We explore integrable Landau-Zener-type Hamiltonians through a Lie-algebraic framework formulated in the Heisenberg picture. This formulation provides a unified method for handling higher-dimensional representations and enables a more direct extraction of the corresponding scattering matrices. We apply this framework to known models, including higher-spin representations of the SU(2) Landau-Zener model and the three-dimensional Demkov-Osherov model, where we demonstrate its effectiveness in obtaining exact scattering matrices minimally. Finally, we extend the analysis to the four-dimensional Demkov-Osherov model, where we present an exactly solvable six-dimensional Landau-Zener Hamiltonian.

We show that the operational definition of contextuality introduced by Spekkens is, in general, not Lorentz invariant. Specifically, we consider an explicit example with particle states consisting of both spin and momentum, we apply a Lorentz transformation to obtain the states in a new inertial frame, and then trace out the momentum degrees of freedom in both frames. We find that, while an observer in the first inertial frame describes a contextual ontological model with respect to spin states and all possible spin measurements, an observer in the boosted frame describes a noncontextual model with respect to the transformed spin states and all transformed spin measurements. Hence, the Spekkens' notion of contextuality, when restricted to spin degress of freedom only, is a frame-dependent concept. We apply our results to predict a relativistic effect concerning the task of discriminating between two quantum states. We show that the probability of success for a moving observer exceeds that of an observer at rest.

We study the influence of dissipation on the Ising-Gamma model. Through observables such as ground-state energy, order parameters, entanglement entropy, etc., we identify each phase region and provide the global phase diagram of the system. The results show that the region of the spiral phase will continuously expand with the increase of dissipation, gradually squeezing the original paramagnetic and antiferromagnetic phase regions. Remarkably, unlike the conservative system, the introduction of dissipation will cause two spiral phases with opposite chiralities to emerge simultaneously in the system, which provides a possibility for the manipulation of spiral chirality in cold atomic experiments. Moreover, we reveal the mechanism of the dependence of the transformation between these two spiral phases with distinct chirality on the strength of the relative coefficient of off-diagonal Gamma interactions in the Ising-Gamma model. Since both the relevant order parameters and dissipation can be well controlled within a detectable range, these phenomena can be observed in ultracold atomic experiments.

Are there consistent and physically reasonable alternatives to the projection postulate? Does it have unique properties compared with acceptable alternatives? We answer these questions by systematically investigating hypothetical state-update rules for quantum systems that Nature could have chosen over the Lüders rule. Among other basic properties, any prospective rule must define unique post-measurement states and not allow for superluminal signaling. Particular attention will be paid to consistently defining post-measurement states when performing local measurements in composite systems. Explicit examples of valid unconventional update rules are presented, each resulting in a distinct, well-defined foil of quantum theory. This framework of state-update rules allows us to identify operational properties that distinguish the projective update rule from all others and to put earlier derivations of the projection postulate into perspective.

We analyze two coupled quantum oscillators in a common Lorentzian environment and control them by detuning (temporarily shifting) their frequencies. The reduced dynamics are solved exactly, without Born or Markov approximations, by propagating each detuning segment in closed form. We study two control schedules: regular detuning, with perfectly periodic on and off pulses of fixed period, width, and amplitude; and irregular detuning, with the same on-off structure but cycle-to-cycle jitter in period, width, and/or amplitude. Our main observable is the average excitation number of each mode. Detuning moves the system away from the bath's spectral peak, suppressing decoherence and damping non-Markovian revivals; in effectively Markovian baths the benefit is small. We quantify performance with a simple time-domain suppression factor. Larger detuning amplitudes and higher duty cycles yield stronger protection. In addition, we evaluate the quantum mutual information between the oscillator pair and the pseudomode bath, showing that detuning control significantly reduces system-bath correlations and information backflow. These results give practical design rules linking detuning, duty cycle, and bath width, and provide an exact benchmark for controlled non-Markovian dynamics.

Recent studies have revealed reentrant-localization transitions in quasiperiodic one-dimensional lattices, where the competition between dimerized hopping and staggered disorder plays a central role. However, it remains unclear under what conditions reentrant localization and, in particular, multiple reentrant localization can occur. Here we investigate localization phenomena in a one-dimensional lattice subject to a periodic potential and an additional quasiperiodic modulation. Using both eigenstate-resolved indicators and experimentally accessible dynamical observables, we identify robust multiple-reentrant-localization transitions. We show that these transitions are uniquely stabilized by the dimer structure of the unit cell, where the competition between the on-site periodic potential and the quasiperiodic modulation becomes most pronounced. By systematically varying the periodicity parameter $\alpha$ and the quasiperiodic frequency $\beta$, we find that the robust multiple-reentrant-localization behavior disappears for any deviation from the dimer configuration, confirming its essential role. Our results suggest that the interplay between these competing factors drives the multiple-reentrant-localization transitions.

