We derive a Lipschitz continuity bound for quantum-classical conditional entropies with respect to angular distance, with a Lipschitz constant that is independent of the dimension of the conditioning system. This bound is sharper in some situations than previous continuity bounds, which were either based on trace distance (where Lipschitz continuity is not possible), or based on angular distance but did not include a conditioning system. However, we find that the bound does not directly generalize to fully quantum conditional entropies. To investigate possible counterexamples in that setting, we study the characterization of states which saturate the Fuchs–van de Graaf inequality and thus have angular distance approximately equal to trace distance. We give an exact characterization of such states in the invertible case. For the noninvertible case, we show that the situation appears to be significantly more elaborate, and seems to be strongly connected to the question of characterizing the set of fidelity-preserving measurements.

We analyze the robustness of Grover's quantum search algorithm performed by a quantum register under a possibly time-correlated noise acting locally on the qubits. We model the noise as originating from an arbitrary but fixed unitary evolution $U$ of some noisy qubits. The noise can occur with some probability in the interval between any pair of consecutive noiseless Grover evolutions. Although each run of the algorithm is a unitary process, the noise model leads to decoherence when all possible runs are considered. We derive a set of unitary $U$'s, called good noises, for which the success probability of the algorithm at any given time remains unchanged with varying nontrivial total number $m$ of noisy qubits in the register. The result holds irrespective of the presence of any time correlations in the noise. We show that only when $U$ is either of the Pauli matrices ${\sigma }_x$ and ${\sigma }_z$ (which give rise to $m$-qubit bit-flip and phase-damping channels, respectively, in the time-correlation-less case), the algorithm's success probability stays unchanged when increasing or decreasing $m$. In contrast, when $U$ is the Pauli matrix ${\sigma }_y$ (giving rise to $m$-qubit bit-phase flip channel in the time-correlation-less case), the success probability at all times stays unaltered as long as the parity (even or odd) of the total number $m$ remains the same. This asymmetry between the Pauli operators stems from the inherent symmetry-breaking existing within the Grover circuit. We further show that the positions of the noisy sites are irrelevant in the case of any of the Pauli noises. The results are illustrated in the cases of time-correlated and time-correlation-less noise. We find that the former case leads to a better performance of the noisy algorithm. We also discuss physical scenarios where our chosen noise model is of relevance.

Quantum networks involving multiqubit entanglement allow exciting applications in quantum communication, quantum sensing, and distributed quantum computation. The efficiency of nonlocal entanglement generation through optical channels drops exponentially with the distance between network nodes. We present a parallel and heralded protocol for generating distributed multiqubit entanglement across multiple nodes. This is achieved by using a high-dimensional single photon that works as a common-data bus connecting all stationary qubits (i.e., silicon-vacancy electron spins), each of which is coupled to a single-sided optical cavity. Parallel multiqubit entangled states are heralded by the detection of the single photon after it interacts with each stationary qubit and passes through each photonic modulation circuit. This parallel protocol can significantly improve the efficiency of distributed entanglement generation and provides a viable route towards distributed multinode quantum networks.

We propose a satellite-based scheme to perform clock synchronization between ground stations spread across the globe using quantum resources. We refer to this as a quantum clock synchronization (QCS) network. Through detailed numerical simulations, we assess the feasibility and capabilities of a near-term implementation of this scheme. We consider a small constellation of satellites equipped only with modest resources. These include quantum devices such as spontaneous parametric down conversion sources, avalanche photodetectors, and moderately stable on-board clocks such as chip-scale atomic clocks. In our simulations, the various performance parameters describing the hardware have been chosen such that they are either already commercially available or require only moderate advances. We conclude that with such a scheme, establishing a global network of ground-based clocks synchronized to subnanosecond level (up to a few picoseconds) of precision would be feasible. Such QCS satellite constellations would form the infrastructure for a future quantum network, able to serve as a globally accessible entanglement resource. At the same time, our clock synchronization protocol provides the subnanosecond level synchronization required for many quantum networking protocols, and thus can be seen as adding an extra layer of utility to quantum technologies in the space domain designed for other purposes.

