Papers

We introduce a framework for distributed quantum inference under communication constraints. In our model, $m$ distributed nodes each receive one copy of an unknown $d$-dimensional quantum state $\rho$, before communicating via a constrained one-way communication channel with a central node, which aims to infer some property of $\rho$. This framework generalizes the classical distributed inference framework introduced by Acharya, Canonne, and Tyagi [COLT 2019], by allowing quantum resources such as quantum communication and shared entanglement. Within this setting, we focus on the fundamental problem of quantum state certification: Given a complete description of some state $\sigma$, decide whether $\rho=\sigma$ or $\|\rho-\sigma\|_1\geq \epsilon$. Additionally, we focus on the case of limited communication between distributed nodes and the central node: we assume each communication channel is limited to only $n_c$ bits and $n_q$ qubits with $n_c + n_q \leq \log d$. When all nodes can make use of a shared source of randomness, we show that the copy complexity of distributed state certification is $\Theta(\frac{d^2}{2^{n_q} 2^{n_c/2}\epsilon^2})$. We further demonstrate that shared randomness is necessary to achieve the above complexity, by proving an $\Omega(\frac{d^3}{4^{n_q} 2^{n_c} \epsilon^2})$ lower bound in the $\textit{private-coin}$ setting. Moreover, we develop a private-coin algorithm that matches this bound up to a $\sqrt{\log d}$ factor, showing this complexity is near-optimal. Together, our work establishes a general framework for distributed quantum inference with communication constraints and characterizes the complexity of distributed state certification with limited communication.

Valley splitting sets the energy scale at which spin and valley degrees of freedom hybridize in silicon quantum-well qubits, but its sensitivity to interface structure makes it difficult to predict. Using the valleyor basis, we formulate a two-band effective-mass model for intervalley coupling in a finite quantum well and develop an analytical framework for treating non-perturbative effects of shear strain and wiggle-well potentials. For a $z$-independent coupling $V_s\tau_2$, corresponding to uniform shear strain, we construct a variational state from the exact plane-wave valleyors and a hard-wall envelope. This yields closed-form expressions for the two lowest states and their splitting, including the characteristic oscillatory $|\sin(k_{\rm min}L)|$ dependence. The variational result agrees with exact diagonalization to within $\sim1\%$ for realistic couplings, and provides a simple prescription for tuning the shear strain away from the nodes to enhance the valley splitting. We further show that finite barrier heights primarily renormalize the effective width of the quantum well while preserving the oscillatory dependence. For a wiggle-well coupling $V_w\cos(k_wz)\tau_1$, the valleyor representation reveals a crossover near the $k_w=2k_1$ resonance from wiggle-dominated splitting to orbital quantization. Remarkably, at high wiggle-well amplitudes, the empty-box energy scale predominantly dictates the near-resonant valley splitting, while the wiggle-well potential enters only as a sub-leading correction. This behavior can be viewed as asymptotic freedom for spin qubits. Away from resonance, the splitting exhibits a broadly peaked resonance with diffraction-like side-lobes as a function of detuning.

Photon-number-resolving (PNR) detectors are essential components of photonic quantum technologies. However, conventional single-channel edge-triggered readout struggles to resolve the photon number $n$ in real time or to characterize how timing jitter depends on $n$. In this work, we use a dual-trigger method on a three-pixel series-connected superconducting nanowire single-photon detector (SNSPD) that triggers on both the rising and falling edges of the detection pulse. By doing so, we preserve the precise arrival time of the detection event while mapping the photon number onto the time interval between the rising and falling edges, allowing clear separation of the events. Using this technique, we assign each detection event to $n = 1, 2,$ or 3 photons with $99\,\%$ posterior confidence across all three classes. The timing jitter decreases as $n$ increases, reaching values below $41\, \text{ps}$ for $n \geq 2$. Comparing edge-triggering with constant-fraction discrimination (CFD) for arrival-time extraction, we find that CFD yields lower jitter for single-photon events and a nearly constant mean arrival time. Altogether, our results establish dual-triggering as a robust, low-latency readout scheme for PNR detectors, while revealing a photon-number dependence of the timing jitter relevant to timing precision achievable in heralded photonic quantum applications.

