Papers

A single operational protocol based on free evolution and projective measurements yields inequivalent quantum time distributions through distinct post-processing procedures. We construct an activity-based time-of-flow (TF) distribution and a presence-based quantum stroboscopic (QS) distribution, providing complementary operational notions of time. Applied to tunneling through a rectangular barrier, the regional QS mean saturates as the barrier width increases, whereas the TF mean first decreases and eventually grows for larger widths. These contrasting behaviors provide an operational interpretation of the Hartman effect, the apparent saturation of tunneling delay with increasing barrier width, in terms of quantum time distributions associated with flow through the exit region and occupation within the barrier, capturing the roles of early penetration, dominant reflection, and spectrally filtered transmission.

Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent developments have demonstrated that even classic models, like the Harper-Hofstadter model of free fermions on a lattice in a magnetic field, yield a host of crystalline symmetry protected topological invariants. Here we review some of these developments, focusing mainly on how to characterize, classify, and detect invariants arising from lattice translation and rotation symmetries along with charge conservation in two-dimensional systems, including integer and fractional Chern insulators.

We formulate a stochastic description of entropy production in scattering theory for coherent transport. We distinguish between the information entropy change due to partial knowledge of the leads' state and the thermodynamic entropy change due to the equilibration of each lead with its bath. By employing a two-point measurement scheme, we access the stochastic entropy production at these different stages of the process, as well as the statistics of generic transport quantities. When restricted to particle or energy transport, our approach reproduces the Landauer-Büttiker formulas. The possibility to consider more general quantities such as the entropy currents and their fluctuations, provides a systematic connection between stochastic thermodynamics and coherent transport.

We develop a general theory of null-constrained parameter estimation in a time-reversed Young (TRY) interferometer, where measurement is performed through programmable source-basis encoding with a fixed detector. We address the fundamental question of how to design source patterns that enforce a true metrological null – vanishing nominal response at the operating point – while preserving finite first-order sensitivity to the parameter. Under a general shot-noise-limited channel model, we show that the optimal null-constrained receiver is obtained by projecting the derivative response onto the subspace orthogonal to the nominal background in the inverse-noise metric. This yields a constructive solution in which the optimal source-basis code is given by the inverse-noise-weighted derivative response with its background-parallel component removed. We further derive an exact and universal information-retention law: the locally accessible Fisher information is reduced by a factor $1-\chi^2$, where $\chi$ quantifies the inverse-noise overlap between the nominal and derivative response vectors. This result establishes a precise geometric interpretation of the cost of null enforcement. Numerical examples demonstrate the null-coded TRY receivers can retain nearly the full local information and can be accurately implemented using binary and positive-only source patterns. These findings identify source-basis null engineering as a distinct and practically viable modality for derivative-mode sensing, with implications for superresolution metrology and programmable optical measurement architectures.

Bell-CHSH-like inequalities have been very successful in benchmarking spatial quantum correlations. However, as this paper illustrates, they are in general not sufficient for benchmarking temporal quantum correlations. To show this, we parametrise classical and quantum stochastic finite state generators based on a single bit and a single qubit, respectively, and compare the temporal correlations of their output sequences using a Bell-CHSH-like inequality. We find that for sequential measurements by two observers, Alice and Bob, classical machines can exceed the Tsirelson bound of $2\sqrt{2}$, due to their fundamental structure. However, when we consider a time delay between consecutive measurements, we find examples where the quantum machines outperform their classical counterparts by maintaining correlations longer under generally scrambling operations. Our result can be used to distinguish quantum from classical processes and to identify novel resources for quantum technology applications.