It is known that there exist a limited number of analytic potentials with the unusual property that any bound quantum state therein will be periodic in time. This is known as a perfect quantum state revival. Examples of such potentials are the infinte well, quantum harmonic oscillator, and the Pöschl-Teller potentials; here, we present a general method of designing such potentials. A key requirement is that their energy eigenvalues have integer spacings (up to a prefactor). We first analyze the required conditions which permit quantum state revivals for potentials in general, and then we use techniques of iterated Hamiltonian intertwining to construct potentials exhibiting perfect quantum revivals. Our method can readily be extended to multiple dimensions.

While the partial transpose operation appears in many fundamental results in quantum theory—such as the Peres-Horodecki criterion for entanglement detection—a physical interpretation of the partial transpose is lacking. In this work, we show that a partial transpose of a bipartite density operator is a two-time pseudodensity operator, which by definition encodes temporal correlations associated with two-point sequential measurement scenarios. As such, it follows that partial transposition admits a precise physical interpretation as mapping spatial correlations to temporal correlations, thus swapping the roles of space and time for bipartite quantum systems. For maximally entangled qubits, we show that partial transposition maps spatial correlations which violate Bell inequalities to causal correlations which cannot be replicated by spacelike separated systems, thus further solidifying the interpretation of partial transpose as a space-time swap. As it is known that gravitational effects swap the roles of space and time inside a black hole, our results suggest that at a quantum mechanical level, a traversal of a black hole's event horizon by a bipartite quantum system may be described by a partial transpose.

While Bell nonlocality can be explained through mechanisms such as retrocausality and superluminal influences, it is not clear why such mechanisms do not manifest at an everyday macroscopic level. In this paper, we show how measurement and nonlocality can be explained consistently with macroscopic realism and no-signaling, and causal relations for macroscopic quantities. Considering the measurement of a field amplitude $\widehat{x}$, we derive theorems that lead to an equivalence between a quantum phase-space probability distribution $Q(x,p,t)$ and stochastic trajectories for real amplitudes $x\left(t\right)$ and $p\left(t\right)$ propagating backward and forward in time, respectively. We present forward-backward stochastic simulations that motivate a $Q$-based objective-field model of reality. Amplification plays a key role in the measurement. With amplification, similar to decoherence, contributions due to interference become unobservable, leading to “branches” in $x$ that correspond to distinct eigenvalues $\lambda$. This elucidates how the system evolves from a superposition to an eigenstate, from which Born's rule follows. For superposition states, we find that the backward and forward trajectories are connected, leading to “hidden loops.” We deduce a hybrid causal structure involving causal deterministic relations for amplified variables, along with microscopic noise inputs and hidden loops for unobservable quantities. Causal consistency is confirmed, removing grandfather-type paradoxes. The simulations allow evaluation of a state inferred for the system, conditioned on a particular branch $\lambda$, from which we deduce a model for projection and the collapse of the wave function. The theory is extended to Einstein-Podolsky-Rosen correlations and Bell nonlocality. We demonstrate consistency with three weak local realistic premises: (1) the existence of real properties (defined for the system after operations that fix measurement settings); (2) a partial locality implying no-signaling; (3) “elements of reality” that apply to the predictions of a system by a meter, once meter settings are fixed. A $Q$-based hidden variable model and mechanism for Bell nonlocality is identified. Our work shows how forward-backward stochastic simulations lead to a hybrid causal structure, involving both deterministic causal relations and “hidden” stochastic loops, explaining measurement and entanglement, with paradoxes typically associated with retrocausality avoided.

Genuine multipartite entanglement is a valuable resource in quantum information science, as it exhibits inseparability across all possible bipartitions of a multimode quantum state. The large degree of quantum correlations can be exploited in various quantum information protocols, such as teleportation, dense coding, and quantum interferometry. Here, we propose a scheme to generate scalable genuine multipartite continuous-variable entangled states of light using a parametric amplifier network. We verify the presence of genuine quadripartite, hexapartite, and octapartite entanglement through a violation of the positive partial transpose criteria. Additionally, we use $\alpha$-entanglement of formation to demonstrate the scalability of our approach to an arbitrary number of $2N$ genuinely entangled parties by taking advantage of the symmetries present in our scheme.

