Self-testing protocols enable the certification of quantum devices without demanding full knowledge about their inner workings. A typical approach in designing such protocols is based on observing nonlocal correlations which exhibit maximum violation in a Bell test. We show that in the Bell experiment known as Hardy's test of nonlocality, not only does the maximally nonlocal correlation self-test a quantum state, rather a nonmaximal nonlocal behavior can serve the same purpose. We, in fact, completely characterize all such behaviors leading to a self-test of every pure two-qubit entangled state except for the maximally entangled ones. Apart from presenting an alternative self-testing protocol, our method provides a powerful tool towards characterizing the complex boundary of the set of quantum correlations.

Concurrence, introduced by Hill and Wootters [Hill and Wootters, Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive for entangled states and vanishes for all separable states. We present an extension of the entanglement measure to general pure continuous variable states of multiple degrees of freedom by generalizing the Lagrange's identity and wedge product framework proposed by Bhaskara and Panigrahi [Bhaskara and Panigrahi, Quantum Inf. Process. 16, 118 (2017)] for pure discrete-variable systems in arbitrary dimensions and extending the concept to mixed continuous-variable states. A family of faithful entanglement measures is constructed that admits necessary and sufficient conditions for separability across arbitrary bipartitions presented by Vedral et al. [Vedral, Plenio, Rippin, and Knight, Phys. Rev. Lett. 78, 2275 (1997)]. The computed entanglement measure in the present approach for general Gaussian states, pair-coherent states, and non-Gaussian continuous-variable Bell states matches with known results. We also quantify entanglement of phase-randomized squeezed states and superposition of squeezed states. Our results also simplify several results in quantum entanglement theory.

Current-generation quantum annealers have already proven to be successful problem solvers. Yet quantum annealing is still very much in its infancy, with suboptimal applicability. For instance, to date it is still an open question which annealing protocol causes the fewest diabatic excitations for a given eigenspectrum, and even whether there is a universally optimal strategy. Therefore, in this paper, we report analytical and numerical studies of the diabatic excitations arising from nonlinear protocols applied to the transverse field Ising chain, the exactly solvable model that serves as a quantum annealing playground. Our analysis focuses on several driving schemes that inhibit or facilitate the dynamic phases discussed in a previous work. Rather remarkably, we find that the paradigmatic Kibble-Zurek behavior can be suppressed with “pauses” in the evolution, both for crossing and for stopping at the quantum critical point of the system.

We present a simultaneous-cooling protocol for a double-resonator system via projective measurements on an ancillary $V$-type qutrit. Through repeated measurements on the ground state of the ancillary system, the two resonators can be cooled down to their respective ground states from thermal states. With respect to the measurement-based cooling, an optimized measurement interval ${\tau }_{\mathrm{opt}}$ is analytically obtained, which is inversely proportional to the collective thermal Rabi frequency ${\mathrm{\Omega }}_{\mathrm{th}}$ as a function of the resonators' average population of the last round. Under about only 20 optimized measurements, the average population of the target resonators can be reduced by six orders in magnitude. Our simultaneous or collective cooling protocol is scalable to the systems with more numbers of resonators and robust to the fluctuation in the resonator frequency. Also we discuss the robustness of our cooling protocol against the thermal environment and the measurement error.

Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits efficiently classically simulable, thereby destroying any quantum advantage potentially offered by an ideal (noiseless) implementation of these circuits. Although the technique of quantum error correction (QEC) allows correcting these errors very accurately, QEC usually requires a large overhead of physical qubits which is not reachable with currently available quantum hardware. This has been the motivation behind the field of quantum error mitigation, which aims at developing techniques to correct an important part of the errors in quantum circuits, while also being compatible with current and near-term quantum hardware. In this work, we present a technique for quantum error mitigation which is based on a technique from quantum verification, the so-called accreditation protocol, together with postselection. Our technique allows for correcting the expectation value of an observable $O$, which is the output of multiple runs of noisy quantum circuits, where the noise in these circuits is at the level of preparations, gates, and measurements. We discuss the sample complexity of our procedure and provide rigorous guarantees of errors being mitigated under some realistic assumptions on the noise. Our technique is tailored to time-dependent behaviors, as we allow for the output states to be different between different runs of the accreditation protocol. We validate our findings by running our technique on currently available quantum hardware.