Strongly coupled quantum field theories in $(1+1)$ dimensions are notoriously hard to solve non-perturbatively. Variational methods, despite their success for quantum many-body physics on the lattice, have long lacked a natural ansatz adapted to the relativistic setting. This monograph explains the intuition behind relativistic continuous matrix product states (RCMPS), a variational ansatz tailored to $(1+1)$-dimensional QFT, and reports on several years of progress in developing and applying this approach. Using Riemannian optimization on the manifold of RCMPS, we obtain competitive non-perturbative approximations to ground state energies and local observables in the $\phi^4$, Sine-Gordon, and Sinh-Gordon models, including in strongly coupled regimes where perturbation theory fails. We then describe extensions to models with several interacting fields. Beyond energy density and local observables, we show how the framework can be used to evaluate non-local observables (defects) and, through an original linear programming approach, to extract spectral data such as particle masses. We close by discussing the current limitations of the method and the most promising directions for future work.

We develop a model-free framework for stabilizing quantum states using only empirical finite-difference evaluations of a measurement-derived Lyapunov observable. The controller requires no knowledge of the Hamiltonian, dissipative structure, or generator of the dynamics, and relies solely on discrete measurement data. The approach combines three key elements: sign-based Lyapunov descent, adaptive gain amplification, and a finite-difference analogue of LaSalle's invariance principle. We provide rigorous conditions under which these mechanisms guarantee asymptotic stabilization along the sampling instants in the drift-free case and practical input-to-state stability (ISS) in the presence of unknown drift and noise. The resulting feedback law is simple, derivative-free, and experimentally feasible. A qubit example illustrates the complete closed-loop scheme and the predicted ISS-type behavior. Although demonstrated on a single qubit, the theory applies to arbitrary finite-dimensional quantum systems and offers a foundation for further developments in stochastic, subspace, and multi-qudit model-free quantum control.

Precise time synchronisation underpins critical infrastructure from telecommunications and financial markets to power grids and scientific metrology. Several families of quantum protocols have been proposed and demonstrated for clock synchronisation and time distribution, exploiting entangled photon pairs, quantum key distribution (QKD) correlations, Hong-Ou-Mandel interference, and entangled clock networks. We critically assess these approaches, reviewing the main quantum time synchronisation (QTS) protocol families, quantifying the gap between theory and experiment, and identifying practical bottlenecks in sources, detectors, and channels. We survey the classical timing landscape from Network Time Protocol (NTP) and GPS to laboratory-grade optical frequency transfer, and compare quantum and classical methods at equivalent maturity. We examine use cases including financial trading, power grids, telecommunications, scientific metrology, and military applications, evaluating whether quantum timing offers a realistic advantage. We show that time transfer, not clock performance, is now the bottleneck for distributed optical timekeeping: the best demonstrated synchronisation uncertainty (2.46~ps) falls two to three orders of magnitude short of what optical clocks with fractional frequency uncertainties of $10^{-18}$–$10^{-19}$ require. Our assessment is that quantum time synchronisation will not replace classical methods for most applications in the near-to-medium future. Its near-term value lies in physical-layer security against timing manipulation and integration with quantum communication networks, while closing the synchronisation gap for scientific metrology remains the most critical open challenge.

Collective subradiant states in waveguide QED are highly sensitive to disorder, limiting their scalability and robustness. We propose a deterministic approach to engineering atom arrays based on a Minkowski sum construction, generating quasi-disordered structures with built-in correlations. This leads to mode-selective radiative coupling: interactions between dark modes are parametrically suppressed, while bright modes can hybridize. We study the stability of these subradiant and bound-state-like modes against moderate positional disorder. Our work provides a route to robust, analytically controllable subradiance through engineered quasi-disorder, with direct relevance to atom-waveguide and circuit QED experiments.

Encrypted cloning enables the redundant storage of an unknown qubit while remaining compatible with the no-cloning theorem, since only one clone can later be recovered through key-consuming decryption. Because encryption in this protocol is introduced to enable cloning-compatible redundancy rather than to guarantee confidentiality by design, its secrecy properties must be assessed explicitly. Here we classify the subsets of the encrypted-clone storage register into authorized, completely non-informative, and partially informative sets. We show that intermediate non-authorized subsets may retain only a restricted residual dependence on the input state, and we characterize exactly when this dependence occurs. The resulting leakage pattern is parity-dependent, revealing a structural confidentiality limitation of encrypted cloning.

