symmetry-driven relaxation to predict energetically favorable muon stopping sites in crystalline solids. MEOWN explicitly incorporates electrostatic interactions, electronic screening, polarization effects, and zero-point motion into the learning workflow, providing physically interpretable predictions with substantially reduced computational cost while maintaining physical consistency and scientific rigor. To validate the framework, we investigated several well-established benchmark materials, including MnSi, CoF2, CaF2, LiF, and NaF. The predicted muon stopping sites and dipolar fields are in close agreement with previously reported DFT+mu results, demonstrating the reliability and transferability of the approach across chemically diverse systems. Notably, MEOWN predicts the equilibrium muon stopping site within a few minutes, offering a significant speedup over conventional DFT-based calculations. This manuscript presents the theoretical foundations, computational methodology, and validation of MEOWN as a general-purpose software for rapid and reliable muon stopping-site prediction in crystalline materials.

In order to circumvent that no universal set of gates can be achieved on a given quantum error-correcting codes, additional gates can be performed through magic state injection. This however requires to have access to high fidelity magic state, which can be obtained by the distillation of low quality states to fewer higher quality ones. In this paper, we provide a family of distillation protocols able to produce diagonal states at every level of the Clifford hierarchy. This family is obtained recursively using code doubling techniques and leveraging qubit recycling, the fact that some idle qubits of the protocols can be measured and re-used. At a given level of the Clifford hierarchy, we show that the protocols we derive can be performed at arbitrary high distance on a fix number of logical qubits. This family recovers many known efficient protocols, and uncovers new ones, such as a $111 \to 1$ protocol for $|T\rangle$ state distillation at distance $7$, which are the most compact in term of volume. Finally, we discuss possible extension of this framework for distillation protocols producing more than one output state.

Eigenstate thermalization fixes the smooth energy-resolved envelope of few-body observables but not the microscopic overlap statistics that realize it. In the multi-resolvent hierarchy, this missing information appears in a two-resolvent fluctuation sector. We solve that sector exactly in a tractable benchmark, random free fermions, obtaining a non-Porter-Thomas intensity hierarchy, a structured channel-distance covariance, and an exact overlap kernel that closes the two-resolvent covariance. We then reconstruct the same sector without using its exact solution: a projected self-consistency scheme fixes the irreducible vertex through independently computable projections, while unconstrained residuals identify the sectors missed by a minimal ansatz and are completed exactly by a finite-size Weingarten evaluation, without fitting. For interacting deformations, we prove a model-independent moment identity showing that the deep-plane coefficients are fixed by Hamiltonian-moment covariances. This yields an exact rigidity law: pair-hopping interactions freeze the sector, dense perturbations add only an isotropic layer, and density-density interactions produce an explicit polynomial deformation in channel geometry. By contrast, the bulk sector requires the interacting eigenstate-overlap kernel and exhibits a logarithmically divergent perturbative response. The fluctuation sector therefore splits into a rigid moment-determined part and an intrinsically nonperturbative eigenstate-resolved part.

We derive a thermodynamic uncertainty relation for work in an open quantum system driven by a time-dependent protocol and subject to repeated projective energy measurements. The protocol is represented by a sequence of protocol quenches separated by finite-time Lindblad evolution, so that work is accumulated at the quenches while dissipation occurs between them. The resulting work statistics obey the Gallavotti-Cohen symmetry to give rise to the Crooks and Jarzynski fluctuation relations. By perturbing the dissipative dynamics and combining the Cramér–Rao inequality with the quantum Fisher information, we obtain $\mathrm{Var}\,W/[\tau\partial_\tau\langle W\rangle]^2\ge 1/F\ge\max(1/A,2/E)$, where $\langle W\rangle$ is the work expectation value, $\mathrm{Var}\,W$ is the variance of work, $F$ is the Fisher information, $A$ is the dynamical activity, $E$ is the dimensionless entropy production, and $\tau$ is the switching time interval between quenches. The two thermodynamic bounds follow from two independent perturbations that generate the same response of the work statistics. We illustrate the relation for a dissipative two-level system under square-wave and sinusoidal driving and show that the tighter thermodynamic bound can depend on the driving protocol and switching time scale.

We study strictly localized mixed states in quantum field theory: states that are indistinguishable from vacuum outside some spacetime region. Such states are generated from the vacuum by so-called Licht maps. While the states associated with individual outcomes of local, projective measurements on the vacuum are not strictly localized, the corresponding non-selective states are strictly localized and even admit decompositions into strictly localized pure states. Remarkably, however, there are strictly localized mixed states that cannot be written as mixtures of pure states strictly localized to the same region. Such states can arise from unsharp local measurements. Finally, we extend Knight's theorem to mixed states, showing that strictly localized bosonic mixed states contain terms with arbitrarily high particle numbers.

