Computations of entropy in thermodynamics rely on discreteness of the spectra of the subsystems. We argue that, for cases with continuous spectra (typically, radiation), there is a useful definition of entropy flow based on discretizing the signal into Gabor's “atoms,” say, by means of a windowed Fourier transform. In particular, applying this method to a degenerate parametric amplifier (paramp) driven by a classical pump and coupled to a zero-temperature Markovian bath, we find that the output entropy flux vanishes at large times, even though the energy and photon number fluxes remain nonzero. This is consistent with the manner in which the paramp is expected to release information about its initial state. We relate the quenching of the entropy flow to development of the off-diagonal coherences in the output and discuss possible relevance of this mechanism to the black-hole information problem. We also propose to use measurements of the off-diagonal coherences as a means of extracting the rates at which high-entropy subsystems release information to linear environments.

We derive multiparty games that, if the winning chance exceeds a certain limit, prove the incompatibility of the parties' causal relations with any partial order. This, in turn, means that the parties exert a backaction on the causal relations; the causal relations are dynamical. The games turn out to be representable by directed graphs, for instance by an orientation of the Möbius ladder. We discuss these games as device-independent tests of space-time's dynamical nature in general relativity. To do so, we design relativistic settings where, in the Minkowski space-time, the winning chance is bound to the limits. In contrast, we find otherwise tame processes with classical control of causal order that win the games deterministically. These suggest a violation of the bounds in gravitational implementations. We obtain these games by uncovering a “pairwise central symmetry” of the correlations in question. This symmetry allows us to recycle the facets of the acyclic subgraph polytope studied by Grötschel, Jünger, and Reinelt in the mid-80s for combinatorial optimization. In addition, we derive multiparty games in a scenario where the polytope dimension grows only linearly in the number of parties. Here, exceeding the limits not only proves the dynamical nature of the causal relations, but also that the correlations are incompatible with any global causal order.

According to the celebrated Gottesman-Knill theorem, magic resource (nonstabilizerness) is necessary to drive universal quantum computation. Thus characterization and quantification of magic resource for quantum states and quantum channels are significant issues. In this work, we propose a method to construct quantifiers of magic resource for quantum channels from those for quantum states by employing the channel-state duality to convert quantum channels to the corresponding Choi states. We focus on a specific quantifier of magic resource based on characteristic functions (Fourier transforms) of quantum states. This quantifier is well defined for all dimensions and easy to calculate, as opposed to those defined via discrete Wigner functions. It satisfies some desirable properties and provides an upper bound to the mana (a kind of logarithmic negativity of discrete Wigner functions) of quantum channels. Using this quantity, we evaluate the amount of magic resource for some typical quantum channels and compare them with some existing quantifiers of generating-power of magic resource. For the dephasing channels in prime dimensional systems, our quantifier of magic resource essentially characterizes the average generating power of magic resource, while, for general channels, they are quite different and some challenging issues arise.

Informational contributions to thermodynamics can be studied in isolation by considering systems with fully degenerate Hamiltonians. In this regime, being in nonequilibrium (termed informational nonequilibrium) provides thermodynamic resources, such as extractable work, solely from the information content. The usefulness of informational nonequilibrium creates an incentive to obtain more of it, motivating the question of how to concentrate it: can we increase the local informational nonequilibrium of a product state $\rho \otimes \rho$ under a global closed system (unitary) evolution? We fully solve this problem analytically, showing that it is impossible for two-qubits, and it is always possible to find states achieving this in higher dimensions. Specifically for two-qutrits, we find that there is a single unitary achieving optimal concentration for every state, for which we uncover a Mpemba-like effect. We further discuss the notion of bound resources in this framework, initial global correlations' ability to activate concentration, and applications to concentrating purity and intrinsic randomness.

