As quantum analogs of the classical Kolmogorov-Sinai entropy, quantum dynamical entropies have emerged as important tools to characterize complex quantum dynamics. In particular, Alicki-Fannes-Lindblad (AFL) entropy, which quantifies the information production rate of a coherent quantum system subjected to repeated measurement, has received considerable attention as a potential diagnostic for quantum chaos. Despite this interest, the precise behavior of quantum dynamical entropy in the presence of symmetry remains largely unexplored. In this work, we establish rigorous inequalities of the AFL entropy for arbitrary unitary dynamics (single particle and many body) in the presence of various types of symmetry. Our theorems encompass three cases: Abelian symmetry, an anticommuting unitary, and non-Abelian symmetries. In particular, we show that, while the cumulative AFL entropy generally saturates to the dimensional bound at late times for chaotic dynamics, this saturation value is distinctively lower when the measurements respect the symmetries. We motivate our main results with numerical simulations of the perturbed quantum cat maps. Our findings highlight the crucial role of symmetry in quantum dynamics under measurements, and our framework is readily adaptable for investigating symmetry's influence across diverse probes of quantum chaos.

Thermal states play a fundamental role in various areas of physics, and they are becoming increasingly important in quantum information science, with applications related to semidefinite programming, quantum Boltzmann machine learning, Hamiltonian learning, and the related task of estimating the parameters of a Hamiltonian. Here we establish formulas underlying the basic geometry of parameterized thermal states, and we delineate quantum algorithms for estimating the values of these formulas. More specifically, we establish formulas for the Fisher–Bures and Kubo–Mori information matrices of parameterized thermal states, and our quantum algorithms for estimating their matrix elements involve a combination of classical sampling, Hamiltonian simulation, and the Hadamard test. These results have applications in developing a natural gradient descent algorithm for quantum Boltzmann machine learning, which takes into account the geometry of thermal states, and in establishing fundamental limitations on the ability to estimate the parameters of a Hamiltonian, when given access to thermal-state samples. For the latter task, and for the special case of estimating a single parameter, we sketch an algorithm that realizes a measurement that is asymptotically optimal for the estimation task. We finally stress that the natural gradient descent algorithm developed here can be used for any machine learning problem that employs the quantum Boltzmann machine ansatz.

We propose a quantum algorithm for calculating the structural properties of complex networks and graphs. The corresponding protocol—deteQt—is designed to perform large-scale community and botnet detection, where a specific subgraph of a larger graph is identified based on its properties. We construct a workflow relying on ground state preparation of the network modularity matrix or graph Laplacian. The corresponding maximum modularity vector is encoded into a ${log}_2\left(N\right)$-qubit register that contains community information. We develop a strategy for “signing” this vector via quantum signal processing, such that it closely resembles a hypergraph state, and project it onto a suitable linear combination of such states to detect botnets. As part of the workflow, and of potential independent interest, we present a readout technique that allows filtering out the incorrect solutions deterministically. This can reduce the scaling for the number of samples from exponential to polynomial. The approach serves as a building block for graph analysis with quantum speedup and enables the cybersecurity of large-scale networks.

The stabilizer states and symmetric informationally complete positive operator valued measure (SIC-POVM) fiducial states are two important families of states in the stabilizer formalism of fault-tolerant quantum computation. They have been demonstrated to be on two extremes with respect to some quantifiers of magic. The present work is devoted to a further study of these two families of quantum states. For a given quantum state in a $d$-dimensional quantum system, employing the generalized variance and the generalized Wigner-Yanase skew information for the set of discrete Heisenberg-Weyl displacement operators, we propose two quantifiers of uncertainty defined in the product form. We reveal that the extremal states of the uncertainty quantifiers are also closely related to the above-mentioned families of states. Explicitly, for prime-dimensional quantum systems, we prove that the minimum uncertainty states correspond to the stabilizer states. While for arbitrary dimensional quantum system, the maximum uncertainty states are the SIC-POVM fiducial states (assuming their existence). For the quantifier of total uncertainty, the conclusions hold under the restriction that the quantum states are pure, while for the quantifier of quantum uncertainty, the conclusions hold for general quantum states. The findings in this work shed light on the characterization of important families of states in the stabilizer formalism of quantum computation, which reveal the close connections between the stabilizer formalism and uncertainty.