We study dynamically coupled one-dimensional Bose-Hubbard models and solve for the wave functions and energies of two-particle eigenstates. Even though the wave functions do not directly follow the form of a Bethe ansatz, we describe an intuitive construction to express them as combinations of Choy-Haldane states for models with intra- and interspecies interactions. We find that the two-particle spectrum of the system with generic interactions comprises in general four different continua and three doublon dispersions. The existence of doublons depends on the coupling strength $\mathrm{\Omega }$ between two species of bosons, and their energies vary with $\mathrm{\Omega }$ and interaction strengths. We give details on one specific limit, i.e., with infinite interaction, and derive the spectrum for all types of two-particle states and their spatial and entanglement properties. We demonstrate the difference in time evolution under different coupling strengths and examine the relation between the long-time behavior of the system and the doublon dispersion. These dynamics can in principle be observed in cold atoms and might also be simulated by digital quantum computers.

We study a cluster Ising model with non-Hermitian external field which can be exactly solved in the language of free fermions. By investigating the second derivative of energy density and fidelity, the possible new critical points are tentatively located. The string order parameter and staggered magnetization are then detected to reveal emergent phases of brand new characteristics. To categorize the exotic phases and phase transitions induced by non-Hermiticity, we calculate the variation mode of the spin-correlation function as well as of the string correlation function, which characterize the emergent phases and critical points with different patterns of decay and critical exponents. With the help of the string order parameter and staggered magnetization, we find that there are four phases after introducing the non-Hermiticity—the cluster phase, the gapless phase, the paramagnetic phase, and the antiferromagnetic phase. A phase diagram is then presented to graphically illustrate, based on two “Kosterlitz-Thouless-like” phase transitions and an Ising phase transition, respectively, the generation of three critical lines as non-Hermitian strength increases. Our theoretical work is expected to be realized in the experiment of ultracold atoms, pushing for progress in exploring novel phases and phase transitions.

Bound states of optical solitons represent ideal candidates to investigate fundamental nonlinear wave interaction principles and have been shown to exhibit intriguing analogies to phenomena in quantum mechanics. Usually, such soliton molecules are created by a suitable balance of phase-related attraction and repulsion between two copropagating solitons with overlapping tails. However, there exists also another type of compound state, where strong binding forces result directly from the Kerr nonlinearity between solitons at different center frequencies. The physical mechanisms as well as the properties of these objects are quite different from those of usual soliton molecules, but are hardly known. Here we characterize and investigate these compound states in greater detail. We demonstrate unique propagation dynamics by investigating the robustness of the compound states under perturbations, such as third-order dispersion and the Raman effect. The constituents are individually affected by the perturbations, but the impact on the compound state is not a mere superimposition. One observes complex dynamics resulting from a strong entanglement between the subpulses. For example, in the case of the Raman effect both subpulses are subject to a cancellation of the self-frequency shift, although only one subpulse is approaching a zero-dispersion frequency. We extend the concept of the molecule states to three and more constituents by adopting appropriate propagation constants. These multicolor soliton molecules open up further perspectives for exploring the complex physics of photonic molecules, but also show great potential for application resulting from their robustness and the possibility to control their properties.

We numerically investigated the interaction of a soliton with nonstationary dispersive waves as well as the soliton interaction induced by them, in a fiber ring laser mode locked by a nonlinear polarization rotation technique. In low-loss mode-locked states, a resonant frequency shifting effect and two time-jittering motions of solitons are found during the interaction. An analysis reveals that an indirect phase-matching interference between a pulsed dispersive wave and a soliton upon cross-phase modulation breaks the conservation of soliton momentum, while the subsequent soliton reconstruction leads to a recovery of the conservation. The interference mechanism, together with the conservation of soliton momentum, accounts for some basic behaviors of soliton laser dynamics.

The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (nonunitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of a (dissipative) lattice Green's function with a real-space decimation technique. Compared to other methods, such a technique enables us to obtain compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its nontrivial topology, which manifests in directional amplification.