We study entanglement dynamics among helicity degrees of freedom in quantum electrodynamics (QED) scattering processes. For generic initial states, we consider scattering at fixed momentum, corresponding to a generalized measurement described by a positive operator-valued measure, resulting in a post-measurement state. Such processes are modeled in terms of quantum maps, whose spectral structure fully determines the associated entanglement dynamics. For scattering involving fermions only, maximal entanglement present in the initial state is always preserved. Moreover, iterating the corresponding quantum maps on arbitrary initial states, we obtain the fixed points of the maps, which, in the largest number of cases, are asymptotic (pure) maximally entangled states. The structure of the maps also accounts for the entanglement dynamics in processes involving both fermions and photons. The defining properties of these maps originate from discrete symmetries of the QED interaction.

The concept of gapped symmetry-protected topological (SPT) states has been generalized to gapless SPT (gSPT) states. Similar to gapped SPT states, gSPT states in one dimension exhibit universal degeneracies in their entanglement spectra. The entanglement spectra of gSPT states are further described by boundary conformal field theories, whose systematic prediction is a key open question. To address this problem, we focus on the class of gSPT states that are obtained by applying unitary SPT entanglers to trivial, critical states in one dimension. We find that the reduced density matrix of a non-trivial gSPT state can be obtained, either exactly or approximately, by applying a quantum channel to the reduced density matrix of the trivial gSPT state. This quantum channel acts only near the entanglement cut and modifies its corresponding conformal boundary condition, allowing us in turn to predict the boundary conformal field theory describing the entanglement spectra. We apply this framework to gSPT states protected by various symmetries and having different central charges, and further analyze the stability of boundary conditions of the entanglement cut. Our work thereby provides a framework for systematically analyzing and understanding the entanglement spectra of gSPT states.

The realization of unitary designs is of fundamental interest in quantum science and typically requires the ability to implement structured quantum circuits. Recent developments have explored the possibility of generating unitary designs using only a small number of quantum quenches, in which the evolution during each interval is governed by a static Hamiltonian. In particular, it has been established that at least three chaotic Hamiltonians are required when only Hamiltonian evolutions are employed. In this work, we propose the emergence of unitary designs in the temporal ensemble of qubit systems evolved under two distinct chaotic Hamiltonians for sufficiently long times, supplemented by an intermediate random Pauli operation inserted between them. This result follows from the universal Pauli spectrum of chaotic Hamiltonians, a central concept in the study of non-stabilizerness. Our theoretical predictions are verified numerically using explicit examples, including Gaussian unitary ensemble Hamiltonians and random spin models. We further investigate finite-time and finite-size corrections to the protocol. Our results provide new insights into the dynamical generation of quantum randomness and offer a new route toward realizing unitary designs in chaotic systems.

Bound states in the continuum (BICs) are spatially localized eigenmodes that remain perfectly confined even though their energies reside within a continuum of radiating modes. BICs were predicted in 1929, but their experimental realization awaited more than 8 decades. Following their experimental observation, BICs were explored in a variety of wave systems, and found to exhibit a plethora of fundamental features such nontrivial topology and extremely high Q-factor. Recently, with foundational advances in the new field of electromagnetic waves in time-varying media, BICs were predicted to exist in the time domain, with their wavenumber embedded in a continuum of unbound momentum modes. Here, we present the first experimental realization of the time-domain Bound States in the Continuum. We use a transmission-line network with a time-modulated wave-impedance and show that a sinusoidal wave launched into the network naturally evolves into a time-domain BIC with a well-defined peak and decaying-oscillating tails. We show that the time-domain BIC is anti-symmetric despite the symmetric nature of the modulation. These experiments pave the way for exploring new phenomena in the fields of BICs and time-varying wave-systems in nonconservative regimes where time-translation symmetry is broken.