We describe Gaussian bound entangled states—entangled states with a positive partial transpose (PPT)—in four-mode continuous-variable systems. These states appear as a transient phase when certain entangled states with a negative partial transpose (NPT), also known as free entangled Gaussian states, are evolved under a noisy environment. Local thermal baths composed of harmonic oscillators are allowed to interact with one or more modes of the system and a wide variety of initial Gaussian entangled (NPT as well as PPT) states are studied. The robustness of entanglement is defined as the time duration for which the entanglement of the initial state is preserved under the noisy dynamics. We access the separability by utilizing standard semidefinite programming techniques. While most states lose their entanglement after a certain time across all bipartitions, an exception is observed for a three-parameter family of states which we call the generalized four-mode squeezed vacuum states, which transition to bound entangled states and remain so for a finite window of time. This dynamical onset of bound entanglement in continuous-variable systems is the central observation of our work. We carry out the analysis for Haar-random four-mode states (both pure and mixed) to scan the state space for a transient bound entangled phase.

In recent years, non-Hermitian parity-time ($\mathcal{P}\mathcal{T}$)-symmetric quantum systems have gained significant attention due to their unique physical properties, with experimental realizations demonstrated across diverse platforms. Two popular approaches have been used to implement $\mathcal{P}\mathcal{T}$-symmetric dynamics: one removes quantum jumps from dissipative natural atoms (e.g., cold atoms, trapped ions) or artificial atoms (e.g., superconducting qubits) through postselection whose experimental fidelity is severely limited by unavoidable population backflow effects; the other embeds the desired non-Hermitian Hamiltonian into a larger Hermitian system, which achieves higher fidelity but typically enables simulating $\mathcal{P}\mathcal{T}$-symmetric dynamics only within restricted parameter regimes. This paper proposes and experimentally demonstrates a trapped-ion-based scheme for digital simulation of $\mathcal{P}\mathcal{T}$-symmetric quantum systems with high fidelity across the full parameter space. By leveraging high-fidelity logic gates and postselection on a four-level single ion to synthesize the target $\mathcal{P}\mathcal{T}$-symmetric dynamics, this approach enables accurate characterization of $\mathcal{P}\mathcal{T}$-symmetric properties, especially the exotic features in the vicinity of the exceptional point (EP). Distinct dynamical properties in the $\mathcal{P}\mathcal{T}$-symmetric unbroken phase (PTS), $\mathcal{P}\mathcal{T}$-symmetric broken phase (PTB), and at the EP are experimentally demonstrated with the data agreeing well with theoretical predictions. This high-fidelity simulation scheme also enables precise measurement of quantum Fisher information (QFI) near the EP, essential for evaluating non-Hermitian quantum sensing performance. It is shown that, after accounting for the low postselection probability, QFI divergence near the EP vanishes, providing no more information than their Hermitian counterparts, which echoes with recent theoretical findings. Our scheme establishes a paradigm for full-parameter-space precise simulation of non-Hermitian effects in quantum systems, and is applicable to various other platforms.

Quantum sensors allow us to measure weak oscillating fields with incredible precision. One common approach is to use the time evolution of a single two-level system (or a qubit) in conjunction with applied control pulses to measure the oscillating field. For high-frequency fields, the time interval required between the applied pulses decreases, meaning that errors due to the finite width of the pulses can become important. This paper presents an alternative scheme that does not rely on applying pulses with short time intervals. Our scheme uses two interacting qubits. In the presence of an oscillating field, the interaction strength changes. The oscillating field can be estimated by measuring the change in this interaction strength. We quantify the precision of this estimate by calculating the Fisher information. We show the effect of noise on our scheme and discuss how control pulses can be applied to mitigate the impact of noise. Importantly, the time interval between these pulses need not be very short.

We report an oscillatory form in the two coupled dissipative Rydberg atomic chains by modulating its spacing. Such oscillation has $\pi$-phase difference between two neighboring sites, which distinguishes it from antiferromagnetic-type synchronization in the previous studies. Theoretically, we find a phase with two coexisting types of continuous time crystals and recognize that the transition belongs to Hopf and pitchfork bifurcation. Furthermore, we generalize the conclusion to multiple chains and verify the uniqueness of the synchronization mode. We also discuss its experimental feasibility.

We present a detailed study of an adiabatic state preparation in an effective three-level quantum system. States can be prepared with high speed and fidelity by adding a counterdiabatic quantum control protocol. As a second step, we invert the preparation protocol to get back to the initial state. This describes an overall cyclic evolution in state space. Using counterdiabatic terms, the resulting composed fast evolution can be repeated many times. We then analyze the control of Berry's phase along the adiabatic cyclic path and show that Berry's phase can act as a sensitive detector of nonperfect state transfer.