Quantum architecture search (QAS) has emerged as a prominent paradigm for designing quantum circuits in recent years. To accelerate the search for optimal circuit structures, circuit performance is often estimated without full training. Neural predictors have shown great potential in providing effective performance estimations by leveraging the power of deep learning. However, training such predictors requires a labeled dataset of circuit-performance pairs, where circuit performance must still be obtained via costly circuit training. A large training set undermines the original intent of using predictors to reduce the cost of obtaining circuit performance, while a small training set may hinder the predictor's generalization ability. To address this dilemma, we propose two data-efficient, predictor-based QAS algorithms that operate in a semi-supervised learning fashion to exploit the latent information of unlabeled circuits. The first algorithm adopts a teacher-student framework, where a teacher model guides the training of a student predictor using unlabeled circuits. The teacher produces smoother and more stable targets, encouraging the student to generate steady predictions under perturbations, thereby enhancing robustness. The second algorithm employs an uncertainty-aware circuit selection strategy that identifies unlabeled circuits with low-uncertainty predictions, which are then incorporated into the training set to effectively expand the available labeled data. Numerical results demonstrate that these two algorithms improve the predictor's generalization ability and facilitate the discovery of higher-performing quantum circuits, thereby enhancing the efficiency of predictor-based QAS in variational quantum algorithms.

A specific type of quantum correlated state achieves optimal precision in parameter estimation under unitary encoding. However, a general, quantitative understanding of how the available entanglement resource fundamentally limits metrological performance has remained largely unexplored. We address this by considering pure probe states undergoing unitary encoding and analyze the achievable precision for a fixed amount of initial entanglement, thereby establishing a direct relation between the optimal precision and the available input entanglement in both bipartite and multipartite scenarios. For two-qubit probes, we analytically derive an exact relationship between the entanglement-constrained optimal quantum Fisher information and the limited initial entanglement, measured via both generalized geometric measure and entanglement entropy. We demonstrate that this fundamental relationship persists across the same range of the entanglement measures even when higher-dimensional bipartite probes are considered. Furthermore, we identify the specific states that realize maximum precision in these scenarios. Additionally, by considering the geometric measure of entanglement, we extend our approach to multiqubit probes. We find that in every case, the optimal quantum Fisher information exhibits a universal behavior: a steep increase in the low-entanglement regime, followed by a gradual and nearly saturated improvement as the probe entanglement approaches values close to those required for achieving the Heisenberg limit.

We propose a non-Markovian perspective on the evolution of electronic coherence in a molecule prepared in a superposition of two electronic states entangled with their vibrational environment. We show that the non-Markovian evolution of electronic coherence is governed by dynamical generalized weak values, which are characteristic averages of the electronic energy difference within the vibrational environment. These complex generalized weak values characterize the dynamics of the vibrational environment and form the memory kernel in the evolution of electronic coherence. They reflect a property essential for the existence of complex electronic coherence: the set coherence of the preselected and postselected states in the vibrational Hilbert space. Anomalous weak values may emerge during the evolution when electronic coherence approaches zero. We numerically simulate several vibrational preparations of a cold diatomic molecule using chirped laser pulses to examine the evolution of electronic coherence in diverse vibrational environments. The complex dynamical weak value serves as a useful theoretical tool for differentiating types of coherence and understanding the evolution of the time-dependent phase of coherence. The occurrence of anomalous weak values in the evolution reveals the existence of sudden large fluctuations in the energy difference between the electronic states due to vibrational dynamics.

Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for solving the GEPs in non-Hermitian systems. The algorithm transforms the generalized eigenvalue problem into a process of searching for unitary transformation matrices. We demonstrate a method for evaluating both the loss function and its gradients on near-term quantum devices. We validate numerically the algorithm's performance through simulations, and demonstrate its application to GEPs in ocean acoustics. The algorithm's robustness is further confirmed through noise simulations.

Entangled basis measurements play a crucial role in distributing quantum entanglement between parties across a quantum network. In this work we adopt a semi-device-independent approach that enables the self-testing of $n$-qubit Greenberger-Horne-Zeilinger basis measurements without requiring shared entanglement between distant parties. Our method relies solely on input-output statistics from a communication scenario involving $n$ spatially separated senders, each receiving two bits of input, and a single receiver with no input. We analyze the robustness of the proposed self-testing protocol for $n\le 7$. Additionally, we introduce a protocol for robust self-testing of the three-outcome partial Bell-basis measurement that is easily implementable in an optical setup.