Quantum speed limits impose intrinsic lower bounds on the shortest time scale for quantum system evolution. As an emerging paradigm in quantum resource theory, quantum-state texture has attracted research interest amid the rapid advancement of quantum theory. Herein, we investigate the interplay between quantum speed limits and quantum-state texture via several canonical quantifiers, including trace distance, state rugosity and Jensen-Shannon divergence. To demonstrate our findings, we analyze the minimum evolution time of physical systems subject to dephasing and dissipative dynamics. For the Jensen-Shannon divergence, we further explore nonunitary dynamics described by completely positive and trace-preserving maps, taking the amplitude damping channel as a typical example. In addition, we explore the tightness of these bounds in the considered dynamical models. Our results reveal that quantum speed limits derived from quantum-state texture capture the fundamental constraints on quantum evolutionary speed, with promising applications in quantum computing, quantum control and quantum metrology.

We study unbiased estimation of scalar-valued polynomial functionals of quantum states from independent copies. We establish an equivalence between the first-order marginal of a permutation-invariant finite-copy observable and the functional gradient. We then prove that, among unbiased permutation-invariant estimators, the quantum U-statistic is the unique extension to an arbitrary number of copies. We further derive a universal variance expansion in which the leading $1/n$ term is determined by the variance of the functional gradient, while higher-order contributions are of order $O(1/n^2)$. This leading variance coincides with the multiparameter quantum Cramér–Rao limit, establishing asymptotic efficiency of quantum U-statistics. We also characterize the higher-order scaling at points where the variance of the first-order gradient vanishes. As an application, we analyze the Bures $\chi^2$-divergence and show that a spectral lower bound on the reference state is sufficient but not necessary for bounded-variance estimation. Beyond asymptotic variance, we establish variance-sensitive exponential concentration bounds, deriving a closed-form Bernstein-type inequality to capture finite-sample tail behaviour, and establish the Moderate Deviation Principle to characterize the intermediate asymptotic regime.

We study the problems of quantum state certification, equivalence testing and independence testing. In certification, given samples of an unknown quantum state $\rho$ and the description of a state $\sigma$, the goal is to test whether $\rho=\sigma$, or whether $\rho$ and $\sigma$ are far in a given distance measure. In equivalence testing, $\sigma$ is also unknown and only accessible via samples. Independence testing decides whether $\rho_{AC}=\rho_A\otimes\rho_C$, or is far from being a product. The sample complexities of these problems are now well-understood for a decision gap $\varepsilon$ in trace distance: in the single-copy measurement setting with $d$-dimensional states, all three tasks can be solved using the same non-adaptive approach, which uses $\Theta(d^{3/2}/\varepsilon^2)$ samples and is optimal in general, even without adaptivity. In this work, we consider decision gaps expressed in fidelity and study possible separations between these problems and how adaptivity can help. We prove that certification with respect to fidelity for a state $\sigma$ of rank $r$ does not benefit from adaptivity and requires $\widetilde{\Theta}(r^{3/2}/\varepsilon)$ samples. For equivalence testing and independence testing, we provide adaptive algorithms using $\widetilde{O}(\min\{d^{3/2}/\varepsilon^2,d^{9/4}/\varepsilon\})$ and $\widetilde{O}(\min\{(d_Ad_C)^{3/2}/\varepsilon^2,d_A^{9/4}d_C^{3/4}/\varepsilon\})$ samples, for $d_A\geq d_C$, respectively. Our main technique is a framework that uses partial learning and a reduction to testing in $\ell_2$-distance, adapted from the distribution testing literature. We show that adaptivity matters for equivalence testing in fidelity by proving that $\widetilde{\Omega}(1/\varepsilon^2)$ samples are necessary in the non-adaptive case even for qubits, showing a separation from certification.