In the thermodynamic limit, the steady states of open quantum many-body systems can undergo nonequilibrium phase transitions due to a competition between coherent and driven-dissipative dynamics. Here, we consider Markovian systems and elucidate structures of the Liouville superoperator that generates the time evolution. In many cases of interest, an operator-basis transformation can bring the Liouvillian into a block-triangular form, making it possible to assess its spectrum. The spectral gap sets the asymptotic decay rate. The superoperator structure can be used to bound gaps from below, showing that, in a large class of systems, dissipative phase transitions are actually impossible and that the convergence to steady states follows an exponential temporal decay. Furthermore, when the blocks on the diagonal are Hermitian, the Liouvillian spectra obey Weyl ordering relations. The results apply, for example, to Davies generators and quadratic systems and are also demonstrated for various spin models.

We study the buildup of the spatial correlation in a two-dimensional dissipative Rydberg system using the time-dependent variational principle. We find that in the sweeping process of the Rabi frequency and detuning, a moderately large decay rate induced by the two-photon excitation scheme suppresses significantly the buildup of correlation in a long-time scale in agreement with experimental results. A relatively large dephasing rate leads to a short relaxation time for the antiferromagnetic correlation to reach a stable value. These results provide a general view about the role of various decoherence mechanisms in the buildup of antiferromagnetic correlations and guide experiments to explore dissipative many-body dynamics using a Rydberg atomic system.

Time-bin encoding of photons offers a robust kind of long-distance quantum communication over lossy channels. The diversity of material nodes in quantum networks operating at natural frequencies requires coherent frequency and wave-form conversion of information-carrying photons to provide an efficient quantum interface with optical fibers and various quantum memories, which has been extensively studied. However, the quantum frequency conversion with transfer of time-bin encoding between single photons of different wavelengths has not yet been explored. In this paper, we present a method for efficiently exchanging time-bin encoding in the conversion process between two photons propagating in cold tripod atoms driven by a strong laser field. The latter is designed to slow down photons and suppress their absorption due to electromagnetically induced transparency. Photons interact parametrically through modified atomic coherence, which is utilized also to achieve equal group velocities of photons. We demonstrate the ability of our model to generate entanglement between distant atoms that equally share the original quantum information stored in the ground-state polarization qubits of both atoms. The proposed method for frequency conversion based on modified atomic coherence is promising because it can simplify the implementation of reliable and high-speed quantum communication protocols based on single-photon entanglement.

Extraction of the photoelectron spectrum (PES) from the time-dependent wave-packet calculations is a fundamental requirement for studying strong-field ionization. To analyze the PES, one needs to extract the physical observables from the time-dependent wave function at the end of the laser pulse. The exact PES can be obtained by projecting this wave function onto the continuum states of the same binding potential, which have to obey the incoming boundary condition. This means that the continuum states at large distances from the atomic or molecular targets have to be localized in momentum space so that asymptotically the continuum states can be approximated by plane waves. In this paper, we extend our previous analysis [B. Fetić, W. Becker, and D. B. Milošević, Extracting photoelectron spectra from the time-dependent wave function: Comparison of the projection onto continuum states and window-operator methods, Phys. Rev. A 102, 023101 (2020)] and investigate two alternative methods of the PES extraction: projecting the time-dependent wave function onto plane waves as well as the so-called time-dependent surface flux (tSURFF) method. A thorough analysis is performed to check the reliability of these methods in comparison with the exact method. The time integral, which appears in the tSURFF ionization amplitude, is divided into smaller time intervals. Analyzing the corresponding partial amplitudes and their interference we relate these time intervals to particular parts of the PES. The method is applied to analyze the high-energy PES as well as the low-energy and very-low-energy structures in the PES.

Acquiring precise information about the mode content of a laser is critical for multiplexed optical communications, optical imaging with active wave-front control, and quantum-limited interferometric measurements. Hologram-based mode decomposition devices, such as spatial light modulators, allow a fast, direct measurement of the mode content, but they have limited precision due to cross coupling between modes. Here, we report a proof-of-principle demonstration of mode decomposition with a metasurface, resulting in significantly enhanced precision. A mode-weight fluctuation of $6\times {10}^{-7}$ was measured with 1 s of averaging at a Fourier frequency of 80 Hz, an improvement of more than three orders of magnitude compared to the state-of-the-art spatial light modulator decomposition. The improvement is attributable to the reduction in cross coupling enabled by the exceptionally small pixel size of the metasurface. We show a systematic study of the limiting sources of noise, and we show that there is a promising path towards complete mode decomposition with similar precision.

