Recently introduced shadow tomography protocols use “classical shadows” of quantum states to predict many target functions of an unknown quantum state. Unlike full quantum state tomography, shadow tomography does not insist on accurate recovery of the density matrix for high rank mixed states. Yet, such a protocol makes multiple accurate predictions with high confidence, based on a moderate number of quantum measurements. One particular influential algorithm, proposed by Huang et al. [Huang, Kueng, and Preskill, Nat. Phys. 16, 1050 (2020)], requires additional circuits for performing certain random unitary transformations. In this paper, we avoid these transformations but employ an arbitrary informationally complete positive operator-valued measure and show that such a procedure can compute $k$-bit correlation functions for quantum states reliably. We also show that, for this application, we do not need the median of means procedure of Huang et al. Finally, we discuss the contrast between the computation of correlation functions and fidelity of reconstruction of low rank density matrices.

This work presents a rigorous theory to unify the two independent theoretical frameworks of Kohn-Sham (KS) density-functional theory (DFT) and reduced-density-matrix-functional theory (RDMFT). The generalization of the KS orbitals to hypercomplex number systems leads to the hypercomplex KS (HCKS) theory, which extends the search space for the electron density in KS-DFT and reformulates the kinetic energy. The HCKS theory provides a general framework, and different dimensions of the HCKS orbitals lead to different HCKS methods, with KS-DFT and RDMFT being two cases corresponding to the smallest and largest dimensions. Furthermore, a series of tests show that HCKS can capture the multireference nature of strong correlation by dynamically varying fractional occupations, while maintaining the same computational scaling as the KS method. With great potential to overcome the fundamental limitations of the KS method, HCKS creates new possibilities for the development and application of DFT.

We theoretically propose a method to generate tripartite entanglement of three mechanical oscillators in an optomechanical array. We consider a system comprised of three bichromatically driven optomechanical systems which are coupled to each other via Coulomb interaction of the mechanical oscillators. We show that, for small Coulomb coupling strength, steady tripartite entanglement of the three mechanical oscillators with time periodicity can be generated due to the combined effect of the two-tone drivings and the Coulomb coupling. At large Coulomb coupling strength, the tripartite entanglement exhibits steady entanglement sudden death and revival. The duration of entanglement death during one period can be controlled by the Coulomb coupling strength. The tripartite entanglement is robust against the mechanical thermal noise. Our paper provides us a route for exploring and exploiting controllable and robust multipartite entanglement among macroscopic mechanical oscillators.

We theoretically study the collective excitation modes of a topological laser device operating in a single-mode steady state with monochromatic emission. We consider a model device based on a two-dimensional photonic Harper-Hofstadter lattice including a broadband gain medium localized on the system edge. Different regimes are considered as a function of the value of the optical nonlinearity and of the gain relaxation time. The dispersion of the excitation modes is calculated via a full two-dimensional Bogoliubov approach and physically interpreted in terms of an effective one-dimensional theory. Depending on the system parameters, various possible physical processes leading to dynamical instabilities are identified and characterized. On this basis, strategies to enforce a stable single-mode topological laser operation are finally pointed out.

This work proposes to investigate the photon statistics of the light transmitted and reflected by a two-dimensional array of interacting atoms. The reflected beam is characterized by photon antibunching. On the other hand, in the transmitted beam the indistinguishability between the driving laser photons and the photons reemitted by the atoms results in photon bunching. The overlap between the driving and scattered fields is enhanced by the cooperative optical response of the atomic array. In the examples used in this paper, up to 25% of the transmitted photons are grouped in pairs. The simulations are carried out using the stochastic method of quantum trajectories.