We present a hybrid continuous variable–discrete variable entanglement generation protocol using linear optics and homodyne measurements, capable of producing multiple high-fidelity Bell pairs per protocol iteration, with an approximate 0.5 success probability. The effectiveness of the protocol is determined by the squeezing strength. To increase the number of Bell pairs, approximately 3 dB of extra squeezing is needed for each additional Bell pair. The protocol also generates single Bell pairs with an approximate 0.75 probability for squeezing strengths $⪅15\mathrm{dB}$, achievable with current technology.

The ${}^{229}\mathrm{Th}$ nucleus possesses a unique low-frequency transition at 8.4 eV, which is being considered for the development of an extremely accurate nuclear clock. We investigate an electronic bridge process in the Th iii ion, where nuclear excitation is mediated by electronic transitions, and show that selecting appropriate laser frequencies can enhance the nuclear excitation probability by up to ${10}^4$ times. Electrons also reduce 1.7 times the lifetime of the nuclear excited state. Moreover, the electronic structure of Th iii offers exceptional opportunities for probing new physics. Notably, the ion contains a metastable electronic state coupled to the ground state via a weak $M2$ transition, which can be utilized for quantum information processing, as well as searches for oscillating dark matter axion and scalar fields, violation of local Lorentz invariance, test of the Einstein equivalence principle, and measurement of the nuclear weak quadrupole moment. Additionally, the electronic states of Th iii present a unique case of level crossing involving the $5f$, $6d$, and $7s$ single-electron states. This crossing renders high sensitivity of the transition frequencies to potential time variation of the fine-structure constant.

The saddle-point solutions for strong-laser-field-induced high-order above-threshold ionization, the complete classification of which was recently presented in Phys. Rev. A 111, 023103 (2025), are considered classically. In the limit of vanishing ionization potential the system of saddle-point equations simplifies, allowing a semi-analytical treatment. For a monochromatic field, the analytical nonlinear equations obtained this way allow one to determine the maximum (cutoff) photoelectron energies for the backward- and forward-scattering saddle-point solutions for all values of the multi-indices introduced by our classification scheme. These cutoffs are determined for all photoelectron momenta and it is shown how the backward-scattering solutions from one half of the momentum plane are related to the forward-scattering solutions from the other. The case of a bichromatic linearly polarized field is analyzed in detail. The results are rederived with the help of a simple graphical method, which can be used to qualitatively discuss the effect of varying the field parameters.

Macroscopic entanglement, as a critical quantum resource in quantum information science, has been extensively studied in coherent optomechanics over the past decades. However, entanglement in dissipative optomechanics, where the cavity linewidth depends on the position of the mechanical resonator, remains largely unexplored. In this work, we investigate quantum entanglement in a dissipative optomechanical system realized by a Michelson-Sagnac interferometer with a movable membrane. This configuration enables the switching between coherent and dissipative optomechanical couplings at will. With experimentally feasible parameters, we demonstrate that the steady-state mechanical displacement exhibits a nonlinear (linear) dependence on the driving power under coherent (dissipative) coupling. Furthermore, we show that the quantum entanglement generated via dissipative coupling is significantly stronger and more robust to noise than that generated via coherent coupling. When both coherent and dissipative couplings are simultaneously present, the entanglement is weakened due to quantum interference. Our results indicate that dissipative optomechanical coupling can be a promising route for engineering strong and noise-resilient quantum entanglement.

This paper numerically investigates the breathing behavior and chaotic self-trapped behavior of scalar vortex solitons (SVSs) and vector vortex solitons (VVSs) modulated with initial spatial chirps in thermally nonlocal nonlinear media, such as lead glass. We found that as for the SVS, small spatial chirp induces breathing behavior, while large spatial chirp leads to chaotic self-trapped behavior. This chaotic self-trapped behavior exhibits both chaotic property and trapping property. The transition between these two behaviors can be achieved by varying the magnitude of the spatial chirp. As for the VVS, small spatial chirp induces an asynchronous or synchronous breather-breather pair under short-range interaction. As spatial chirp increases, chaos-chaoticon, entangled and nonentangled chaoticon-chaoticon, and chaoticon-quasisoliton pairs are formed. By adjusting the spatial chirp, we achieve controllable conversion between soliton, breather, chaos, chaoticon, and quasisoliton. The controllable chaotic self-trapped beams and switchable propagation states may provide ideas for chaotic secure communication.