We calculate the bound-electron $g$ factor for a wide range of rovibrational states in the ground $\left(1s\sigma \right)$ electronic state of the molecular hydrogen ions ${\mathrm{H}}_2^{+}$ and ${\mathrm{HD}}^{+}$. Relativistic and QED corrections of orders up to ${\alpha }^5$ are taken into account. All contributions are calculated in a nonrelativistic QED framework, except for relativistic corrections of order ${\left(Z\alpha \right)}^4$ and above, which are obtained by calculating the relativistic $g$ factor using a precise minmax finite element solution of the two-center Dirac equation. A relative accuracy of $(4–5)\times {10}^{-11}$ is achieved for the scalar $g$−factor component, which represents an improvement by more than three orders of magnitude over previous calculations. These results are useful for internal state identification and rovibraional spectroscopy of single molecular hydrogen ions in Penning traps, and open an avenue toward precision tests of QED.

Ultracold condensates provide a unique platform for exploring soliton physics. Motivated by the recent experiments realizing the sine-Gordon model in a split one-dimensional (1D) BEC, we demonstrate that this system naturally supports various density and phase solitons. Many theories of the 1D Bose gas rely on mean-field or quasiparticle frameworks, which may suffer from infrared singularities, often causing the small-fluctuation expansion to lose validity in long-wavelength regimes. Thus, we explore the physics using the bosonization technique as a complement in the long-wavelength regime, in which the phase and density are conjugate pairs, and determine its effective Language equation and the associated equation of motion. We show that in the presence of asymmetry between the two condensates, alternative solutions beyond those in the sine-Gordon model emerge. We calculate the traveling-wave solutions and soliton solutions in this model and determine their corresponding energy densities analytically. Finally, we discuss the relevance of these solutions to the experiments and discuss their observations. Since the physical models have already been realized in experiments, this work opens alternative possibilities for the realization of various soliton and periodic solutions using two coupled condensates.

Quench dynamics of first-order phase transitions in a homogeneous Bose-Einstein condensate with Raman-type spin-orbit coupling is investigated. By adjusting the coupling strength, the system can be driven across the critical point between the plane-wave phase and stripe phase in two opposite directions, and we find the scaling-law behaviors for both processes of phase transitions. This is different from previous studies, which only focus on the quench dynamics in the unidirectional transitions from a higher symmetric phase to a lower symmetric phase. Subsequently, we obtain the power law of the domain numbers (correlation length) and formation time (correlation time) of these phase transitions and extract the critical exponents. The results reveal the effect of the directionality of the phase transition on the dynamic scaling law.

Atom interferometers provide a powerful tool for measuring physical constants and affirming fundamental physics with unprecedented precision. The sensitivity of atom interferometers is significantly enhanced by optical lattices and coherent atomic sources. However, their interplay gives rise to additional complexities and intriguing phenomena. Here, we report on realizing a Ramsey-Bordé interferometer of coherent matter waves modified by a moving optical lattice in a gravitational field, and explore a resulting multipath interference with tunable coherence. We investigate spatial correlations of atoms both within the lattice and between two arms by interferometry, and observed the emerging multiple interference peaks of the Bose-Einstein condensate with sublattice site resolution. Our findings agree well with simulations, paving the way for high-precision interferometry and exploring rich interferometer phenomena using ultracold atoms.

We propose a method for using a single-axis atom interferometric gravity gradiometer to measure off-diagonal elements of the gravity gradient tensor. By tilting the gradiometer, the measured gradient becomes a linear combination of different components of the gravity gradient tensor, and through multiple measurements at different tilts the separate tensor components can be inferred. We present a theoretical and numerical investigation of this technique, both for terrestrial surveys where the tilt is statically set by the user and for surveys where a strapdown sensor is dynamically tilted by the motion of the platform. We show that the gradiometer's sensitivity to the vertical gravity gradient is only slightly reduced by this method while allowing for more gradiometer information to be obtained. Major sources of error and loss of sensitivity on dynamic platforms are shown to be mitigated using an optical-gimbal technique employing commercially-available fiber-optic gyroscopes and tip-tilt mirrors.