The advent of free-electron lasers (FELs) in the soft- and hard-x-ray spectral regions has introduced the possibility to probe electronic, magnetic, and structural dynamics, in both diluted and condensed matter samples, with femtosecond time resolution. In particular, FELs have strongly enhanced the capabilities of several analytical techniques, which have taken advantage of the high degree of transverse coherence provided. Free-electron lasers based on the harmonic up-conversion of an external coherent source (seed) are characterized also by a high degree of longitudinal coherence, since electrons inherit the coherence properties of the seed. For the state of the art, the shortest wavelength delivered to user experiments by an externally seeded FEL light source is about 4 nm. In this paper we demonstrate that pulses with a high longitudinal degree of coherence (first and second order) covering the water window and with photon energy extending up to 790 eV can be generated by exploiting the so-called nonlinear harmonic regime, which allows generation of radiation at harmonics of the resonant FEL wavelength. In order to show the suitability of the nonlinear harmonics generated by a seeded FEL for research in the water window and beyond, we report the results of two proof-of-principle experiments: one measuring the oxygen $K$-edge absorption in water ($\sim 530$ eV) and the other analyzing the spin dynamics of Fe and Co through magnetic small-angle x-ray scattering at their $L$ edges (707 and 780 eV, respectively).

We point out in this Comment a misleading remark made by Gu and Beiersdorfer [Phys. Rev. A 101, 032501 (2020)] that the Debye-Hückel (DH) model “performs rather poorly” compared with the ion sphere model is due to their questionable use of the Debye length by assuming the same mobility for the plasma electrons and ions. Actually, our recent works based on a judicious application of the DH approximation, which meets the spatial and temporal criteria, have led to good agreements with all the available line shift experimental measurements on $\alpha$ and $\beta$ emission lines of He-like ions.

We study the quantum dynamics of a one-dimensional $\mathrm{SU}(3$)-symmetric system of cold atoms in the presence of two-body losses. We exploit the representation theory of $\mathrm{SU}(3$), the so-called eightfold way, as a scheme to organize the dark states of the dissipative dynamics in terms of generalized Dicke states and show how they are dynamically approached, both in the weakly and strongly interacting and dissipative regimes. Our results are relevant for a wide class of alkaline-earth(-like) gas experiments, paving the way to the dissipative preparation and exploitation of generalized Dicke states.

Geodesics are the shortest curves between any two points on a given surface. Geodesics in the state space of quantum systems play an important role in the theory of geometric phases, as these are also the curves along which the acquired geometric phase is zero. Null-phase curves (NPCs) are the generalization of the geodesics, which are defined as the curves along which the acquired geometric phase is zero even though they need not be the shortest curves between two points. Here, we present a geometric decomposition of geodesics and NPCs in higher-dimensional state space, which allows understanding of the intrinsic symmetries of these curves. We use Majorana star representation to decompose a geodesic in the $n$-dimensional Hilbert space to $n-1$ curves on the Bloch sphere and show that all the $n-1$ curves are circular segments with specific properties that are determined by the inner product of the end states connected by the given geodesic. We also propose a method to construct infinitely many NPCs between any two arbitrary states for $(n>2)$-dimensional Hilbert space using our geometric decomposition.

In Foldy-Wouthuysen representation, this paper deduces the effective quantum mechanics for a relativistic particle confined to a curved surface in an external field by using the thin-layer quantization scheme. It is found that the quantum effects caused by introducing the confining potential can be taken as the results of relativistic correction in the nonrelativistic limit. Meanwhile, the spin connection of the curved surface can produce a Zeeman-like gap through the relativistic correction term. In addition, the confining potential can provide a curvature-independent energy shift resulting from the Zitterbewegung effect. As an example, this paper applies the effective Hamiltonian to a torus surface, in which the spin effects related to the introduced confining potential are obtained. These results demonstrate the scaling of the noncommutation of the nonrelativistic limit and the thin-layer quantization procedure.