We study the dynamics of two giant atoms interacting with a coupled resonator waveguide (CRW) beyond the Markovian approximation. The distinct atomic configurations determine the number of bound states in the continuum (BICs), leading to different dynamical behaviors. Our results show that when the system supports two BICs, Rabi oscillations dominate the dynamics, whereas fractional population dynamics emerge in the presence of a single BIC. The connection between these dynamics and the existence of BICs is further verified by analyzing the photonic distribution in the CRW during time evolution. These findings challenge the conventional notion that the environment always induces dissipation and decoherence. Instead, the bound states in the CRW-emitter coupled system can suppress complete dissipation of the emitters. We also quantitatively illustrate the memory effect of the waveguide, which serves as the environment of the giant-atom feature that can only be captured within our non-Markovian treatment. This work offers an effective approach for controlling dissipative dynamics in open quantum systems.

In this paper, we propose a high-fidelity scheme for generating entangled states in a system of two and three giant atoms coupled to the coupled resonator waveguide. Our approach leverages the bound state in the continuum, which is robust against waveguide disorder. Specifically, we achieve a fidelity exceeding $98\%$ for Bell state generation, overcoming the limitations of conventional decoherence-free interaction mechanisms. This scheme can be readily extended to a three-giant-atom system for generating $W$ states. In both the two- and three-atom setups, the maximally entangled states are generated in a short time and remain stable even as time approaches infinity. Our proposal is feasible for implementation on state-of-the-art solid-state quantum platforms and significantly broadens the applications of giant atoms and waveguide QED systems in quantum information processing.

Cavity quantum electrodynamics (cavity QED) enables the control of light-matter interactions at the single-photon level, rendering it a key component of many quantum technologies. Its practical realization, however, is complex since it involves placing individual quantum emitters close to mirror surfaces within a high-finesse cavity. In this work, we propose a cavity QED architecture fully based on atoms trapped in free space. In particular, we show that a pair of two-dimensional, ordered arrays of atoms can be described by conventional cavity QED parameters. Such an atom-array cavity exhibits the same cooperativity as a conventional counterpart with matching mirror specifications even though the cavity coupling strength and decay rate are modified by the narrow bandwidth of the atoms. We estimate that an array cavity composed of ${}^{87}\mathrm{Rb}$ atoms in an optical lattice can reach a cooperativity of about 10. This value can be increased suppressing atomic motion with larger trap depths and may exceed ${10}^4$ with an ideal placement of the atoms. To reduce the experimental complexity of our scheme, we propose a spatially dependent ac Stark shift as an alternative to curving the arrays, which may be of independent interest. In addition to presenting a promising platform for cavity QED, our work creates opportunities for exploring novel phenomena based on the intrinsic nonlinearity of atom arrays and the possibility to dynamically control them.

Creating macroscopic spatial superposition states is crucial for investigating matter-wave interferometry and advancing quantum sensor technology. Currently, two potential methods exist to achieve this objective. The first involves using inverted harmonic potential (IHP) to spatially delocalize quantum states through coherent inflation [New J. Phys. 19, 123029 (2017)]. The second method employs a spin-dependent force to separate two massive wave packets spatially [Phys. Rev. Lett. 111, 180403 (2013)]. The disadvantage of the former method is the slow initial coherent inflation, while the latter is hindered by the diamagnetism of spin-embedded nanocrystals, which suppresses spatial separation. In this study, we integrate two methods: first, we use the spin-dependent force to generate initial spatial separation, and second, we use IHP to achieve coherent inflating trajectories of the wave packets. This approach enables the attainment of massive large spatial superposition in minimal time. For instance, a spatial superposition with a mass of ${10}^{-15}\mathrm{kg}$ and a size of around $50\mu \mathrm{m}$ is realized in 0.1 s. We also calculate the evolution of wave packets in both harmonic potential (HP) and IHP using the path integral approach.