The Control Variational Quantum Eigensolver (ctrl-VQE) directly optimizes microwave pulses to enable faster and lower-error quantum-state preparation, but its continuous control landscape re- quires efficient search strategies. We demonstrate that a reinforcement-learning agent based on a deep Q learning network can autonomously discover high-performance pulse sequences using only system parameters and a reward function. The approach is fully general for superconducting qubit platforms, requires no ansatz, and operates at nanosecond resolution compatible with hardware con- straints. As a proof of concept, we apply the method to ground-state preparation of the Hydrogen molecule on a simulated superconducting device. The agent consistently identifies optimized control sequences that achieve high fidelity and outperform random-search baselines. These results highlight adaptive learning as a promising hardware-ready framework for pulse-level quantum control.

This paper gives a categorical interpretation of Baumeler & Wolf's logically consistent non-causal circuits, connecting them to postselected quantum teleportation. Looped feedback is represented by a trace in the category of non-negative matrices, and it is shown that the traced process is stochastic precisely when the induced loop transition matrix has trace $1$ for every external input, a condition shown to be equivalent to a unique fixed point for the loop for each input to a deterministic circuit. A classical non-causal circuit is represented by a measure-and-prepare quantum channel with an internal register utilising a maximally entangled Bell-state with postselection. The main result is that classical logical consistency is equivalent to the postselected Bell outcome having, for loop dimension $d$, probability exactly $1/d^2$ for each classical input distribution. The subsequent normalised conditional output then agrees exactly with the classical categorical trace. This work identifies a class of quantum Bell-postselection constructions whose conditional evolution maintains linear dependence on classical input distributions.

Uniform acceleration induces a thermal response to the Minkowski vacuum and can thereby modify quantum correlations. For measurement-induced nonlocality (MIN), a form of nonclassical correlation distinct from entanglement, previous field-mode analyses of bosonic fields found that it decreases with increasing acceleration and vanishes in the infinite-acceleration limit. This raises the question of whether the disappearance of MIN is a generic consequence of the Unruh effect or depends on the physical description of the accelerated quantum system. To address this question, we study two uniformly accelerating Unruh-DeWitt detectors interacting with a massless scalar field. We find that the response of MIN to the Unruh temperature depends sensitively on the initial detector state: it can decrease monotonically, vanish at an intermediate temperature and subsequently recover, or increase monotonically. Moreover, for a broad class of initial states, MIN approaches a nonzero value in the high-temperature limit. These results show that the suppression of MIN under strong acceleration is not universal. Instead, Unruh-induced detector dynamics gives rise to a state-dependent response in which measurement-induced nonlocality can be suppressed, restored, or enhanced.

Higher-order quantum transformations allow multiple channel uses to be combined through different causal architectures, from parallel and fixed-order sequential networks to general higher-order processes. Whether this causal freedom improves channel transformation when the higher-order operation is also constrained by a resource theory remains largely unexplored. We study this question in the dynamical resource theory of coherence using a unified semidefinite-programming framework. For two qubit amplitude-damping channels and the identity target, we prove a strict causal hierarchy at every nontrivial damping strength under both maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC). In contrast, mixed-Pauli channels admit a common teleportation simulation that transfers the channel dependence to Bell-diagonal program states prepared in parallel. The remaining processing can then be absorbed into a single quantum operational, so parallel, fixed-order sequential, and general higher-order strategies achieve the same optimal error for any target. These results identify free program-state parallelisation as a structural obstruction to causal enhancement.

Certifying entanglement in high-dimensional systems usually requires full state tomography, whose cost grows rapidly with the system dimension. Local randomized measurements offer a scalable alternative, but existing tests based on second-order correlations access only limited information about the state. Here, we derive a finite-size entanglement certificate that extends local randomized measurements to third order. The additional third-order information reveals entanglement that remains undetected at second order, while a dimension-independent concentration bound provides rigorous control of finite-sample errors. Our result opens a practical route to extracting stronger entanglement information from experimental platforms without the dimension-dependent overhead of state tomography.

