Superoscillation (SO) offers a theoretical pathway to unlimited far-field superresolution, yet the associated physical costs lack a unified quantitative scaling description. In this work, we investigate the fundamental limits of deep SO by establishing a scaling law that links the field dynamic range (FDR) and the weight dynamic range (WDR) and validate it through numerical synthesis of one-dimensional SO fields. We observe a strong, near-linear correlation between FDR and WDR in the log-log domain, described by ${\xi }_{\text{(dB)}}=0.104{\eta }_{\text{(dB)}}+6.863$. This relation reveals that extreme resolution is governed by two coupled constraints: a $0.0018\lambda$ focus requires not only a 1661-dB FDR, corresponding to a detection bottleneck, but also a 177-dB WDR, which imposes a comparably stringent requirement on field synthesis and fabrication.

Achieving adiabatic high-fidelity state transfer on photonic chips is essential for scalable quantum information processing, but remains challenging due to the trade-off between robustness and device compactness. The recently reported adiabaticity control limit (ACL) overcomes this challenge by inverse designing compact couplers. However, the numerical nature and example restriction of the ACL to three-waveguide systems hinder generally analytical insight and scalability. Here we develop an analytically optimized coupling framework that pushes the multiwaveguide topological pumping toward the ACL. By generalizing the conventional trigonometric modulations to a power-law profile in a Su-Schrieffer-Heeger lattice, guided by a global adiabatic criterion to minimize spatial nonadiabatic fluctuations, we suppress the nonadiabatic transitions even in dramatically shortened devices. Numerical simulations demonstrate a fourfold reduction in the required device length while maintaining a transfer fidelity exceeding $95\%$. Furthermore, we showcase the versatility of this approach by designing a compact topological photonic splitter for applications in functional photonic devices. Our work establishes a practical paradigm for fast, high-fidelity topological state transfer, bridging the critical gap between analytic design and the ACL in scalable photonic networks.

We introduce a general framework for realizing parity-time $\left(\mathcal{PT}\right)$-like phase transitions in non-Hermitian systems without imposing explicit $\mathcal{PT}$ symmetry. The approach is based on constructing a Hamiltonian as the square root of a supersymmetric partner energy shifted by a constant. This formulation naturally leads to bipartite dynamics with balanced gain and loss and can incorporate nonreciprocal couplings. The resulting systems exhibit entirely real spectra over a finite parameter range precisely when the corresponding passive Hamiltonian lacks a zero mode. As the non-Hermitian parameter representing gain and loss increases, the spectrum undergoes controlled real-to-complex transitions at second-order exceptional points. We demonstrate the versatility of this framework through several examples, including well-known models such as the Hatano-Nelson and complex Su-Schrieffer-Heeger lattices. Extending the formalism to $q$-commuting matrices further enables the systematic realization of higher-order exceptional points in systems with unidirectional couplings. Overall, this work uncovers links between non-Hermitian physics and supersymmetry, offering a practical route to engineer photonic arrays with tunable spectral properties beyond what is achievable with explicit $\mathcal{PT}$ symmetry.

We investigate the quantum optical scattering of two-photon wave packets by a macroscopic lossy sphere by means of macroscopic quantum electrodynamics in the form of modified Langevin noise formalism. Building on our recently developed general scattering framework, we show that under the far-field approximation, the probability amplitudes for photon detection exhibit a direct correspondence to the classical electric field. This allows us to effectively map the quantum interference calculation for the spherical geometry onto a solvable classical electromagnetic problem, specifically by expressing the quantum-scattering amplitudes in terms of the classical Mie coefficients. The two ingoing photons with an arbitrary frequency-polarization spectrum impinge onto the sphere along two different directions and, as a consequence of matter losses, their scattering involves the three independent processes where two, one, and zero outgoing photons survive. Noncollinearity of ingoing photons causes the existence of two different quantum paths they can follow upon scattering, producing interference effects in the detection of the above three processes, which is governed by the wave-packet spectral symmetry. Furthermore, we demonstrate that the sphere's rotational and reflectional symmetries can be exploited to identify specific scattering geometries that enforce perfect constructive or destructive (Hong-Ou-Mandel) interference, both for symmetric and antisymmetric wave packets. To assess the impact of matter dispersion or losses on quantum interference effects accompanying photon detection, we analyze the scattering of narrow-band two-photon wave packets by high-index dielectric lossy spheres. We show that classical Mie resonance peaks, due to their Fano-like traits, yield very strong constructive and destructive interference effects, occurring when the wave packet carrier frequency matches the resonance frequency and side Fano dip frequency, respectively. In addition, we consider the overall scattering probabilities of two, one, and zero photons, and we prove that, at the Mie resonance frequencies, they exhibit quantum interference effects that are extremely sensitive to the spectral symmetry of the input wave packet, thus suggesting an efficient spectral technique assisted by matter losses to identify entanglement.