We study two spatially separated boundary subsystems coupled to a common structured environment under relative motion within a Gaussian open-system framework. By integrating out the environment, we obtain an influence functional governed by a dressed environmental correlator evaluated at the boundary positions. Its retarded and Hadamard components govern coherent mediation and correlated fluctuations, respectively. Relative motion activates the leading resonant contribution to correlated decoherence through Doppler-shifted spectral overlap of the boundary excitations. For identical boundary dispersions, this contribution has an ideal narrow-linewidth onset at $v>2u_\phi$. Below this value, no resonant momentum shell exists, whereas above it a finite shell opens and produces an enhanced correlated-decoherence contribution. Finite spectral linewidth generates subthreshold tails and rounds the ideal onset into a crossover centered on the same kinematic condition. The leading resonant contributions to motion-induced excitation production and correlated decoherence probe the same on-shell environmental structure. The proposed readout of this two-subsystem reduced-dynamics signature uses either differential-coherence measurements or a two-node noise cross-spectrum.

Variational quantum circuits (VQCs) solving partial differential equations (PDEs) on near-term quantum hardware face a critical challenge: hardware noise degrades solution fidelity and disrupts convergence. We present a systematic study of three noise channels; depolarizing, amplitude damping, and bit-flip on VQCs constrained by PDE residual loss functions for the heat equation, Burgers' equation, and the Saint-Venant shallow water equations. We benchmark three error mitigation strategies: zero-noise extrapolation (ZNE) via Richardson polynomial fitting, probabilistic error cancellation (PEC), and measurement error mitigation through inverse confusion matrices. Our numerical experiments on 6-qubit, 4-layer circuits demonstrate that ZNE reduces absolute error by 82-96% at low noise (p = 0.001), with effectiveness degrading gracefully at higher noise strengths. We prove analytically and confirm numerically that physics-constrained circuits exhibit inherent noise resilience: at p = 0.01, constrained circuits maintain 25-47% higher fidelity than unconstrained counterparts, with the advantage scaling with PDE complexity. PEC provides near-exact correction at low gate counts but incurs exponential sampling overhead, rendering it impractical beyond ~60 gates at p >= 0.02. Error budget decomposition reveals that systematic errors dominate at all noise levels (43-58%), while the PDE residual component grows from ~10% to ~31% as noise increases, indicating that physics constraints absorb noise through structured gradient information. These results establish practical guidelines for deploying variational PDE solvers on NISQ hardware.

We report the experimental signature of holographically motivated quantum teleportation on a quantum processor, driven by the highly entangled, chaotic dynamics of a many-body system. Specifically, we implement the traversable-wormhole (TW) protocol utilizing a chaotic binary sparse $N = 8$ Sachdev–Ye–Kitaev (SYK) model. This optimized approach dramatically reduces circuit depth for noisy intermediate-scale quantum (NISQ) hardware while rigorously preserving the spectral chaos required for gravitational duality. Diagnosing the teleportation signal via mutual information, we find that while inherent noise in NISQ hardware precludes perfect quantitative agreement with exact numerical simulations, our experimental results provide evidence for the essential qualitative signature: a sign-dependent asymmetry. This work establishes a practical framework for holographic quantum simulations, offering a novel empirical testbed for exploring holographic quantum gravity.

The non-Hermitian skin effect is nonreciprocity-induced localization phenomena in which a macroscopic number of eigenstates accumulate anomalously at the boundary, accompanied by the extreme sensitivity to boundary conditions. Here, we develop a geometric characterization of the non-Hermitian skin effect. We demonstrate that the localization length scale associated with the skin effect is encoded in the quantum metric defined solely from right eigenstates, but not in the biorthogonal quantum metric. Moreover, we show that the quantum metrics can exhibit the power-law divergences at gapless points that depend on the different boundary conditions. We also reveal that cusps of the generalized Brillouin zone in non-Bloch band theory are signaled by discontinuities in the quantum metrics. We illustrate these behavior using prototypical non-Hermitian models, such as the Hatano-Nelson model and the non-Hermitian, nonreciprocal Su-Schrieffer-Heeger model.