The performance of superconducting-qubit magnetometers depends not only on magnetic-field encoding during Ramsey interrogation, but also on how efficiently the encoded information is recovered during readout. Squeezed microwaves provide a promising route to improve information extraction by suppressing readout noise, yet how such readout enhancement translates into accessible information for magnetic-field estimation remains unclear. Here we develop an effective detected-mode framework linking projected quadrature noise, state-assignment error, and the classical Fisher information accessible from binary readout outcomes. A finite mismatch between the squeezed quadrature and the discrimination axis produces an optimal squeezing strength through the competition between squeezed and anti-squeezed fluctuations. We further show that squeezed readout improves the readout-limited magnetic-field sensitivity by recovering information otherwise lost during state assignment, with the enhancement remaining robust against quadrature mismatch, transmission loss, and added noise. These results establish a quantitative connection between squeezed-microwave readout and measurement-stage information recovery in superconducting quantum sensing.

Nowadays, the realization of quantum computations and communications based on continuous variables has attracted a significant attention due to a substantial expansion of the system dimensionality. The main progress in this area is attributed to the implementation of multimode systems based on squeezed states of light. One of the simplest ways to generate such states relies upon their producing in a single-pass optical parametric amplifier (OPA) using ultrafast pumping. However, for homodyne detection of such multimode states, the profile of the local oscillator (LO) must perfectly match the profile of the measured mode. Usually, this is not the case; therefore a proper treatment of multimode squeezing is required. In this work, we study both theoretically and experimentally the multimode squeezed light generated in type-0 and type-II OPA. We characterize such sources and investigate the degree of squeezing in dependence on the LO spectral profile, employing a pulse shaping technique. The theoretical analysis is performed using the Schmidt-mode theory. This work might have a significant impact on the realization of multimode quantum protocols

We revisit gravitational decoherence of matter superpositions using the leading soft sector of the graviton $S$-matrix. Starting from Weinberg's soft theorem and the overlap of coherent radiation states, we derive, for branch configurations with the same total four-momentum, a gauge-invariant, nonnegative leading-soft decoherence exponent and evaluate the polarization sum and angular integrals exactly at this order. In the vacuum, coherence between branches with distinguishable soft radiation vanishes as the infrared cutoff is removed. The leading nonrelativistic term is purely quadrupolar as a consequence of energy–momentum conservation. We extend the analysis to single- and two-mode squeezed graviton states, including the two-mode case motivated by inflation. Squeezing can enhance or suppress decoherence depending on the relative phase, while phase averaging gives an enhancement governed by the graviton occupation. For a phase-averaged relic background with an approximately flat energy-density spectrum over the relevant soft frequency band, the sharp-cutoff identification of the infrared scale with the inverse observation time gives a contribution that grows with the gravitational-wave energy density and with the fourth power of the observation time. These results connect soft-graviton scattering, infrared quantum information, and decoherence in nonvacuum gravitational backgrounds.

We characterize several quantum resources carried by the spins of the $\tau^{+}\tau^{-}$ pair produced in $e^{+}e^{-}$ annihilation. At the Belle-II energy, $\sqrt{s}=10.579\,\mathrm{GeV}$, Bell nonlocality, steerability, entanglement of formation, and coherence are governed by the production angle and are largest for transverse emission, $\vartheta=\pi/2$. Their common kinematic origin is exposed by expressing the spin state as a velocity and angle-dependent mixture of a separable contribution and a maximally entangled component. Within the physical production domain, this representation connects the weakly correlated threshold state at $\sqrt{s}=2m_{\tau}$ to the Bell-state limit approached at ultrarelativistic energies. We then propagate the two-spin state through a phenomenological correlated-dephasing channel to determine how environmental memory and inter-channel classical correlations affect the available resources. Memory effects generate collapses and revivals that are absent from the monotonic Markovian evolution. The analysis therefore separates the kinematic mechanism that creates the spin correlations from the noise properties that control their subsequent survival.