We quantify the quantum-to-classical transition of the single-mode Kerr nonlinear dynamics in the presence of loss. We establish three timescales that govern the dynamics, each with distinct characteristics. For times short compared with the Ehrenfest time, the evolution is classical, characterized by Gaussian dynamics. For sufficiently long times, as we increase the initial photon number, unitary Kerr evolution would generate macroscopic superpositions of coherent states (so-called kitten states). However, this is severely restricted in the presence of small photon loss, and the expectation values of observables coincide with their classical values. The intermediate timescale, however, shows resilient quantum behavior in the macroscopic limit. We show that in the mean-field non-Gaussian regime, the Kerr Hamiltonian (with small photon loss) generates a significant amount of Wigner-negativity, and classical flow is recovered only if the loss rate grows with system size. Our results broaden the usual understanding of quantum-to-classical transitions and demonstrate the potential for creating robust nonclassical resources for continuous-variable quantum information processing in the presence of loss.

Active matter is characterized by a constant influx and dissipation of energy that gives rise to directed motion. Dissipation requires interactions with an external environment, such that extending the paradigm of active matter to a quantum framework requires an appropriate description of this environment. In this work, we consider a driven quantum particle undergoing noise and dissipation, with external driving exhibiting characteristics of classical activity. We model the nonunitary dynamics with time-local master equations and analyze the particle motion at different timescales for different forms of the master equations, satisfying different criteria. We systematically compare predictions on the dynamics of particle trajectories and thereby we uncover how the particle motion evolves under the interplay of quantum effects, dissipation, and activelike dynamics. These results are essential for guiding possible experiments aimed at realizing quantum analogs of classical active systems.

Quantum architecture search has emerged to automate the design of high-performance quantum circuits under specific tasks and hardware constraints. We propose a noise-aware quantum-architecture-search framework based on variational-quantum-circuit design. By incorporating a noise model into the training of parameterized quantum circuits, the proposed framework identifies the noise-robust architectures. We introduce a hybrid parameter-sharing $\varepsilon$-greedy strategy to optimize evaluation costs and circumvent local optima. Furthermore, an enhanced variable-depth nondominated sorting genetic algorithm is employed to navigate the vast search space, enabling an automated trade-off between architectural expressibility and quantum hardware overhead. The effectiveness of the framework is validated through quantum-machine-learning classification tasks and variational-quantum-eigensolver tasks under noisy conditions. Compared to existing approaches, our framework can search for quantum architectures with superior performance and greater resource efficiency under noisy conditions.

Electron-molecule collisions play a central role in both natural processes and modern technological applications, particularly in plasma processing. Conventional computational strategies such as the $R$-matrix method have been widely adopted yet encounter significant scaling challenges in treating more complex systems. In this work we present a quantum computational approach that utilizes the variational quantum eigensolver (VQE) and variations thereof to overcome these limitations. We explore a number of methods, including the use of number projection operators and simultaneous optimization. We demonstrate the feasibility of our method on a model problem of electron scattering from the hydrogen molecule, with numerical results obtained using a noiseless classical simulator. We recover the full spectrum of the Hamiltonian within a chosen symmetry sector. Moreover, the optimal circuit parameters directly encode the $R$-matrix boundary amplitudes needed for subsequent scattering computations. We formulate the $R$-matrix inner-region problem for electron-molecule scattering in a variational quantum-computing framework.