The Lattice Boltzmann method (LBM) is a well-established mesoscopic approach for simulating fluid dynamics by evolving particle distribution functions on discrete lattices. While the LBM is highly parallelizable on classical hardware, its translation to quantum algorithms is impeded by the collision process, which is intrinsically nonlinear and irreversible. Several existing quantum formulations implement this process through repeated quantum tomography and state preparation at every timestep, leading to significant overheads. We introduce a quantum LBM based on a denoising-type collision operator that avoids tomography-based updates. The collision dynamics are reformulated as an orthogonal projection onto the linearized manifold of equilibrium distributions around a reference state. This geometric approach filters non-equilibrium components while preserving lattice symmetries and approximating nonlinear terms needed to recover hydrodynamic behavior. A complete pipeline is presented with efficient gate-level realizations, incorporating encoding of distributions, collision, streaming, boundary conditions, and measurement of physical quantities such as hydrodynamic forces. In addition, we outline an approach for implementing projector-based operators deterministically without postselection, paving the way to fully coherent multi-timestep LBM simulations. Numerical experiments for advection-diffusion and flow problems demonstrate that the method reproduces macroscopic behaviors with high accuracy, with performance depending on the choice of reference state.

Boolean satisfiability (SAT) problem is of fundamental importance in computer science and many application domains. For Grover's algorithm, solving the SAT problem requires $\mathcal{O}(\sqrt{2^n})$ queries–where n denotes the number of logic variables in the problem. However, Grover's algorithm suffers from the Souffle problem: specifically, when the number of solutions is unknown, terminating the algorithm too early or too late leads to a significant reduction in the probability of obtaining a solution. In this paper, we propose a parallel fixed-point (PFP) search algorithm to solve the SAT problem. By exploiting entanglement, each clause in the conjunctive normal form (CNF) formula can be processed independently, leading to a significant reduction in circuit depth. We also discuss how to perform the algorithm in distributed manner. These make the PFPS algorithm particularly suitable for the noisy intermediate-scale quantum (NISQ) era.

Quantum energy teleportation (QET) has been studied in continuum field theory and in lattice many-body systems, but the relation between the two within a single interacting model is still not well understood. To address this question, we consider the massive Thirring model, equivalently the sine–Gordon theory. In the continuum, the trigonometric measurement is a weak binary Positive Operator-Valued Measure (POVM), and its leading signal is set by a conserved-current correlator in the bosonized theory, with both gapless behavior and gapped large-distance asymptotics. On the lattice, the conventional protocol does not access this neutral current sector. For Alice's local measurement, a lattice $U(1)$ selection rule removes the neutral current contribution from Bob's subsystem, and the separated signal lies in charged sectors. On the same lattice Hamiltonian we construct a neutral current protocol whose weak signal is exactly a coarse-grained current correlator and whose extracted energy scales quadratically with the measurement strength. This identifies the neutral sector shared by the lattice and continuum descriptions, while separating it from the charged sector that governs the conventional qubit protocol.

Hybrid quantum-classical models offer a promising route for learning from complex data; however, their application to multi-band remote sensing imagery often relies on generic, data-agnostic quantum circuits that fail to account for channel-specific statistical variability. In this work, we propose a data-driven framework that maps band-level statistics such as Shannon Entropy, Variance, Spectral Flatness, and Edge Density to the hyperparameters of customized quantum circuits. Building on this framework, we introduce QMC-Net, a hybrid architecture that processes six data channels using band-specific quantum circuits, enabling adaptive quantum feature encoding and transformation across channels. Experiments on the EuroSAT and SAT-6 datasets demonstrate that QMC-Net achieves accuracies of 93.80 % and 99.34 %, respectively, while a residual-enhanced variant further improves performance to 94.69 % and 99.39 %. These results consistently outperform strong classical baselines and monolithic hybrid quantum models, highlighting the effectiveness of data-aware quantum circuit design under NISQ constraints.

Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite accuracy. In this perspective, we argue that this mismatch points to the need for a new mathematical program: a rigorous constructive theory for effective descriptions to identify essential degrees of freedom. We propose an observation-centered point of view in which signals are treated as the primary objects of analysis, while wave functions and Hamiltonians are reconstructed as auxiliary structures to rationalize the observed data. Our starting point is a signal-based spectral equation that reformulates frequency analysis as an operator problem. We connect this point of view to results on prolate Fourier theory, spectral analysis with finite observation time, and short-time quantum simulation. We highlight a sharp accuracy transition relating necessary observation time to the effective spectral density of a signal for achieving accurate resolution. The resulting framework integrates approximation as a fundamental necessity more directly into the foundations of quantum mechanics and points toward a broader program for the effective description of complex quantum systems, such as those found in the molecular sciences.

Quantum correlations can be harnessed to improve the precision in parameter estimation beyond classical capabilities. Under a standard interferometric or rotation protocol, it is well established that the optimal single-mode Gaussian state is a standard squeezed vacuum, which enables Heisenberg limited precision. In this work, we investigate the potential metrological advantage of two distinct families involving high-order squeezing, namely, mth-phase and multisqueezed states. Our results show that these non-Gaussian states can grant a significant metrological advantage with respect to the optimal squeezed vacuum under equivalent conditions, i.e. at equal occupations. Their advantage holds both at low and large occupations, but its behavior critically depends on the chosen family of high-order squeezing. While higher squeezing orders enhance the advantage, this comes at the cost of higher-order observables in the measurement for full metrological performance. Finally, we study their robustness to standard decoherence channels, i.e. pure dephasing and zero-temperature damping. Employing standard squeezing as reference state, our results indicate a reasonable robustness against damping up to a certain noise strength, while their metrological advantage becomes fragile under pure dephasing. Our work shows the potential enhancement in quantum metrology beyond Gaussian states, carefully detailing the main challenges and limitations.

The barren plateau phenomenon; where cost function gradients vanish exponentially with system size; remains a fundamental obstacle to training variational quantum circuits (VQCs) at scale. We demonstrate, both theoretically and numerically, that embedding partial differential equation (PDE) constraints into the VQC loss function provides a natural and effective mitigation mechanism against barren plateaus. We derive analytical gradient variance lower bounds showing that physics-constrained loss functions composed of local PDE residuals evaluated at spatial collocation points inherit the favorable polynomial scaling of local cost functions, while additionally benefiting from constraint-induced landscape narrowing that concentrates gradient information. Systematic numerical experiments on the one-dimensional heat equation, Burgers' equation, and the Saint-Venant shallow water equations quantify the gradient variance across 4-8 qubits and 1-5 layer depths, comparing global cost, local cost, PDE-constrained, and PDE-constrained with structured ansatz configurations. We find that PDE-constrained circuits exhibit favorable gradient variance scaling with system size, with the physics constraints creating a stabilizing effect that resists exponential gradient vanishing. Entanglement entropy analysis reveals that structured ansatze operate in a sub-maximal entanglement regime consistent with trainability. Convergence experiments confirm that physics-constrained VQCs achieve lower loss values in fewer epochs. These results establish PDE constraints as a principled, physically motivated strategy for designing trainable variational quantum circuits, with direct implications for quantum physics-informed neural networks and variational quantum simulation.

Recent advancements in quantum computing have enabled practical use of quantum error detecting and correcting codes. However, current architectures and future proposals of quantum computer design suffer from limited qubit counts, necessitating the use of high-rate codes. Such codes, with their code parameters denoted as $[[n, k, d]]$, have more than $1$ logical qubit per code (i.e., $k > 1$). This leads to reduced error tolerance of the code, since $\lceil (d-1)/2\rceil$ errors on any of the $n$ physical qubits can affect the logical state of all $k$ logical qubits. Therefore, it becomes critical to optimally map the input qubits of a quantum circuit to these codes, in such a way that the circuit fidelity is maximized. \par However, the problem of mapping program qubits to logical qubits for high-rate codes has not been studied in prior work. A brute force search to find the optimal mapping is super exponential (scaling as $O(n!)$, where $n$ is the number of input qubits), making exhaustive search infeasible past a small number of qubits. We propose a framework that addresses this problem on two fronts: (1) for any given mapping, it performs logical-to-physical compilation that translates input gates into efficiently encoded implementations utilizing Hadamard commutation and gate merging; and (2) it quickly searches the space of possible mappings through a merge-optimizing, noise-biased packing heuristic that identifies high-performing qubit assignments without exhaustive enumeration. To the best of our knowledge, our compiler is the first work to explore mapping and compilation for high-rate codes. Across 71 benchmark circuits, we reduce circuit depth by $34\%$, gate counts by up to $31\%$ and $17\%$ for one-qubit and two-qubit gates, and improve total variation distance by $1.75\times$, with logical selection rate improvements averaging $86\%$ relative to naive compilation.