Affleck-Kennedy-Lieb-Tasaki (AKLT) states are an important class of many-body quantum states that are useful in quantum information processing, including measurement-based quantum computation in particular. Here we propose a general approach for constructing efficient verification protocols for AKLT states on arbitrary graphs with local spin measurements. Our verification protocols build on bond verification protocols and matching covers (including edge coloring) of the underlying graphs, which have a simple geometric and graphic picture. We also provide rigorous performance guarantee that is required for practical applications. With our approach, most AKLT states of wide interest, including those defined on one- and two-dimensional lattices, can be verified with a constant sample cost, which is independent of the system size and is dramatically more efficient than all previous approaches. As an illustration, we construct concrete verification protocols for AKLT states on various lattices and on arbitrary graphs up to five vertices.

We report on an experimental and theoretical study of double $K$-shell photoionization of Ne over the 2.3–8.5 keV x-ray energy range. The ratio of double-to-single $K$-shell photoionization cross sections was determined experimentally by measuring the relative rates of the $KK-K{L}_{2,3}{L}_{2,3}$ (${}^{2}D$) Auger hypersatellite and the $K-L_{2,3}{L}_{2,3}$ (${}^{1}D$) diagram Auger transitions. By scaling the hypersatellite-diagram Auger-electron ratios to $KK/K$ cross-section ratios, comparison was made with theoretical cross-section ratios of He-like ${\mathrm{Ne}}^{8+}$ determined by the $R$ matrix with pseudostates method. The experimental Ne and theoretical ${\mathrm{Ne}}^{8+}$ cross-section ratios show similar variations with energy, but the experimental ratios systematically exceed the calculated ratios and also show a lower threshold energy for double $K$-shell photoionization onset compared to the computed ${\mathrm{Ne}}^{8+}$ threshold. The discrepancy is attributed to effects of $L$-shell electrons not included in the He-like ${\mathrm{Ne}}^{8+}$ calculations. Quantified scaling with nuclear charge $Z$ along the He-like isoelectronic sequence indicates that the measured 10-electron $Z=10$ double $K$-shell photoionization cross section behaves like the computed He-like $Z=8.9$ cross section, suggesting an effective nuclear screening parameter of $s_L=1.1$ by the additional eight outer $L$-shell electrons. Experimental results for the energy variations of Auger electron transitions from other multielectron hole states are also discussed.

We theoretically consider the phenomenon of field-free long-lasting orientation of symmetric-top molecules ionized by two-color laser pulses. The anisotropic ionization produces a significant long-lasting orientation of the surviving neutral molecules. The degree of orientation increases with both the pulse intensity and counterintuitively with the rotational temperature. The orientation may be enhanced even further by using multiple-delayed two-color pulses. The long-lasting orientation may be probed by even harmonic generation or by Coulomb-explosion-based methods. The effect may enable the study of relaxation processes in dense molecular gases and may be useful for molecular guiding and trapping by inhomogeneous fields.

We theoretically analyze the operating principles of a proposed matter-wave Sagnac interferometer utilizing Bose-Einstein-condensate (BEC) phonon modes as an interference medium. Previous work found that the orbital angular momentum phonon modes of a ring-trapped BEC are split in frequency by rotations, leading to a measurable rotation signal. We develop an alternate description in which an imbalance in the counterpropagating modes' amplitudes (populations) is induced by the rotation of the system during condensation. This description gives analytic forms for the interferometic phase shift in one dimension and is readily generalized to include mean-field interactions. To validate our findings, we simulate a ring-trapped BEC Sagnac interferometer in one dimension and demonstrate that measurement of an unknown rotation rate can be performed using a modified analysis. Our simulation data show strong agreement with our analytic results, and we further employ simulations to explore and clarify the role of superfluidity in this matter-wave Sagnac interferometer.