Two important ingredients necessary for obtaining Bell nonlocal correlations between two spatially separated parties are an entangled state shared between them and an incompatible set of measurements employed by each of them. However, not all entangled states can give rise to Bell nonlocality. Here, we are interested in a complementary question, regarding the role of the sets of incompatible measurements in enabling Bell nonlocality, for arbitrary entangled states. It is known that for some sets of more than two jointly incompatible measurements performed by one of the parties, there does not exist an entangled state and another set of incompatible measurements for the other party, which will result in Bell nonlocality. However, in the two-input and two-output setting per party, measurement incompatibility at a single party will always guarantee Bell nonlocality. Thus, it is interesting to ask whether all sets of incompatible measurements at both parties, in the two-input and two-output setting per party, will result in Bell nonlocality for some shared state. We first observe that Bell nonlocality can always be established when both parties employ any set of incompatible projective measurements. On the other hand, going beyond projective measurements, we present a class of incompatible positive operator-valued measures, employed by both observers, which can never activate Bell nonlocality. Furthermore, we find a sufficient criterion for achieving Bell nonlocal correlations given a fixed amount of pure two-qubit entanglement and a fixed amount of incompatibility of projective measurements applied by either both parties or a single party.

Thermodynamics is based on a coarse-grained approach, from which its fundamental variables emerge, effectively erasing the complicated details of the microscopic dynamics within a macroscopic system. The strength of thermodynamics lies in the universality provided by this paradigm. In contrast, quantum mechanics focuses on describing the dynamics of microscopic systems, aiming to make predictions about experiments we perform, a goal shared by all fundamental physical theories, which are often framed as gauge theories in modern physics. Recently, a gauge theory for quantum thermodynamics was introduced, defining gauge-invariant work and heat, and exploring their connections to quantum phenomena. In this work, we extend that theory in two significant ways. First, we incorporate energy spectrum degeneracies, which were previously overlooked. Additionally, we define gauge-invariant entropy, exploring its properties and connections to other physical and informational quantities. This results in a complete framework for quantum thermodynamics grounded in the principle of gauge invariance. To demonstrate some implications of this theory, we apply it to well-known critical systems.

Quantum error correction represents a significant advancement in large-scale quantum computing. However, achieving fault-tolerant implementations of non-Clifford logical gates with reduced overhead remains a challenge in the popular surface code strategy. Recent advances have underscored the need for a substantial code distance to attain complete fault tolerance. Here, we introduce a continuous fault-tolerant scheme for non-Clifford logical gates via multiple injections. Unlike existing protocols that focus on a single logical chain, our approach utilizes multiple logical chains, each of which can employ the same or different logical rotation angles to initialize a non-Clifford state. Compared to previous efforts, our protocol significantly alleviates the challenges associated with the requirement for a large code distance and reduces the corresponding resource overheads, making it more feasible to be implemented in current midscale chips via the surface code strategy.

We develop a framework for describing the effects of systematic state-preparation error in quantum-enhanced atom interferometry on sensing performance. We do this in the context of both spin-squeezed and non-Gaussian states for the two-axis-twisting (TAT), one-axis-twisting (OAT), and twist-and-turn (TNT) state-preparation schemes, and derive general conditions for robustness and susceptibility of quantum states to state-preparation error. In the spin-squeezing regime, we find that OAT is more susceptible to state-preparation error than TAT due to its parameter-dependent phase-space rotation. In the non-Gaussian regime, we find that OAT is robust to state-preparation errors, which can be explained by a small ratio of off-diagonal to diagonal elements in its Fisher-covariance matrix. In contrast, TNT does not exhibit this robustness. We find that the single-parameter unbiased estimators that are habitually used in quantum-enhanced atom interferometry are not always optimal, and that there may be occasions where biased estimators, or two-parameter unbiased estimators, lead to lower net error.