Bell nonlocality describes a manifestation of quantum mechanics that cannot be explained by any local hidden variable model. Its origin lies in the nature of quantum entanglement, although understanding the precise relationship between nonlocality and entanglement has been a notorious open problem. In this paper, we develop a dynamical framework in which quantum Bell nonlocality emerges as a special form of entanglement and both are unified as resources under local operations and classical communication (LOCC). Our framework is built on the notion of classical and quantum processes, which are defined as channels that map elements between specific intervals in space and time. Entanglement is identified as a process that cannot be generated by LOCC while Bell nonlocality is the subset of these processes that have an instantaneous input-to-output delay time. LOCC preprocessing is a natural set of free operations in this theory, thereby providing previous nonlocality activation results a clear resource-theoretic foundation. We provide a systematic method to quantify the Bell nonlocality of a bipartite quantum channel. It is shown that both the relative entropy and the max relative entropy of nonlocality are nonadditive for a family of bipartite classical channels. This family includes the channel obtained when using the singlet state to maximally violate the CHSH inequality. We also find that the regularized relative entropy of Bell nonlocality provides an upper bound on the asymptotic rate of converting (i.e., simulating) many copies of one classical instantaneous resource to another.

Wick's theorem provides a connection between time ordered products of bosonic or fermionic fields, and their normal ordered counterparts. We consider a generic pair of operator orderings and we prove, by induction, the theorem that relates them. We name this the general Wick's theorem (GWT) because it carries Wick's theorem as special instance, when one applies the GWT to time and normal orderings. We establish the GWT both for bosonic and fermionic operators, i.e., operators that satisfy c-number commutation and anticommutation relations respectively. We remarkably show that the GWT is the same, independent of the type of operator involved. By means of a few examples, we show how the GWT helps treat demanding problems by reducing the amount of calculations required.

The multipartite Greenberger-Horne-Zeilinger (GHZ) entangled state is an important resource for anonymous quantum communication tasks. But its low intensity and fragility limit the practical applications of these anonymous communication tasks under current conditions. Here, we present a feasible anonymous communication protocol in the measurement-device-independent framework. We analyze its performance in a quantum network under certain types of noise. Then we compare the performance of our protocol with the GHZ-state-based anonymous protocol. We demonstrate that our protocol has a unique advantage, i.e., it can tolerate an arbitrary number of nonresponsive nodes. We prove that the security of our protocol in an active adversary scenario in which active malicious agents and an untrusted ancillary node are taken into account. Utilizing the measurement-device-independent technology, our proposal suggests an important avenue for practical anonymous quantum communication.

Recently, a theoretical and an experimental protocol known as quantum-gravity-induced entanglement of masses (QGEM) has been proposed to test the quantum nature of gravity using two mesoscopic masses, each placed in a superposition of two locations. If after eliminating all nongravitational interactions between them the particles become entangled, one can conclude that the gravitational potential is induced via a quantum mediator, i.e., graviton. In this paper we explore extensions of the QGEM experiment to multidimensional quantum objects and examine a range of different experiment geometries, in order to determine which would generate entanglement faster. We conclude that when a sufficiently high decoherence rate is introduced, multicomponent superpositions can outperform the two-qubit setup. With low decoherence however, and given a maximum distance $\mathrm{\Delta }x$ between any two spatial states of a superposition, a set of two qubits placed in spatial superposition parallel to one another will outperform all other models given realistic experimental parameters. This is further verified with an experiment simulation, showing that $O\left({10}^3\right)$ measurements are required to reject the no-entanglement hypothesis with a parallel-qubit setup without decoherence at a $99.9\%$ confidence level. The number of measurements increases when decoherence is introduced. When the decoherence rate reaches 0.125 Hz, six-dimensional qudits are required as the two-qubit system entanglement cannot be witnessed anymore. However, in this case, $O\left({10}^6\right)$ measurements will be required. One can group the witness operators to measure in order to reduce the number of measurements (up to tenfold). However, this may be challenging to implement experimentally.

