In a recently demonstrated quantum-state tomography scheme [P. Yang, M. Yu, R. Betzholz, C. Arenz, and J. Cai, Phys. Rev. Lett. 124, 010405 (2020)], a random-control field is locally applied to a multipartite system to reconstruct the full quantum state of the system through single-observable measurements. Here, we analyze the robustness of such a tomography scheme against measurement errors. We characterize the sensitivity to measurement errors using the condition number of a linear system that fully describes the tomography process. Using results from random matrix theory we derive the scaling law of the logarithm of this condition number with respect to the system size when Haar-random evolutions are considered. While this expression is independent of how Haar randomness is created, we also perform numerical simulations to investigate the temporal behavior of the robustness for two specific quantum systems that are driven by a single random-control field. Interestingly, we find that before the mean value of the logarithm of the condition number as a function of the driving time asymptotically approaches the value predicted for a Haar-random evolution it reaches a plateau whose length increases with the system size.

Present-day quantum devices require precise implementation of desired quantum channels. To characterize the quality of implementation one uses the average operation fidelity $F$, defined as the fidelity between an initial pure state and its image with respect to the analyzed operation, averaged over an ensemble of pure states. We analyze the statistical properties of the operation fidelity for low-dimensional channels and study its extreme values and probability distribution. These results are obtained with the help of the joint numerical range of the set of Kraus operators representing a channel. Analytic expressions for the density $P\left(F\right)$ are derived in some particular cases including unitary and mixed unitary channels as well as quantum maps represented by commuting Kraus operators. We propose a scheme for fidelity-based channel estimation which uses the distribution of operation fidelity.

Decoy-state measurement-device-independent quantum key distributions (MDI-QKD) can remove all the loopholes of detection devices and establish secure keys using weak coherent sources. To further extend the secure distance and enhance the key rate, Chau proposed a novel framework for decoy-state MDI-QKD that supports an arbitrary number of intensities and investigated its performance in detail [H. F. Chau, Phys. Rev. A 102, 012611 (2020)]. Here, we experimentally demonstrate its one kind, i.e., the five-intensity MDI-QKD protocol, and achieve a positive key rate over 442 km of ultralow-loss optical fibers. Our results verify that the five-intensity protocol outperforms four-intensity protocols in terms of both distance and key rate, setting a record distance for typical MDI-QKD.

A practical implementation of a quantum computer requires robust qubits that are protected against their noisy environment. Dynamical decoupling techniques have been successfully used in the past to offer protected high-fidelity gate operations in negatively charged nitrogen-vacancy (${\mathrm{NV}}^{-}$) centers in diamond, albeit under specific conditions with the intrinsic nitrogen nuclear spin initialized. In this work, we show how the sinusoidally modulated, always rotating, and tailored (SMART) protocol, an extension of the dressed-qubit concept, can be implemented for continuous protection to offer Clifford gate fidelities compatible with fault-tolerant schemes, whilst prolonging the coherence time of a single ${\mathrm{NV}}^{-}$ qubit at room temperature. We show an improvement in the average Clifford gate fidelity from $0.940\pm 0.005$ for the bare qubit to $0.993\pm 0.002$ for the SMART qubit, with the nitrogen nuclear spin in a random orientation. We further show a $\gtrsim 30$ times improvement in the qubit $T_2^{*}$ coherence times compared to the bare qubit.

We demonstrate a combined experimental and theoretical study to measure attosecond-resolved resonance-enhanced multiphoton ionization (REMPI) of NO molecules using the phase-locked strong 400-nm and weak 800-nm laser pulses. By performing the time-dependent wave-packet simulation, our results show that a vibrational-dependent REMPI occurs through two intermediate electronic states $A{}^2{\mathrm{\Sigma }}^{+}$ and $B{}^2\mathrm{\Pi }$, from which a molecular wave packet at different internuclear distances results in an ionization time delay up to 630 as. We find that the nonadiabatic coupling between electronic states $A{}^2{\mathrm{\Sigma }}^{+}(\nu =2)$ and $B{}^2\mathrm{\Pi }({\nu }^{\prime }=4)$ plays a crucial role in the angular-dependent phase variations of emitted electrons. This work extends the application of the REMPI technique to visualize the effect of vibrational motions of intermediate resonance states on the strong-field-induced ionization in attosecond timescales.