Quantum backflow refers here to the appearance of a negative Schrödinger current for a state whose momentum support is entirely positive. We ask for the smallest modification of the free Schrödinger current that makes it nonnegative for every such state, while preserving the current of each individual momentum component. We show that the required minimal modification changes the free-particle momentum kernel according to \[ K_{\rm Sch}(p,p')=\frac{p+p'}{2m} \;\longrightarrow\; K_{\min}(p,p')=\frac{\sqrt{pp'}}{m}. \] The resulting current is positive and normalized and therefore defines an arrival-time POVM. Extending the directional no-backflow requirement to states containing both momentum signs forces the cross-sector kernel to vanish, \[ K_{\min}^{+-}=K_{\min}^{-+}=0, \] so that the full current is the sum of two independent directional contributions. The resulting POVM is exactly the Kijowski time-of-arrival POVM, providing a current-based physical motivation for both its directional kernels and their separation. Within the diagonal-preserving pairwise-minimal construction considered here, the result is unique. The construction itself does not impose a first-arrival condition.

We revisit the almost century-old question of which functional of the local energy best optimizes a trial wave function, a problem of central importance in Variational Monte Carlo (VMC) and, more recently, in Neural-Network VMC (NN-VMC). While variance optimization dates back to the 1930s, the high statistical noise and heavy-tailed local energy distributions inherent to modern neural-network wave functions have renewed interest in this approach. We retrace its long and largely forgotten history here, showing its direct relevance to modern Neural Quantum States (NQS) frameworks. Minimizing the variance (an $L^2$ norm) implicitly assumes a Gaussian local energy distribution: an unjustified assumption. For Coulombic systems, the local energy distribution exhibits $E^{-4}$ power-law tails, causing the Central Limit Theorem to fail for the variance estimator. This instability can be mitigated by robust cost functions: the Mean Absolute Deviation (MAD, an $L^1$ norm), the Cauchy loss, or the $L_{-4}$ functional, which features a tail analytically designed to match the $E^{-4}$ exponent. We benchmark these functionals on $H_2^+$, an exactly solvable system at every internuclear distance, using the Guillemin-Zener wave function across the full potential energy curve. While energy minimization by construction yields the lowest energy, variance minimization is surpassed at every $R$ by alternative functionals: MAD proves superior in the bonding region, while $L_{-4}$ performs best in the dissociation regime.

Predicting how molecular weight distribution and monomer sequence evolve during polymerization is central to polymer science, yet classical approaches face a trade-off between molecular resolution and computational cost: for copolymers, the number of distinguishable species grows exponentially with chain length. Quantum computing offers a potential alternative, provided the non-unitary rate matrices governing the kinetics can be embedded into unitary quantum circuits, a task known as block encoding. Here we construct explicit block-encoding circuits for two kinetic models of living polymerization: Model A, single-monomer polymerization, whose lower-bidiagonal rate matrix is encoded via a sparse-oracle construction and a two-term linear combination of unitaries (LCU) decomposition; and Model B, two-monomer copolymerization, where a bijective labeling of polymer species by an integer index (the m-index) yields a structured sparse matrix encoded via either a five-term LCU or a sparse-oracle construction. Numerical simulations with the sparse-oracle encodings reproduce the classical time evolution for reactivity ratios drawn from reported olefin copolymerization systems spanning near-random ($r_1 r_2 \simeq 1$) and blocky ($r_1 r_2 > 1$) microstructures, and the LCU encodings are verified by explicit reconstruction of the encoded matrix block. Resource estimation shows that both implementations require only $O(\log N)$ qubits in the matrix dimension $N$ (an exponential memory saving over the classical state space), with gate counts growing gradually, reaching $10^4$ to $10^5$ gates at $10^3$ system qubits. These results establish a concrete quantum circuit foundation for simulating polymerization kinetics on fault-tolerant quantum hardware, and a first step toward exploiting exponential state-space compression for high-dimensional polymer reaction networks.