Recently, thulium has been condensed to Bose-Einstein condensate. Machine learning was used to avoid a detailed study of all obstacles, making cooling difficult. This paper analyzes the atomic loss mechanism for the 532-nm optical trap, used in the Bose-condensation experiment, and compares it with the alternative and more traditional micrometer-range optical dipole trap. We also measured the scalar and tensor polarizability of thulium at 1064 nm, which were found to be $167\pm 25$ a.u. ($275\pm 41\times {10}^{-41}\mathrm{F}{\mathrm{m}}^2$) and $-4\pm 1$ a.u. ($7\pm 2\times {10}^{-41}\mathrm{F}{\mathrm{m}}^2$), respectively.

We study the field-intensity fluctuations of two independent four-wave-mixing signals generated in a cold rubidium sample as well as the transmission signals. We employ an experimental setup using a single cw laser to induce the nonlinear process in a forward geometry using either parallel and circular or orthogonal and linear polarizations of the input fields. Even though the spectra of each experimental configuration are significantly different due to the distinct level structures of each scenario, both cases present intensity-intensity cross correlations of the four-wave-mixing signals. We also calculate the cross correlation between the input fields and draft a theoretical model that indicates that resonant phase-noise to amplitude-noise conversion allows the observation of Rabi oscillations in the cross-correlation curves.

We propose an optimal protocol using phase-preserving quantum measurements and phase-dependent modulations of the trapping potential at parametric resonance to cool a quantum oscillator to an occupation number of less than one quantum. We derive the optimal phase relationship and duration for the parametric modulations and compute the lowest-possible occupation number in the steady state. The protocol is robust against moderate amounts of dissipation and phase errors in the feedback loop. Our work has implications for the cooling of levitated mechanical resonators in the quantum regime.

A quantum emitter in a dynamic environment may have its energy levels drift uncontrollably in time with the fluctuating bath. This can result in an emission and/or absorption spectrum that is spread over a broad range of frequencies and presents a challenging hurdle for various applications. We consider a quantum emitter in an environment that alters the energy levels so that the emission frequency is represented by a Gaussian random distribution around a given mean value with given standard deviation and correlation time. We study the emission spectrum of this system when it is placed under the influence of a periodic sequence of finite-width $\pi$ pulses. We show that this external field protocol can effectively overcome spectral diffusion in this system by refocusing the bulk of the emission spectrum onto the pulse carrier frequency. We further consider two such emitters in different noisy environments and find that the two-photon interference operation can be made efficient by the sequence of finite-width pulses applied on both systems. Finally, we show that an ensemble of nominally similar emitters, each with its different environment, and thus randomly shifted emission frequency, can have its overall emission spectrum that would otherwise be inhomogeneously broadened according to the random distribution, refocused onto a lineshape with a well-defined central peak that has the linewidth of an individual isolated non-noisy emitter. These results demonstrate for this specific model of noisy environments, the protection of spectral properties by an external control protocol here represented by a periodic sequence of finite-width pulses.

We propose theoretically a quantum scar affecting the motion of three interacting particles in a circular trap. We numerically calculate the quantum eigenstates of the system and show that some of them are scarred by a classically unstable periodic trajectory, in the vicinity of which the classical analog exhibits chaos. The few-body scar we consider is stabilized by quantum mechanics, and we analyze it along the lines of the original quantum scarring mechanism [Phys. Rev. Lett. 53, 1515 (1984)]. In particular, we identify towers of scarred quantum states which we fully explain in terms of the unstable classical trajectory underlying the scar. Our proposal is within experimental reach owing to very recent advances in Rydberg atom trapping.

We provide a different perspective on the close relationship between entanglement and time. Our main focus is on bipartite entanglement, where this connection is foreshadowed both in the positive partial transpose criterion due to Peres [A. Peres, Phys. Rev. Lett. 77, 1413 (1996)] and in the classification of quantum within more general nonsignaling bipartite correlations [M. Frembs and A. Döring, Phys. Rev. A 106, 062420 (2022)]. Extracting the relevant common features, we identify a necessary and sufficient condition for bipartite entanglement in terms of a compatibility condition with respect to time orientations in local observable algebras, which express the dynamics in the respective subsystems. As an outlook and a program for future work, we discuss the relevance of the latter in the broader context of von Neumann algebras and the thermodynamical notion of time naturally arising within the latter.