Vibrational modes of trapped ions have traditionally served as quantum buses to mediate entanglement between internal qubits. However, with recent advances in quantum control, it has become possible to use these modes directly as quantum computational resources. Here, we propose a dual-rail encoding scheme in which two vibrational modes sharing a single phonon encode a qubit and show that such dual-rail qubits can serve as additional system qubits in trapped-ion quantum computing. The interaction between internal qubits and vibrational modes enables universal quantum computation on dual-rail qubits, and incorporating them into a hybrid system with internal qubits nearly doubles the number of available system qubits while preserving all-to-all connectivity. Additionally, we propose a method for implementing multiqubit controlled gates and discuss potential applications that can leverage the advantages of the hybrid system. Our scheme provides a practical framework for an internal qubit-bosonic qubit hybrid system in trapped-ion systems.

We examine multiphoton interference with a symmetric $\mathrm{SU}\left(N\right)$ beam splitter $S_N$, an extension of features of the $\mathrm{SU}\left(2\right)$ 50/50 beam splitter extended Hong-Ou-Mandel (eHOM) effect, whereby one obtains a zero amplitude (probability) for the output coincidence state (defined by equal number of photons $n/N$ in each output port), when a total number $n$ of photons impinges on the $N$-port device. These are transitions of the form $|n_1,n_2,...,n_N\rangle \stackrel{S_N}{\to }{|n/N\rangle }^{\otimes N}$, where $n={\sum }_{i=1}^N{n}_i$, which generalize the Hong-Ou-Mandel effect $|1,1\rangle \stackrel{S_2}{\to }|1,1\rangle$, the eHOM effect $|n_1,n_2\rangle \stackrel{S_2}{\to }|\frac{n_1+n_2}{2},\frac{n_1+n_2}{2}\rangle$, and the generalized HOM effect ${|1\rangle }^{\otimes N}\stackrel{S_N}{\to }{|1\rangle }^{\otimes N}$, which have previously been studied in the literature. The emphasis of this work is on illuminating how the overall destructive interference occurs in separate groups of destructive interferences of subamplitudes of the total zero amplitude. We also consider the more general case for zero-coincidences for the symmetric $\mathrm{SU}\left(N\right)$ beam splitter transformations on multiphoton Fock input states $|n_1,n_2,...,n_N\rangle \stackrel{S}{\to }|m_1,m_2,...,m_N\rangle$ such that ${\sum }_{i=1}^N{n}_i={\sum }_{i=1}^N{m}_i\stackrel{\mathrm{def}}{=}n$. We relate these zero-coincidences to the symmetry properties of $S_N$, beyond the well-known condition that zero-coincidence implies zero-permanent Perm $\left(S_N\right)$=0, which governs the transformation ${|1\rangle }^{\otimes N}\stackrel{S_N}{\to }{|1\rangle }^{\otimes N}$ for arbitrary $N\in \mathrm{even}$. We extend these symmetry properties to the case of the generalized eHOM effect (geHOM) $|n_1,n_2,...,n_N\rangle \stackrel{S_N}{\to }{|n/N\rangle }^{\otimes N}$ involving a zero amplitude governed by $\text{Perm}\left(\mathrm{\Lambda }\right)=0$, for an appropriately constructed matrix $\mathrm{\Lambda }\left(S_N\right)$ built from the matrix elements of $S_N$. We develop an analytical constraint equation for $\text{Perm}\left(\mathrm{\Lambda }\right)$ for arbitrary $N$ that allows us to determine when it is zero, implying complete destructive interference on the geHOM output coincident state $|\frac{n}{N}{\rangle }^{\otimes N}$. We generalize the SU(2) beam splitter feature of the central nodal line, which has a zero diagonal along the output probability distribution when one of the input states is of odd parity (containing only odd number of photons), to the general case of $N=2\times N^{\prime }$ where $N^{\prime }\in \mathrm{odd}$.