Inspired by the no-cloning theorem in quantum theory, a variety of quantum cryptographic primitives with unclonable functionalities, such as secure key leasing and copy protection, have been proposed and attracted significant attention. However, trapdoor functions (TDFs), fundamental primitives in public-key cryptography, have not been extensively studied in these areas. In this work, we initiate a study of TDFs in both secure key leasing and copy protection settings. We first introduce the definition of TDFs with secure key leasing (TDF-SKL), which enables leasing and deleting of quantum trapdoors. We formalize TDF-SKL both with and without domain sampler, and give a construction of TDF-SKL without domain sampler based on the LWE assumption and a construction of TDF-SKL with domain sampler based on any standard PKE schemes combined with hinting pseudorandom generators [Koppula and Waters, CRYPTO 2019]. Next, we define TDFs with copy protection (TDF-CP), where the inversion functionality is copy protected by a quantum trapdoor. We establish a construction of TDF-CP assuming indistinguishability obfuscation and the LWE assumption, following a modular framework of copy protection proposed by Ananth and Behera [CRYPTO 2024]. We also present applications of TDF-SKL and TDF-CP. Existing constructions of public-key encryption with secure key leasing (PKE-SKL) and single-decryptor encryption (SDE) suffer from a critical vulnerability: quantum decryption keys may be destroyed after decrypting maliciously chosen ciphertexts. We construct PKE-SKL schemes and SDE schemes with robust quantum decryption keys that remain reusable after decrypting arbitrary ciphertexts from TDF-SKL and TDF-CP, respectively.

The time-dependent quantum Monte Carlo method represents a many-electron state by an ensemble of replicas, in which each electron is described by a cloud of walkers which samples its density in physical space, one walker and one guide wave per replica, and it replaces the Hartree potential by a conditional interaction built from the walker positions. The sampling is in physical space rather than in configuration space, which keeps the cost polynomial. Here we derive that conditional interaction. Treating the walker as a localization of its electron to a finite resolution, we show that Bayes' theorem and a single empirical substitution yield the Nadaraya-Watson form which the method has used heuristically. The nonlocality length then becomes the width of the conditioning, and the pair and mean-field limits follow from one construction. Because the conditioning removes the gauge freedom which eliminates the orthonormality multipliers in Hartree-Fock, we enforce orthonormality by a term derived from the constraint. We generalize the formulation to spinors, where the Pauli suppression at coincidence becomes graded by the local spin alignment, and it reduces through the collinear and mean-field limits to the known two-particle spin equations. For two electrons in a double quantum dot in an inhomogeneous magnetic field, compared with the exact solution, the spinor equations reproduce the non-collinear spin geometry which collinear calculations cannot represent and recover the larger part of the entanglement missing from a single determinant. In the crossover between the exchange and the Zeeman regimes, where the singlet-triplet coherence sets the spin geometry, the replicas must carry that coherence themselves, as in the spin-coupled pair of valence-bond theory.

Preparation and verification of specific quantum states is an important capability for quantum devices to realise advantages over classical computations and algorithms. In this work, we have demonstrated an end-to-end framework that combines resource-efficient quantum state preparation with rapid, robust fidelity verification on near-term quantum hardware. By experimentally preparing and validating a structured complex quantum state encoding a digitized acoustic signal on the Quantinuum H2-1 trapped-ion platform, we achieved a high hardware fidelity of $F_{\mathrm{hw}} = 0.929$. Crucially, this milestone was realized without relying on idealized assumptions or deep fault-tolerant overhead, but rather through resource-minimal circuits optimized for NISQ-era and early fault-tolerant devices. Furthermore, we addressed a key limitation in current quantum state certification. While validation methods like shadow overlap work well for random states, their sample complexity can become prohibitively high for the structured states used in practical algorithms. We mitigate this by introducing a pre-measurement basis-change technique that reduces the verification parameter, $\tau$, by over 10 orders of magnitude for structured targets. This approach tightens the theoretical certification guarantees of the shadow overlap method and integrates tensor-network preparation and shadow validation into a unified workflow. These results shift the paradigm of how structured classical data can be mapped to and verified on quantum hardware under realistic noise and measurement budgets. By compressing a robust verification procedure to just 1,000 measurement shots, this framework offers an immediate, scalable benchmarking standard.