We theoretically investigate the indistinguishability of single photons generated from single trapped $^{40}$Ca$^+$ ions in a Raman scattering process driven by few-nanosecond excitation pulses. Of particular interest is how spontaneous decay back to the initial state affects Hong-Ou-Mandel (HOM) photon interference. Numerical simulations identify the mean number of back-decays as a measurable quantity that correlates with achievable HOM visibility. Optimization of the excitation pulse with respect to a trade-off between photon yield and indistinguishability is analyzed. Finally, we compare the performance of different trapped-ion species for long-range dual-rail entanglement swapping via HOM photon interference.

Low-dimensional Dirac systems offer a versatile platform for quantum-geometric non-linear transport. Hexagonal warping in topological insulator (TI) surface states generates rich momentum-space geometric textures. However, mirror and time-reversal symmetries strictly constrain both the Berry curvature and quantum metric dipoles to zero. Here, we show that proximity-coupling a hexagonally warped TI to a d-wave altermagnet lifts spatial mirror symmetry via the interplay of C_{3v} warping and d-wave spin-splitting. This symmetry breaking enables finite Berry curvature dipole components, which, however, remain heavily suppressed near charge neutrality, establishing the intrinsic quantum metric dipole as the sole driver of the non-linear Hall response. This scattering-independent response vanishes at \mu = 0 and exhibits odd parity under chemical potential inversion. Importantly, rotating the altermagnetic orientation angle \phi continuously tunes quantum metric dipole and induces a sign reversal, peaking near \phi=0 and vanishing at \phi = \pi/4. Our findings highlight TI-altermagnet interfaces as ideal candidates for gate- and orientation-tunable quantum metric spintronics.

Entanglement can enhance precision in phase estimation and in frequency estimation with atomic clocks, but it remains a central challenge to identify useful states and measurements under realistic noise processes. Here, we study quantum metrology with an ensemble of atoms subject to spontaneous emission, which limits frequency estimation by constraining the useful interrogation time. We identify spin grid states (SGSs) as the relevant near-optimal probes beyond a crossover at an ensemble size of 51, where GHZ-like states cease to be optimal. SGSs display a periodic grid on the Bloch sphere and can be generated with two one-axis-twisting (OAT) operations separated by a collective rotation. By optimizing the quantum Fisher information over permutationally symmetric states, we find that SGSs perform close to the globally optimal probes for intermediate and large ensembles, which turn out to be spin GKP states. We further present a sequential readout strategy that nearly saturates the corresponding quantum Fisher information. This strategy uses an OAT echo to map spontaneous-emission events onto collective rotations, making the corresponding jump sectors distinguishable and allowing the measurement basis to be conditioned on the number of decay events. Together, these results show that SGSs provide a practical route to quantum-enhanced phase and frequency metrology in atomic ensembles limited by spontaneous emission.

We introduce a robust quantum communication protocol that integrates classical error-control coding, entanglement distribution, and superdense coding. Classical error-correcting codes are used to mitigate dark counts and photon losses by determining the positions of qubit transmissions and protecting the data embedded through superdense coding. We derive conditions on the employed codes that guarantee successful error correction under a bounded error-frequency model. Moreover, upper bounds are derived on the performance of conventional superdense coding protected by classical error correction. It is shown that, under the same constraints on error frequency, suitable code configurations of the proposed protocol can exceed those upper bounds both in terms of data rate and energy efficiency. Finally, we develop a physical error model based on fiber attenuation, detector efficiency, dark counts, and time-slot duration, and use it to evaluate the effective performance of different configurations of error-correcting codes. The proposed approach is primarily suited for short-distance quantum links, as in Quantum Local Area Network (QLAN) where it can provide high communication throughput while integrating entanglement distribution directly into the communication process.

Nonlocal magic quantifies the minimum nonstabilizerness attainable under independent local unitary transformations on the two subsystems. Here, we use min-relative nonlocal magic (NLM) to characterize the crossover from ergodicity to many-body localization (MBL) in the random-field XXZ chain. Unlike entanglement entropy, NLM probes how entanglement is organized through the distance of the Schmidt spectrum from dyadic-flat stabilizer spectra. From weak to intermediate disorder, NLM evolves from an $O(1)$ Haar-like value into a size-enhanced dome, while entanglement remains volume-law, revealing a spectral reorganization not visible in the entropy. Deep in the MBL regime, a two-level cut-hybridization model captures the nearly binary Schmidt spectrum and explains why the mean and median NLM decay approximately as $W^{-1}$ and $W^{-2}$, respectively. Following a product-state quench, NLM overshoots and relaxes in the ergodic regime, whereas at strong disorder it grows slowly and approximately logarithmically. These results show that NLM resolves Schmidt-spectrum structure not visible in the entanglement entropy and provides a complementary probe of ergodicity breaking.