Variational quantum algorithms that are used for quantum machine learning rely on the ability to automatically differentiate parametrized quantum circuits with respect to underlying parameters. Here we propose the rules for differentiating quantum circuits (unitaries) with arbitrary generators. Unlike the standard parameter-shift rule valid for unitaries generated by operators with spectra limited to at most two unique eigenvalues (represented by involutory and idempotent operators), our approach also works for generators with a generic nondegenerate spectrum. Based on a spectral decomposition, we derive a simple recipe that allows explicit derivative evaluation. The derivative corresponds to the weighted sum of measured expectations for circuits with shifted parameters. The number of function evaluations is equal to the number of unique positive nonzero spectral gaps (eigenvalue differences) for the generator. We apply the approach to relevant examples of two-qubit gates, among others showing that the so-called fermionic simulation (fSim) gate can be differentiated using four measurements. Additionally, we present generalized differentiation rules for the case of Pauli-string generators, based on distinct shifts (here referred to as the triangulation approach), and analyze the variance for derivative measurements in different scenarios. Our work offers a toolbox for the efficient hardware-oriented differentiation needed for circuit optimization and operator-based derivative representation.

Resonant dissipation-enabled adiabatic quantum state transfer processes between the polarization degrees of freedom of a single-photon wave packet and quantum emitters are discussed. These investigations generalize previous work [Trautmann and Alber, Phys. Rev. A 93, 053807 (2016)] by taking into account the properties of the spontaneously emitted photon wave packet and of nonadiabatic corrections. It is demonstrated that the photonic degrees of freedoms of these adiabatic one-photon quantum state transfer processes can be used for the passive, heralded, and deterministic preparation of Bell states of two material quantum emitters and for realizing a large family of symmetric and asymmetric quantum cloning processes. Although these theoretical investigations concentrate on waveguide scenarios they are expected to be relevant also for other scenarios as long as the processes involved are adiabatic so that the Fourier-limited bandwidth of the single-photon wave packet involved is small in comparison with the relevant dissipative rates.

Experimental cross sections for $m$-fold photodetachment ($m=3$–6) of silicon anions via $K$-shell excitation and ionization were measured in the photon-energy range of 1830–1900 eV using the photon-ion merged-beams technique at a synchrotron light source. All cross sections exhibit a threshold behavior that is masked by prethreshold resonances associated with the excitation of a $1s$ electron to higher, either partly occupied or unoccupied atomic subshells. Results from multiconfiguration Dirac-Fock calculations agree with the experimentally derived cross sections for photoabsorption if small energy shifts are applied to the calculated resonance positions and detachment thresholds. Moreover, a systematic approach is applied for modeling the deexcitation cascades that set in after the initial creation of a $K$-shell hole. The resulting product charge-state distributions compare well with the measured ones for direct $K$-shell detachment but less well for resonant $K$-shell excitation. The present results are potentially useful for identifying silicon anions in cold plasmas such as interstellar gas clouds.

In this paper, the propagation characteristics of three-dimensional spatiotemporal nondiffracting parabolic cylinder beams in free space are studied. From the (3+1)-dimensional paraxial wave equation, we obtain an exact solution by the method of separating variables. The solution is constructed using parabolic cylinder functions, described by the three optical mode numbers. The spatiotemporal intensity distribution of the parabolic cylinder beam at five times Rayleigh range with different mode parameters is presented analytically and simulated numerically. Our results indicate that the intensity distribution can be well controlled by adjusting the values of the three mode numbers. They are of great significance for improved understanding of the formation mechanism of parabolic cylinders and other nondiffracting beams.

In this work, we investigate the quantum phase transition of light in the dissipative Rabi-Hubbard lattice under the framework of the mean-field theory and quantum dressed master equation. The order parameter of photons in strong qubit-photon coupling regime is derived analytically both at zero and low temperatures. Interestingly, we can locate the localization and delocalization phase transition very well in a wide parameter region. In particular for the zero-temperature limit, the critical tunneling strength approaches zero generally in the deep-strong qubit-photon coupling regime, regardless of the quantum dissipation. This is contrary to the previous results with the finite minimal critical tunneling strength based on the standard Lindblad master equation. Moreover, a significant improvement of the critical tunneling is also observed at finite temperature, compared with the counterpart under the Lindblad description. We hope these results may deepen the understanding of the phase transition of photons in the Rabi-Hubbard model.