In this paper we study performance of the subcarrier-wave quantum key distribution system (SCW QKD) in the presence of spontaneous Raman scattering (SpRS) noise generated by classical channels of dense wavelength division multiplexing (DWDM) network within a single-mode optical fiber. We present the mathematical model for evaluation of the quantum bit error rate (QBER) and the secure key generation rate with the SpRS noise taken into account. We consider two regimes of the SCW QKD system: the continuous wave regime that uses continuous wave laser and the pulsed regime. For these regimes, performance of the system is analyzed depending on receiver sensitivity of classical DWDM. It is found that the pulsed regime outperforms the continuous wave regime in both the secure key generation rate and the maximum achievable distance.

In this paper we study the performance of subcarrier-wave quantum key distribution (SCW QKD) in the presence of classical channels of optical transport network utilizing dense wavelength division multiplexing (DWDM). We consider the impact of spontaneous Raman scattering noise as well as the four-wave mixing and channel isolation efficiency. We calculate quantum bit error rate as well as the secure key generation rate of SCW-QKD protocol for different parameters of DWDM system and quantum channel allocations. Our calculations show, that quantum channel allocation at the wavelength of 1310 nm is preferable to allocation at C-band due to lower nonlinear noise, despite fiber's larger attenuation at this wavelength.

The exploration of the effect of non-Hermitian (NH) in quantum systems is gaining renewed momentum as a result of the recent progress in experiments. It has been indicated that the ability to engineer the orders of exceptional points (EPs) can be fundamental to its applications in quantum control, such as accelerating entanglement generation; however, an initial survey of the interactions between different orders of EPs is still missing. In this work, we try to partially address this issue by employing a non-reciprocally coupled cavity system which can be experimentally realizable with a two-dimensional reconfigurable NH gauged laser array. With deliberate design, our systems display both second and third orders of EPs. The sign of a novel, purely quantum continuous entanglement phase transition is observed, which reveals how multi-EP interactions alter entanglement dynamics across different regimes while maintaining accelerated generation. Our findings reveil the genuinely quantum NH physics of higher-order EPs, which has opened up a new avenue for future investigations of the higher-order degeneracy application and the dynamic phase transitions of quantum systems.

We present an analytical study of the dynamics of a qubit coupled to the zigzag edge of a photonic honeycomb lattice. Leveraging a resolvent operator approach and exact lattice Green's functions, we map the spectrum of qubit-photon bound states and complex poles to uncover the long-time scaling laws of the qubit population. Unlike a qubit coupled to the bulk of graphene, the presence of a zero-energy flat band connecting the Dirac points suppresses long-time branch-cut-induced tails, instead driving damped Rabi oscillations. Potential experimental platforms are briefly discussed.

Quantum measurements of large qubit ensembles are often performed indirectly by coupling the ensemble to a detector and subsequently measuring the detector. Despite the importance of rapid collective readout, it remains unclear what determines how the readout time scales with the number of qubits $N$. Here, we first establish a benchmark $N^{-1/2}$ for a broad class of detectors without ultraviolet high-frequency modes. We then show that the detector with unbounded high-frequency modes can surpass this benchmark and yield a characteristic time scaling $N^{-1/(2-\nu)}$ for $0 < \nu < 2$, where $\nu$ characterizes the spectral structure of the detector. Our results establish high-frequency detector modes as a resource for achieving a scaling advantage in collective quantum readout, with the detector spectrum directly controlling the scaling exponent of the readout time.