Recently, there has been growing interest in the study of genuine nonlocality, which serves to explore the local accessibility of global information encoded in orthogonal multipartite quantum states under scenarios where not all subsystems are joined together. For this form of nonlocality, a probably most fundamental question is upon what states it is prone to be manifested. To tackle this, we present in this work genuinely nonlocal sets with the smallest possible cardinality. We first show the existence of genuinely nonlocal sets of three pure states in arbitrary $N$-partite systems. As a by-product, this also provides examples of strongly nonlocal sets with dramatically smaller cardinality than previous studies for all possible systems, settling some related questions effortlessly. Then, for mixed hypothetical states, we show that genuinely nonlocal sets of two even exist, regardless of the number of copies available. In particular, it turns out for both our constructions that certain genuinely entangled states necessarily exist, nontrivially indicating their potential of raising difficulty in locally accessing multipartite quantum information.

Recent studies have demonstrated that coherent weak measurements allow Einstein-Podolsky-Rosen steering to be shared sequentially between a single Alice and multiple Bobs. Theoretically, this permits an unbounded sequence in the high-dimensional limit. In this work, we investigate whether the experimentally simpler strategy of probabilistic projective measurements (PPM) can achieve similar results. We identify a fundamental distinction between the two approaches: while coherent weak measurements perturb the quantum state quadratically $\left[\mathcal{O}\left({\eta }_k^2\right)\right]$, PPM induces an effective linear depolarizing contribution $\left[\mathcal{O}\left({\gamma }_k\right)\right]$. We prove that this linear scaling restricts the information-to-disturbance ratio to $\mathcal{O}\left(1\right)$, causing the quantum correlations to decay in an arithmetic progression. This imposes a strict bound on the number of accessible Bobs in finite-dimensional systems, severely limiting sequence lengths for qubits. However, we demonstrate that high-dimensional entanglement is robust enough to sustain the sequence, yielding an asymptotic sharing capacity of $N\sim d/lnd$. Ultimately, our results reveal a crucial physical trade-off: while PPM offers experimental simplicity, it consumes quantum correlations at a significantly higher rate than coherent weak measurements.

Grover's algorithm provides a quadratic speedup over classical algorithms for searching an unstructured database and is known to be strictly optimal in oracle query complexity, with tight bounds on its success probability. Although the standard Grover search cannot be further accelerated in the full-search setting, a trade-off between accuracy and query complexity gives rise to the partial search problem. The Grover-Radhakrishnan-Korepin (GRK) algorithm is the standard and most extensively studied protocol for this task. In this work, we provide systematic numerical evidence that the GRK operator sequence gives the highest success probability in all examined cases, supporting it as the optimal ansatz among admissible compositions of global and local Grover operators. Guided by this numerically supported GRK ansatz, we derive an asymptotically tight upper bound on the maximal success probability within the GRK family and establish the corresponding lower bound on the minimal expected number of oracle queries. Furthermore, we investigate parallel quantum search within the partial-search framework. While a direct GRK-based parallelization does not outperform established parallel Grover schemes, we demonstrate that a hybrid strategy combining partial and full search protocols yields a strict, though subleading, improvement over the outer parallel Grover scheme. Our results clarify the fundamental limits of quantum partial search and its role in optimizing parallel quantum search algorithms.

Quantum computing is gaining popularity due to its potential to detect complex patterns in data by leveraging unique quantum phenomena. It is particularly promising for complex data applications, such as those in biomedicine. However, in these contexts, it is often necessary to share and then aggregate data from multiple participants to achieve sufficient statistical power. Sharing data, especially sensitive information such as personal medical records, raises significant privacy concerns. To address these challenges, we propose a quantum-native method for encoding entire data cohorts directly into special quantum states, which we refer to as composite states. These quantum states provide a generic encoding suitable for a wide variety of downstream computations while preventing the inference of individual-level information. Quantum computations can be performed directly on composite states without accessing the underlying raw data. Building on this, we present the theoretical foundations of our scheme's utility and privacy guarantees, demonstrating resistance to membership inference attacks as measured via differential privacy. Furthermore, we introduce protocols that support multiparty collaborative quantum neural network training across diverse domains. Finally, we validate the effectiveness of composite states on three different datasets, focusing on genomic studies while also indicating how the approach can be applied in other domains without adaptation.