Large-scale quantum communication systems often require different channels to be connected to multiple networks via frequency conversion, which requires frequency converters to act as relay points for system connectivity. We propose a quantum network for single-photon frequency conversion based on time-bin entanglement, where legitimate users can realize the spanning of communication bands between users by independently choosing the target conversion frequency mode. The results show that the converter in the network can be used as a bridge to completely connect the two networks by cascading the quadratic nonlinear process. Meanwhile, the converted quantum entangled states are demonstrated in entanglement measurements and can be used for entanglement swapping. This scheme is expected to be widely used in scenarios where different networks share quantum resources, switching communication channels and effectively connecting different multiplexed spectrum. This concept also provides significant applications in large-scale metropolitan area networks.

Single and double photoionization of the Li-like ${\mathrm{B}}^{2+}\left(1s^{2}2s{}^{2}S\right)$ ion were studied both experimentally and theoretically in the energy range from approximately 250–1200 eV. The cross section ${\sigma }_{23}$ for net single ionization in that range is dominated by direct removal of one $K$-shell electron, a process that is described very well by theory. Accordingly, measured yields of ${\mathrm{B}}^{3+}$ photoproducts were normalized to theory to obtain absolute cross sections ${\sigma }_{23}$. Aside from direct single ionization, there are additional contributions to ${\sigma }_{23}$ from photoabsorption resonances. The parameters of the Fano profile of the most prominent of these resonances, the triply excited $2s^{2}2p{}^{2}P$ state, were calculated by employing the convergent close coupling (CCC) approach and the theoretical results were experimentally verified. Using the normalization procedure obtained from the investigation of single ionization, also the measured yields of ${\mathrm{B}}^{4+}$ product ions could be put on an absolute cross-section scale. The resulting experimental cross section ${\sigma }_{24}$ is in good accord with the CCC calculations revealing unexpectedly strong contributions that arise from ionization with excitation of ${\mathrm{B}}^{2+}\left(1s^{2}2s{}^{2}S\right)$ forming intermediate autoionizing ${\mathrm{B}}^{3+}\left(n\ell n^{\prime }{\ell }^{\prime }\right)$ levels, which subsequently decay to ${\mathrm{B}}^{4+}$ by Auger-electron emission. In addition, contributions to ${\sigma }_{24}$ from resonant excitation of ${\mathrm{B}}^{2+}\left(n\ell n^{\prime }{\ell }^{\prime }{n}^{\prime \prime }{\ell }^{\prime \prime }\right)$ with $n,n^{\prime },n^{\prime \prime }\ge 2$ could be identified. These triply excited resonances with an empty $K$ shell can decay by simultaneous or sequential emission of two electrons and thus contribute to net double photoionization of the parent ${\mathrm{B}}^{2+}$ ion.

The presence of a single attractive impurity in an ultracold repulsive bosonic system can drive a transition from a homogeneous to a localized state, as we here show for a one-dimensional ring system. In the few-body limit, the localization of the bosons around the impurity, as seen in the pair correlations, is accompanied by low-lying modes that resemble finite-sized precursors of Higgs-Anderson- and Nambu-Goldstone-like modes. Tuning the impurity-boson mass ratio allows for the exploration of the transition from a spontaneous to an explicit breaking of the continuous rotational symmetry of the Hamiltonian. We compare the minimum of the Higgs-Anderson-like mode as a marker of the onset of localization in the few-body limit to mean-field predictions of binding. We find improved agreement between the few-body exact-diagonalization results and mean-field predictions of binding with increasing boson-boson repulsion.