We report on the sticking time of the AlF dimer in the ultracold regime. We employ a full-dimensional potential energy surface for AlF-AlF, constructed using a machine learning approach [X. Liu et al., J. Chem. Phys. 159, 144103 (2023)], to compute the density of states using a semiclassical counting method. Next, using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory, we determine an RRKM sticking time of 216.0 $\pm$ 4.8 ns, which is shorter than that of other previously reported nonreactive dimers. Then, based on the available potential energy surfaces and RRKM sticking time data for a few dimers, we observe that the RRKM sticking time correlates with the ratio of the dimer dissociation energy to the dissociation energy of its parent molecule. Thus, we propose this ratio as a parameter to estimate RRKM sticking times. Furthermore, using ab initio methods, we optimize and calculate the energies of the equilibrium geometries of AlCl-AlCl, CaH-CaH, and MgF-MgF, thereby determining the ratio of the dimer dissociation energy to the parent molecule dissociation energy. Based on this ratio, we propose a hierarchy to order the sticking lifetimes of those dimers in the ultracold regime.

The influence of van der Waals (vdW) interaction on the nonlinear optical properties of Rydberg atoms is investigated within a three-level cascade scheme established using two probe and control laser fields. It is demonstrated that vdW interaction can induce reverse saturable absorption (RSA) in the Rydberg atoms in the two-photon resonance condition, enabling controllable optical limiting behavior. Furthermore, the presence of vdW interaction facilitates a switch between saturable absorption and RSA and vice versa beyond the two-photon resonance condition, thereby enabling intrinsic optical bistability in the system.

Bimodal Fabry-Pérot interferometer is a model generalizing the conventional Fabry-Pérot interferometer, in which not one but two kinds of waves propagate between the interfaces. Here, we study coherent perfect absorption (CPA) and lasing at threshold in bimodal Fabry-Pérot interferometers. We show that CPA and lasing appear only in certain “allowed” regions in the parameter space, which, as we demonstrate, are described by closed-form inequalities imposed on the elements of the scattering matrix of the interferometer interfaces. We demonstrate topologically governed annihilation of CPA points as they approach the boundary of a CPA-allowed region. In the particular case when the absorption losses tend to zero, the presented model describes the formation of bound states in the continuum exactly at the CPA annihilation points. The presented analytical model is in perfect agreement with the rigorous numerical simulation results of high-contrast gratings and ridge resonators implementing the bimodal Fabry-Pérot interferometer model.

The calculation of the natural lineshape of an excited two-level system (TLS) has long been known to be gauge dependent, with experiments and classical predictions in better agreement with the lineshape calculated with the dipole gauge ($-\mathbf{r}·\mathbf{E}$ coupling). We show that by using a Coulomb-gauge ($\mathbf{p}·\mathbf{A}$ coupling) Hamiltonian truncated in a manner consistent with the gauge principle, the correct output spectrum can, in fact, be obtained. For TLSs undergoing dynamics arising from additional Hamiltonian couplings, we also show that the master equation is gauge invariant under the same conditions of validity as the Markov approximation, despite different gauges having different spectral densities. These results highlight the importance of using correctly truncated gauge-invariant Hamiltonians in input-output theory for accurate frequency-dependent spectra, even in weak-coupling regimes.

We investigate the interactions between two-level emitters mediated by time-dependent, one-dimensional, structured photonic baths, focusing on Floquet topological lattices. Building on the framework of periodically driven photonic lattices, we demonstrate and characterize the emergence of tunable-range emitter interactions mediated by bound states absent in static photonic lattices. In particular, we show that one can obtain different spatial interaction dependencies not only with respect to the static bath scenarios, but also in qualitatively different regimes due to the time-dependent nature of the bath, for example, when the emitters have different frequencies. This work sheds light on the interplay between nonequilibrium photonics and quantum optics and can serve as a basis for analyzing Floquet photonic lattices in higher dimensions.

The implementation of quantum routers is an important and desired task in quantum information science, since quantum routers are important components of quantum networks. Here we propose a scheme for implementing single-photon routers in a waveguide-QED system, which consists of two coupled two-level atoms coupled to two waveguides to form a four-port quantum device. We obtain the exact analytical expressions of the single-photon scattering amplitudes using the real-space method. By taking into account or disregarding the propagating time of photons between two coupling points, we consider the system working in the Markovian and non-Markovian regimes, respectively. In addition, we introduce the chiral coupling, which breaks the symmetry of the waveguide model, to manipulate the transmission of single photons. We find that when the system works in the non-Markovian regime, the single photon can be transmitted on demand by adjusting the asymmetry coefficient. More interestingly, the complete single-photon routing in this device does not require an ideal chiral coupling, loosening the photon transport conditions. This work should motivate studies concerning the nonreciprocal and chiral quantum devices in the waveguide-QED platform.