We study the performance of quantum sensors composed of four qubits arranged in different geometries for magnetometry and thermometry. The qubits interact via the transverse-field Ising model with both ferromagnetic and antiferromagnetic couplings, maintained in thermal equilibrium with a heat bath under an external magnetic field. Using quantum Fisher information, we evaluate the metrological precision of these sensors. For ferromagnetic couplings, weakly connected graphs (e.g., the chain graph $P_4$) perform optimally in estimating weak magnetic fields, whereas highly connected graphs (e.g., the complete graph $K_4$) excel at strong fields. Conversely, $K_4$ achieves the highest sensitivity for temperature estimation in the weak-field regime. In the antiferromagnetic case, we uncover a fundamental trade-off dictated by spectral degeneracy: Configurations with nondegenerate energy spectra, such as the panlike graph (three qubits in a triangle with the fourth attached), exhibit strong-magnetic-field sensitivity due to their pronounced response to perturbations. In contrast, symmetric structures like the square graph, featuring degenerate energy levels (particularly ground-state degeneracy), are better suited for precise thermometry. Notably, our four-qubit sensors achieve peak precision in the low-temperature weak-field regime. Finally, we introduce a spectral sensitivity measure that quantifies energy spectrum deformations under small perturbations, providing a simple heuristic indicator of metrological sensitivity.

Additional state evolutions performed before measurement, also called measurement-after-interactions (MAI) protocols, have shown a great potential for increasing the sensitivity of metrological scenarios. Here, we go beyond this result and show that MAI techniques can significantly enhance the detection capability of witnesses for quantum correlations. In particular, we show the possibility of detecting Einstein-Podolsky-Rosen steering and mode entanglement of non-Gaussian states from linear measurements only. Moreover, we show that such approach allows for a significantly higher noise robustness.

Decoherence-free subspace (DFS) provides a crucial mechanism for passive error mitigation in quantum computation by encoding information within symmetry-protected subspaces of the Hilbert space, which are immune from collective decoherence. Constructing a complete set of orthogonal basis states for the DFS is essential to realize fault-tolerant quantum computation by using the DFS codes. However, existing methods for preparing these basis states are often nonscalable, platform-specific, or yield mixed states. Here, we propose a deterministic approach to prepare pure, orthogonal, and complete DFS basis states for systems of arbitrary size composed of qubits. Our method employs projective measurements and quantum circuits with single-qubit, two-qubit, and Toffoli gates. We provide a rigorous resource cost analysis both mathematically and numerically. Meanwhile, we demonstrate the realizability of our method on NISQ devices by discussing how to implement our method on a superconducting chip. The proposed method offers a universal solution for preparing the DFS basis states across diverse quantum computing platforms and system sizes, which is realizable in the NISQ era.

Filtering refers to the process of using algorithms to enhance desired or mask undesired states in quantum computing and is essential for preparing or isolating quantum many-body states. One class of filters is based on quantum phase estimation (QPE). Such QPE-based filters have a simple circuit implementation, but their performance remains unclear, particularly when compared to other filtering methods such as those with quantum signal processing. In this work we investigate the performance of QPE-based filters with three commonly used window functions: a rectangular window, a sine window, and a Kaiser window. We analyze how the choice of window affects results; one noticeable observation is that the oscillation of the filter (the Gibbs phenomenon) seen in the conventional rectangular-window result can be mitigated when the sine and Kaiser windows are applied. Furthermore, we compare the performance of QPE-based methods to quantum eigenvalue transformation of unitary matrices with real polynomials (QETU) and find that the Kaiser-window-based filter and QETU result in a similar number of queries to the Hamiltonian time-evolution operation. QPE-based filtering methods may therefore be an alternative to signal-processing-based methods. Finally, as an application of the QPE-based filter, we propose a two-step QPE algorithm for low-energy spectral simulations, composed of a coarse grid for filtering and a fine grid for obtaining final high-resolution spectra. As a benchmark of the proposed scheme for realistic continuous spectra, we present the calculation of the density of states of antiferromagnetic type-II MnO in a one-particle approximation.

Efficiently uploading data into quantum states is essential for many quantum algorithms to achieve advantage across various applications. In this paper, we address this challenge by developing a method to upload a polynomial function $f\left(x\right)$ on the interval $x\in [-1,1]$ into a pure quantum state consisting of qubits, where a discretized $f\left(x\right)$ is the amplitude of this state. The preparation cost has $\mathcal{O}(nlogn)$ scaling in the number of qubits $n$ and linear scaling with the degree of the polynomial $Q$. This efficiency allows the preparation of states whose amplitudes correspond to high-degree polynomials (up to ${10}^4$), enabling accurate approximation of functions that admit efficient polynomial series representations and whose amplitude profiles are not extremely localized. We provide a fully explicit circuit realization, based on four real polynomials that meet specific parity and boundedness conditions. We extend this construction to cover piecewise polynomial functions, a case not previously addressed explicitly in the literature, the algorithm scaling linearly with the number of piecewise parts. Our method achieves efficient quantum circuit implementation and we present detailed gate counting and resource analysis.