The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider the effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady-state absorption (outside the cavity), transmission spectra (inside the cavity), and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady-state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. The effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective $N$) and therefore the Rabi splitting contraction occurs with orientational disorder. Moreover, we find that static disorder is more destructive to collective behavior than dynamic disorder.

In nature, everything occurs at finite temperature, and quantum phase transitions (QPTs) cannot be an exception. Nevertheless, they are still mainly discussed and formulated at zero temperature. We show that the condensation QPTs recently introduced at zero temperature can naturally be extended to finite temperature just by replacing ground-state energies with corresponding free energies. We illustrate this criterion in the paradigmatic Grover model and in a system of free fermions in a one-dimensional inhomogeneous lattice. In agreement with expected universal features, the two systems show structurally similar phase diagrams. Last, we explain how finite-temperature condensation QPTs can be used to construct quantum annealers having, at finite temperature, output probability exponentially close to 1 in the system size. As examples we consider again the Grover model and the fermionic system, the latter being well within the reach of present heterostructure technology.

A set of orthogonal multipartite quantum states is said to be distinguishability-based genuinely nonlocal (also genuinely nonlocal, for abbreviation) if the states are locally indistinguishable across any bipartition of the subsystems. This form of multipartite nonlocality, although more naturally arising than the recently popular “strong nonlocality” in the context of local distinguishability, receives much less attention. In this work, we study the distinguishability-based genuine nonlocality of a typical type of genuine multipartite entangled states—the $d$-dimensional Greenberger-Horne-Zeilinger (GHZ) states, featuring systems with local dimension not limited to two. In the three-partite case, we find the existence of small genuinely nonlocal sets consisting of these states: we show that the cardinality can at least scale down to linear in the local dimension $d$, with the linear factor $l=1$. Specifically, the method we use is semidefinite programming and the GHZ states to construct these sets are special ones which we call “GHZ lattices”. This result might arguably suggest a significant gap between the strength of strong nonlocality and the distinguishability-based genuine nonlocality. Moreover, we put forward the notion of $(s,n)$-threshold distinguishability and, utilizing a similar method, we successfully construct (2,3)-threshold sets consisting of GHZ states in three-partite systems.

The quantum fusion technique enables the bonding of two cluster states together, and therefore provides a promising method to grow large-scale cluster states. Quantum fusion was first proposed in a discrete-variable regime. In terms of the resource usage, quantum fusion can be divided into two categories, which are type-I and type-II fusions. Type-I fusion consumes one qubit in the fusion procedure, while type-II consumes two qubits. However, for continuous-variable (CV) analogs, concrete schemes for realizing quantum fusions of cluster states with arbitrary topologies have not been shown yet. In this paper, we present the CV analog of quantum fusion schemes. We show that CV type-I fusion can be realized by an ancilla and two quantum nondemolition interactions, and CV type-II fusion can be realized by an entanglement swapping scheme. With finite squeezing considered, we analyze the extra errors added by the fusion procedures in CV cluster-state quantum computation. Our schemes are universal and can be generalized to fuse cluster states with arbitrary topologies.

We show that a qubit transfer protocol can be realized through a flat band hosted by a disordered XX spin-1/2 diamond chain. In the absence of disorder, the transmission becomes impossible due to the compact localized states forming the flat band. When off-diagonal disorder is considered, the degeneracy of the band is preserved but the associated states are no longer confined to the unit cells. By perturbatively coupling the sender and receiver to the flat band, we derive a general effective Hamiltonian resembling a star network model with two hubs. The effective couplings correspond to wave functions associated with the flat-band modes. Specific relationships between these parameters define the quality of the quantum-state transfer which, in turn, are related to the degree of localization in the flat band. Our findings establish a framework for further studies of flat bands in the context of quantum communication.