To perform achieve fault-tolerant quantum computation, one can use flagged syndrome extraction with fewer ancilla qubits. However, it suffers from long circuit depth if one stabilizer is measured at a time. Previously, Reichardt showed that it is possible to measure multiple stabilizers with at most one shared flag qubit for certain small quantum codes. In this paper, we propose a procedure for general Calderbank-Shor-Steane codes of distance three so that multiple $Z$ stabilizers ($X$ stabilizers) can be fault tolerantly measured in parallel with one shared flag qubit. We simulate the memory and computation pseudothresholds for various code schemes. In particular, our parallel scheme based on Shor's nine-qubit code performs better than known seven- and nine-qubit schemes in the literature.

We consider a weakly interacting Bose-Einstein condensate that is loaded into an optical lattice with a two-point basis and described by a two-band Bose-Hubbard model with generic one-body and two-body terms. By first projecting the system onto the lower Bloch band and then applying the Bogoliubov approximation to the resultant Hamiltonian, we show that the inverse effective-mass tensor of the superfluid carriers in the Bogoliubov spectrum has two physically distinct contributions. In addition to the usual inverse band-mass tensor that is originating from the intraband processes within the lower Bloch band, there is also a quantum-geometric contribution that is induced by the two-body interactions through the interband processes. We also discuss the conditions under which the latter contribution is expressed in terms of the quantum-metric tensor of the Bloch states, i.e., the natural Fubini-Study metric on the Bloch sphere.

High-order harmonic generation (HHG) normally requires a careful adjustment of the driving laser intensity (typically ${10}^{14}–{10}^{15}$ W/${\mathrm{cm}}^2$) and gas medium parameters to obtain a microscopically and macroscopically optimized output. In contrast to conventional wisdom, we present experimental results indicating efficient HHG in all rare gases, using a high-density medium and a driving laser intensity of around ${10}^{16}$ W/${\mathrm{cm}}^2$. The experimental results are corroborated by theoretical simulations, which indicate that ionization-induced self-phase modulation and plasma defocusing self-regulate the driver laser intensity to a level that allows efficient HHG. A tenfold broadening of the driving near-infrared spectrum is observed, which results in the generation of continuous spectra from 18 to 140 eV in spite of using 50-fs-long driving pulses. The presented scheme represents a simple and versatile concept for the generation of extreme-ultraviolet and soft-x-ray continua, which could be used for transient absorption and reflection spectroscopy.

It is known that the superposition of two bound states in the continuum (BICs) leads to the phenomenon of an oscillating bound state, where excitations mediated by the continuum modes oscillate persistently. We perform exact calculations for the oscillating BICs in a one-dimensional photonic lattice coupled to a “giant atom” at multiple points. Our work is significantly distinct from previous proposals of oscillating BICs in continuous waveguide systems due to the presence of a finite energy band contributing band-edge effects. In particular, we show that the bound states outside the energy band are detrimental to the oscillating BIC phenomenon, and can be suppressed by increasing either the number of coupling points or the separation between each coupling point. Crucially, non-Markovianity is necessary for the existence of oscillating BICs, and the oscillation amplitude increases with the characteristic delay time of the giant atom interactions. We also propose an initialization scheme in the BIC subspace. Our work be experimentally implemented on current photonic waveguide array platforms and opens up prospects in utilizing reservoir engineering for the storage of quantum information in photonic lattices.

We study a driven-dissipative duo of two-level systems in an open quantum systems approach, modeling a pair of atoms or (more generally) meta-atoms. Allowing for complex-valued couplings in the setup, which are of both a coherent and incoherent character, gives rise to a diverse coupling landscape. We consider several points on this landscape, for example where the coupling between the two coupled two-level systems is dominated by coherent, incoherent, unsymmetrical, and even unidirectional interactions. Traversing the coupling terrain leads to remarkable features in the populations of the pair, correlations, and optical spectra. Most notably, the famous Mollow triplet spectrum for a single atom may be superseded for a pair by a Mollow quintuplet (or even by a spectral singlet) and the setup allows for population trapping to arise, all depending upon the precise nature of the coupling between the two-level systems.