We introduce a continuous one-dimensional non-Hermitian matrix gauge potential and study its effect on dynamics of a two-component field. The model is emulated by a system of evanescently coupled nonlinear waveguides with distributed gain and losses. The considered gauge fields lead to a variety of unusual physical phenomena in both linear and nonlinear regimes. In the linear regime, the field may undergo superexponential convective amplification. A total power of an input Gaussian beam may exhibit a finite-distance blowup, which manifests itself in absolute delocalization of the beam at a finite propagation distance, where the amplitude of the field remains finite. The defocusing Kerr nonlinearity initially enhances superexponential amplification, while at larger distances it suppresses the growth of the total power. The focusing nonlinearity at small distances slows down the power growth and eventually leads to the development of the modulational instability. Complex periodic gauge fields lead to the formation of families of stable fundamental and dipole solitons.

Uncertainty principle is one of the most essential features of quantum mechanics, and it reveals the intrinsic difference that distinguishes the quantum world from the classical world. In this paper, we focus on the uncertainty relations based on metric-adjusted skew information. By making full use of the norm property, we establish an uncertainty relation for arbitrary finite $n$ observables based on metric-adjusted skew information, and we give two new uncertainty relations for arbitrary finite $N$ quantum channels based on metric-adjusted skew information. For arbitrary two observables and two channels, the uncertainty relations we give are not only better than the uncertainty relations detailed in [Quantum Inf. Process. 20, 72 (2021)], but also are the equations. The equation of the uncertainty relation is more accurate than the inequation of the usual uncertainty relation, which has important advantages in the application of quantum information technology, such as quantum communication and the quantum precision measurement. Meanwhile, our results are suitable to Wigner-Yanase-Dyson skew information that is a special metric-adjusted skew information and Wigner-Yanase skew information that is a special Wigner-Yanase-Dyson skew information. Some examples about Wigner-Yanase-Dyson skew information are given and show that the new lower bounds are tighter. The results play an important role in quantum information processing in this paper.

We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similar to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device's noise model, e.g., avoiding gate-set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), leading to partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise-reduction factors can be further postprocessed with ZNE to better approximate the zero-noise limit.

We considered the multiphoton resonance in the periodically driven quantum oscillator with Kerr nonlinearity in the presence of weak high-order nonlinearities. Multiphoton resonance leads to the emergence of peaks and dips in the dependence of the stationary occupations of the stable states on detuning. We demonstrated that due to high-order nonlinearities, these peaks and dips acquire additional fine structure and split into several closely spaced ones. Quasiclassically, multiphoton resonance is treated as tunneling between the regions of the oscillator phase portrait, and the fine structure of the multiphoton resonance is a consequence of a special quasienergy dependence of the tunneling rate between different regions of the classical phase portrait. For different values of damping and high-order nonlinearity coefficients, we identified the domain of quasienergies where tunneling strongly influences the system kinetics. The corresponding tunneling term in the Fokker-Planck equation in quasienergy space was derived directly from the quantum master equation.

We study the superradiance transition of a two-component three-dimensional Fermi gas interacting with a single-mode light field of Dicke-type coupling. We find that for a noninteracting gas, due to the Fermi blocking, a unique superradiant state with a superradiant outer shell surrounding an inner Fermi sea may appear, and the critical atom-light coupling strength $g_c$ to trigger the superradiance approaches $\sqrt{{\omega }_c{E}_F/3}$ even for a vanishing transition frequency between a two-spin state (${\omega }_a\to 0$), in contrast to $g_c\sim \sqrt{{\omega }_c{\omega }_a}\to 0$ for a bosonic or spin system. When the atom-atom attraction is included, we find that the atomic superfluid would compete with the superradiance directly and both orders cannot coexist, giving rise to an interesting ground-state phase diagram with a tricritical point. The resultant phases and phase transitions are characterized by the unique fluctuation spectrum beyond the mean-field level. We further analyze the effects caused by the decay of the light field, which is inevitable for a possible realization in a cavity with a cold atom system. Our results would be beneficial for the understanding of the interplay between Fermi superfluid and superradiance.