Constructing a quantum computer requires immensely precise control over a quantum system. A lack of precision is often quantified by gate-error metrics, such as the average infidelity or the diamond distance. However, usually such gate-error metrics are only considered for individual gates and not the errors that accumulate over consecutive gates. Furthermore, it is not well known how susceptible the metrics are to the assumptions which make up the model. Here we investigate these issues using realistic simulation models of quantum computers with flux-tunable transmons and coupling resonators. Our main findings reveal that (i) gate-error metrics are indeed affected by the many assumptions of the model, (ii) consecutive gate errors do not accumulate linearly, and (iii) gate-error metrics are poor predictors for the performance of consecutive gates. Additionally, we discuss a potential limitation in the scalability of the studied device architecture.

We present precise measurements of the quantum defects of cesium $n{F}_J$ Rydberg levels. We employ high-precision microwave spectroscopy of $(n+2)D_{5/2}\to n{F}_{5/2,7/2}$ transitions for $n=45$ to 50 in a cold-atom setup. Cold cesium $(n+2)D_{5/2}$ atoms, prepared via two-photon laser excitation, are probed by scanning weak microwave fields interacting with the atoms across the $n{F}_{5/2,7/2}$ resonances. Transition spectra are acquired using state-selective electric-field ionization and time-gated ion detection. Transition-frequency intervals are obtained by Lorentzian fits to the measured spectral lines, which have linewidths ranging between 70 and 190 kHz, corresponding to about one to three times the Fourier limit. A comprehensive analysis of relevant line-shift uncertainties and line-broadening effects is conducted. We find quantum defect parameters ${\delta }_0\left(F_{5/2}\right)=0.03341537\left(70\right)$ and ${\delta }_2\left(F_{5/2}\right)=-0.2014\left(16\right)$, as well as ${\delta }_0\left(F_{7/2}\right)=0.0335646\left(13\right)$ and ${\delta }_2\left(F_{7/2}\right)=-0.2052\left(29\right)$, for $J=5/2$ and $7/2$, respectively. Fine-structure parameters $A_{\mathrm{FS}}$ and $B_{\mathrm{FS}}$ for Cs $n{F}_J$ are also obtained. Results are discussed in context with previous works, and the significance of the results is discussed.

We report on a theoretical study of nonsequential double ionization (NSDI) of magnesium atoms by circularly polarized intense laser pulses. We introduce a concise model considering the laser-induced dynamic core polarization, which is an often overlooked effect in understanding strong-field double ionization. By tracing back the electron trajectories, we demonstrate how the ionic response to the instantaneous laser field enhances the NSDI probability, which plays a crucial role in circular polarization. Furthermore, we propose a method to extract the ionic polarizability from the ratio of double to single ionization. This scheme can be applied to other polar targets and serves as a potential way to probe nonequilibrium states of strongly driven systems on the subfemtosecond timescale.

We simulate the so-called “rainbow reconstruction of attosecond beating by interference of two-photon transitions” (Rainbow RABBITT) technique with R-matrix with time-dependence (RMT) theory for neutral argon. We compute the energy-resolved spectral phase induced by the autoionizing $\left[\mathrm{Ne}\right]3s3p^{6}4p{}^{1}P$ resonance with simulations incorporating semirelativistic atomic descriptions. This allows us to isolate the $j=1/2$ and $j=3/2$ spin-orbit component contributions to the energy-resolved spectral phase and compare these against experiment. We analyze changes to the spectral phase resolved in energy and emission angle induced by the autoionizing state.

Based on the expansion of the time-dependent Dirac equation in the second order on the reciprocal of the speed of light, we derive a simplified second-order time-dependent Pauli equation (second-TDPE) for single-active-electron systems, in which the time-dependent spin-orbit interaction is taken into account. A numerical method is presented for calculating the observables for atoms interacting with the electric fields of laser pulses. It is shown that the energy-level splitting between the $p_{+}^{\uparrow }$ and $p_{+}^{\downarrow }$ (as well as the $p_{-}^{\uparrow }$ and $p_{-}^{\downarrow })$ orbitals can be reproduced by the spin-orbit coupling (SOC) term of the second-TDPE. By numerically solving the second-TDPE, we demonstrate the SOC effect in single-photon, multiphoton, and tunneling ionization of atomic Kr with valence $p$ orbitals. In particular, a few counterintuitive strong-field ionization phenomena are discussed and analyzed. The present work provides a convenient way to explore the SOC effect in strong-field interactions.