The quantum dynamics of an externally driven ensemble of nuclear two-level systems embedded in a leaky broadband cavity is investigated theoretically. In the considered scenario both the nuclear ensemble and the cavity mode are coherently pumped by two externally applied x-ray electromagnetic fields. When the frequencies of the applied coherent fields are identical, cross-correlations among the existing decay channels increase the nuclear excitation probabilities depending on the phase difference of the applied fields. Our results show that the excited state of the nuclear ensemble may exhibit sub- to super-Poissonian nuclear statistics, demonstrating induced correlations during photon absorption or emission processes. The role of cross-correlations for the superradiant decay and the collective Lamb shift of the ensemble is also investigated.

Our goal in this paper is twofold. First, we characterize the class of pairwise interactions for which the Seidl conjecture on the structure of optimal plans for the symmetric multimarginal optimal transport problem with one-dimensional marginal holds. This extends previous results by Colombo, De Pascale, and Di Marino [Can. Jou. Math., 67 (2015), https://doi.org/10.4153/CJM-2014-011-x], which treated the case of translation-invariant, convex and decreasing interactions. In particular, our results apply to physically relevant interactions for electrons living on a quantum ring. The second main goal of the paper is to rigorously derive the leading order asymptotics of the adiabatic connection potential for strongly interacting systems. More precisely, we show that for electrons in a quantum ring (or one-dimensional interval), not only the Lieb density functional converges to the optimal transport (or strictly correlated) functional in the semiclassical limit, but also the representing potential converges to a regular Kantorovich potential. As an intermediate step, we also extend previous results on the strongly interacting limit of the Lieb functional to periodic systems in arbitrary dimensions.

We examine the relation between the quantum Landau-Lifshitz equation ($q$-LL) [Phys. Rev. Lett. 110, 147201 (2013)] and quantum Landau-Lifshitz-Gilbert equation ($q$-LLG) [Phys. Rev. Lett. 133, 266704 (2024)]; two non-linear purity preserving master equations that extend classical atomistic spin dynamics into the quantum regime. While the classical LL and LLG counterparts for any number of spins are known to be equivalent, i.e., give identical spin trajectories up to a rescaling of the time parameter, the quantum formulations are equivalent only in certain cases, such as for pure states or for arbitrary single spin-$\frac{1}{2}$ states. Here, we demonstrate that this equivalence breaks down even at the level of a single spin, provided $s \geq 1$. Focusing on a spin-1 particle in an anisotropic crystal field, we show that the $q$-LL and $q$-LLG equations generate inequivalent time evolution. We introduce temporal rescaling misfits that quantify the inequivalence of the two types of dynamics. Although our results highlight fundamental differences in dissipation mechanisms encoded in these equations, the resulting trajectories remain qualitatively similar for this system.

Exceptional points (EPs) represent non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to enhanced sensitivity and critically damped dynamics. We demonstrate that when an EP coincides with a dissipative phase transition in an extended open Dicke model of two cavities coupled to a collective spin, the critical fluctuations are strongly amplified and governed by modified critical exponents. Numerical results reveal enhanced critical scaling in both the normal and superradiant phases, in agreement with an analytical theory based on the Jordan-block structure of the linearized dynamical matrix at the EP. Our results establish EPs as a mechanism to engineer critical scaling in open quantum systems, with potential applications to critical quantum sensing.