Parametric two-qubit gates using tunable couplers are a promising approach to scalable superconducting quantum processors. However, conventional theories formulated in the idle eigenbasis break down in the large-amplitude regime required for fast gate operations. Here, we show that parametric gates are more naturally and accurately described as coherent rotations between instantaneous eigenstates rather than idle eigenstates. This approach may appear counterintuitive, since instantaneous eigenbases are usually associated with adiabatic dynamics. However, they also form a natural moving frame for driven dynamics, where the non-Abelian Berry connection governs transitions and provides a compact description of the exchange and effective $ZZ$ couplings. We show that this theory achieves quantitative agreement with exact numerical simulations across representative tunable-coupler architectures, including double-transmon, capacitively shunted double-transmon, and single-transmon couplers. The description remains accurate even in regimes where idle-frame descriptions fail, while substantially reducing the reliance on computationally demanding exact simulations. These results establish an instantaneous-frame theory of parametric gates beyond conventional idle-frame models and provide a new perspective on driven quantum dynamics.

We characterize the uniform theta graph $\Theta(t,2)$ by the spectrum of its normalized adjacency matrix, or equivalently, by the spectrum of its normalized Laplacian matrix. We also investigate the periodicity of Grover walks on nonregular graphs, which is closely related to the eigenvalues of the normalized adjacency matrix and those of the time evolution matrix of the Grover walk. We show that the Dutch windmill graph $D_n^{(t)}$ is $2n$-periodic and that the uniform theta graph $\Theta(t,n)$ is $(2n+2)$-periodic. Furthermore, we completely determine the connected $6$-periodic graphs and prove that they are precisely $D_3^{(t)}$ with $t \geq 2$ and $\Theta(t,2)$ with $t \geq 1$.

Nuclear slowing-down factors account for the sharing of angular momentum between the electron and the nucleus in the effective Bloch description of alkali-metal spin dynamics in the spin-exchange-relaxation-free (SERF) regime. For collinear optical pumping and magnetic field, we find that longitudinal and transverse spin dynamics are characterized by different polarization-dependent slowing-down factors. Transverse dynamics are governed by the conventional factor $q(p)$, with $p$ the electron spin polarization, whereas longitudinal relaxation is governed by $q(p)+p\,dq(p)/dp$. The two factors coincide at zero polarization but differ substantially at high polarization, where the single-factor description overestimates the underlying pumping and relaxation rates inferred from longitudinal transients by factors approaching two to four, depending on the nuclear spin. We further derive closed-form expressions, valid at arbitrary polarization, for the residual spin-exchange relaxation of the transverse spin components at finite magnetic field along the pumping axis. This contribution is quadratic in the magnetic field and can become comparable to the zero-field linewidth at fields well within the SERF regime. The results are obtained by perturbation theory on the density-matrix dynamics linearized around the stationary state and are verified by numerical solutions of the microscopic density-matrix equation. These findings refine the effective Bloch description of alkali-metal spin dynamics and are directly relevant to atomic magnetometers and alkali-metal–noble-gas comagnetometers, including those used in precision searches for physics beyond the Standard Model.

We study the asymptotic behavior of positive ground states of $N$-particle atomic Coulomb Hamiltonians in a two-cluster region. For the $N$-particle ground state $\psi$, its one-particle density $\rho$, and $(N-1)$-particle ground state $\phi$, we show that for $0<\alpha<1$, as $|x_N|\to\infty$, $\psi(x_1,\dots,x_N)/\sqrt{\rho(x_N)}= \phi(x_1,\dots,x_{N-1})+O(|x_N|^{-2+\alpha} \ln |x_N|)$ uniformly in the region $|x_i|\le |x_N|^{\alpha}$. In the region $|x_i|\le R_0\ln |x_N|$, the convergence rate is $O(|x_N|^{-2} (\ln |x_N|)^2)$. We also establish an $O(|x_N|^{-2})$ bound on the squared $L^2$ error. These results hold both below the essential spectrum and at threshold.