We investigate the transport properties of a Fermi-Hubbard chain with an impurity which is formed by a site with a periodically modulated chemical potential. We determine the momentum-resolved transmission through this impurity in dependence of the modulation frequency and strength for a single particle and a pair of fermions. We find that the pair transmission has a very distinct behavior from the single-particle transmission. Different situations can occur, where only the single particle or the pair with a certain momentum is transmitted or filtered out.

A theoretical study of the propagating electromagnetic surface waves confined to a plane vacuum–homogeneous jellium interface is carried out. A classification of the entangled surface plasmon ($L$) and plasmariton ($T$) modes, which we name surface jellions, is given. The collective mode structure is obtained using the Weyl (angular spectrum) expansion of the screened electromagnetic jellium propagator $\mathbf{G}$. The pole structure of $\mathbf{G}$ relates to the collective-mode pattern. The surface jellion dispersion relation is a central concept in our analyses. We derive this for interfaces with and without self-consistently determined surface currents, i.e., for so-called active and passive boundary conditions. A numerical calculation of the dispersion relation is carried out for the hydrodynamic model. For this model the dispersion relation has three branches in the region of strong surface plasmon-plasmariton coupling. Starting from a finite-relaxation time $\tau$ calculation, the surface jellion eigenmode structure is obtained in the limit $\tau \to \infty$. Exponentially confined surface jellion eigenmodes carry electromagnetic momentum along the surface, and we calculate the $T$, $L$, and $TL$ parts of the momentum, emphasizing numerical data for the hydrodynamic model. It is shown that the entangled $TL$ part carries a momentum backflow. The energy carried by the confined surface jellions is expressed in terms of an equivalent mass concept. The equivalent mass formulation is useful for a harmonic-oscillator description of the surface jellions and their quantization. The equivalent mass of the three branches of the hydrodynamic jellion dispersion is calculated numerically and the $T$, $L$, and $TL$ contributions to the equivalent mass are determined. All numerical calculations presented in the article are carried out as a function of the surface jellion wave number along the surface.

We study theoretically quantum eigenstates in an array of two-level atoms coupled to the waveguide. We show that this system features double-excited states where the two excitations are localized at the opposite edges of the array. Such bound states of distant excitations result from the long-ranged photon-mediated coupling in the waveguide setup, which mediates repulsion at larger distances. These results could be useful for the rapidly developing field of waveguide quantum electrodynamics, studying waveguide-coupled arrays of cold atoms or superconducting qubits.

Many-body localization (MBL) can occur when strong disorders prevent an interacting system from thermalization. To study the dynamics of such systems, performing an ensemble average over many different disorder configurations is typically necessary. Previous works have utilized an algorithm in which different disorder profiles are mapped into a quantum ancilla. By preparing the ancilla in a quantum superposition state, quantum parallelism can be harnessed to obtain the ensemble average in a single computation run. In this work, we modify this algorithm by performing a measurement on the ancilla. This enables the determination of conditional dynamics not only by the ensemble average but also by the quantum interference effect. Using a phenomenological analysis based on local integrals of motion, we demonstrate that this protocol can lead to an enhancement of the dephasing effect and a boost in entanglement growth for systems in the deep MBL phase. For a typical MBL system with short-range interactions, reaching saturation in entanglement usually takes an exponentially long time, which makes experimental explorations of long-time properties challenging. With our protocol, we demonstrate a significant reduction in the saturation time by several orders. This advancement facilitates easier access to the behavior in the long-time regime. We also present numerical simulations of the random $XXZ$ model where this enhancement is also present in a smaller disorder strength, beyond the deep MBL regime.