Assumption-free reconstruction of quantum states from measurements is essential for benchmarking and certifying quantum devices, but it remains difficult due to the extensive measurement statistics and experimental resources it demands. An approach to alleviating these demands is provided by adaptive measurement strategies, which can yield up to a quadratic improvement in reconstruction accuracy for pure states by dynamically optimizing measurement settings during data acquisition. A key open question is whether these asymptotic advantages remain in realistic experiments, where readout is inevitably noisy. In this work, we analyze the impact of readout noise on adaptive quantum state tomography with readout-error mitigation, focusing on the challenging regime of reconstructing pure states using mixed-state estimators. Using analytical arguments based on Fisher information optimization and extensive numerical simulations using Bayesian inference, we show that any nonzero readout noise eliminates the asymptotic quadratic scaling advantage of adaptive strategies. We numerically investigate the behavior for finite measurement statistics for single- and two-qubit systems with exact readout-error mitigation and find a gradual transition from ideal to suboptimal scaling. We furthermore investigate scenarios where detector tomography is performed with a limited number of state copies for calibration, showing that insufficient detector characterization leads to estimator bias and limited reconstruction accuracy. Although our result imposes an upper bound on the reconstruction accuracy that can be achieved with adaptive strategies, we observe numerically a constant-factor gain in reconstruction accuracy, which becomes larger as the readout noise decreases. This indicates potential practical benefits in using adaptive measurement strategies in well-calibrated experiments.

We present a microscopic derivation of a master equation for two-component bosons (bosonic qubits) which tunnel between spatially separated modes under local dephasing noise. Starting from the full system-bath Hamiltonian with Lorentzian coupling distributions, we analytically obtain a time-local master equation whose structure reveals intrinsic non-Markovian features and recovers the standard phenomenological dephasing model in the short-time limit. Comparison with exact pseudomode simulations confirms its validity beyond weak-coupling and Markovian regimes. We identify a resonance condition between tunneling and bath frequencies for which dephasing drives the system toward correlated steady states, stabilizing coherence and entanglement instead of suppressing them. These results establish a rigorous microscopic foundation for dephasing models in bosonic tunneling systems and reveal a noise-induced mechanism for steady-state entanglement.

Entanglement in open quantum systems can vanish abruptly through entanglement sudden death (ESD) under dissipative evolution, posing a challenge for quantum technologies. Here, we show that the timing of a single local unitary operation can deterministically steer the trajectory of entanglement decay. This introduces temporal steering of dissipative quantum dynamics as a control resource. We develop a time-dependent open-system framework in which a time-shift operator generates a family of effective conditional maps parametrized by $x\in [0,1]$, connecting independent and correlated amplitude damping. Within this framework, we derive analytic conditions for ESD and show that a single intermediate local ${\sigma }_x$ operation can avoid, delay, or hasten ESD by redirecting the dissipative trajectory rather than modifying the environment. We further prove that this single-shot protocol is optimal within a broad class of local control strategies. Experimentally, a displaced Sagnac interferometer realizes the correlated-damping-like regime and, for the first time in one photonic platform, demonstrates avoidance, delay, and hastening of the separability transition. Our results establish temporal steering of open-system dynamics as a practical paradigm for decoherence control, and demonstrate operational advantages in use cases such as teleportation, illustrating that in dissipative quantum systems, knowing when to act can be as important as knowing which operation to perform.

Within the framework of resource theory, the research on quantum coherence has not only furnished a rigorous and systematic methodology for investigating quantum coherence and developing coherence quantification methods, but also tackled key issues regarding the conversion and practical utilization of coherence. Notably, in practical applications, the order of the diagonal elements in an incoherent state is directly linked to the core requirements of thermodynamics under noisy conditions, and constitutes a necessary prerequisite for translating the coherence theory into practical use. Addressing this, we establish a resource theory framework with $\pi$-ordered incoherent states as free states. Concretely, we explore quantum resource theory in which incoherent states featuring specific diagonal element orderings qualify as free states, propose suitable measures for quantifying the resource states, and construct valid witnesses for their identification. Comparative analysis with concrete examples reveals that the variation trends of $\pi$-ordered coherence in certain quantum states are asynchronous with their coherence characteristics. This further underscores the independent significance of the $\pi$-ordered coherence resource theory, separate from the general coherence resource theory.