We identify and study a particular class of distinguishability problems for quantum observables (positive-operator-valued measures), in which observables with permuted effects are involved, which we call the labeling problem. Consequently, we identify binary observables, which can be labeled perfectly. In this work, we study these problems in the single-shot regime.

Going beyond the standard quantum limit in noisy quantum metrology is an important and challenging task. Here we show how Dicke states can be used to surpass the standard quantum limit and achieve the Heisenberg limit in open quantum systems. The system we study has qubits symmetrically coupled to a resonator, and our objective is to estimate the coupling between the qubits and the resonator. The time-dependent quantum Fisher information with respect to the coupling is studied for this open quantum system where the same decay rates are assumed on all qubits. We show that when the system is initialized to a Dicke state with an optimal excitation number one can go beyond the standard quantum limit and achieve the Heisenberg limit even for finite values of the decays on the qubit and the resonator, particularly when the qubits and resonator are strongly coupled. We compare our results against the highly entangled GHZ state and a completely separable state and show that the GHZ state performs quite poorly, whereas under certain noise conditions the separable state is able to go beyond the standard quantum limit due to subsequent interactions with a resonator.

The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth of the required number of measurements. The conceptual solution for this dimensionality curse relies on a simple idea—a complete description of a quantum state is excessive and can be discarded in favor of experimentally accessible information about the system. The probably approximately correct learning theory has been recently successfully applied to a problem of building accurate predictors for the measurement outcomes using a data set which scales only linearly with the number of qubits. Here, we present a constructive and numerically efficient protocol which learns a tensor network model of an unknown quantum system. We discuss the limitations and the scalability of the proposed method.

The ionization by photon or electron impact of the inner ($2a_1$) and outer ($1t_2$) valence orbitals of the ${\mathrm{CH}}_4$ molecule is investigated theoretically. In spite of a number of approximations, including a monocentric approach and a rather simple distorting molecular potential, the calculated cross sections are overall similar to those of other theoretical methods and in reasonable agreement with experimental data. The originality of the present approach stands in the way we evaluate the transition matrix elements. The key ingredient of the calculation scheme is that the continuum radial wave function of the ejected electron is represented by a finite sum of complex Gaussian-type orbitals. This numerically expensive optimization task is then largely compensated by rather simple and rapid analytical calculations of the necessary integrals, and thus all ionization observables, including cross section angular distributions. The proposed and implemented Gaussian approach is proved to be numerically very reliable in all considered kinematical situations with ejected electron energy up to 2.7 a.u. The analytical formulation of the scheme is provided here for bound molecular states described by monocentric Slater-type orbitals; alternatively, one may also use monocentric Gaussian-type orbitals for which the formulation is even simpler. In combination with complex Gaussian functions for the continuum states, an all-Gaussian approach with multicentric bound states can be envisaged.

Subshell-resolved single-electron capture has been investigated in collisions between ${\text{O}}^{4+}$ ions and He atoms at energies from 7 to 70 keV/nucleon, using high-resolution cold-target recoil-ion momentum spectroscopy. Analysis of the $Q$-value spectra, $n$-shell dependence, relative branching ratios, and angular distributions provides insight into the dominant reaction channels. Capture into the $n=3$ state remains dominant in the entire projectile energy, agreeing with predictions from the molecular Coulombic over barrier model. At low energies, capture preferentially populates the $3s$ subshell, while higher $l$ states like $3d$ become dominant at higher projectile energies. The oscillatory transverse momentum distribution of $3s$ states is attributed to de Broglie wave Fraunhofer diffraction, indicative of the quantum nature of the collision dynamics.

In interatomic Coulombic decay (ICD) an excited neutral atom or excited ion transfers its excess energy to ionize a neighboring atom. If the excitation or ionization involves valence electrons, the process is efficient (typically in the femtosecond regime), becomes more efficient the more neighbors are present, and often dominates all other relaxation processes. The situation changes when considering the excitation or ionization of core electrons. For light atoms, core-level ICD is inferior to Auger decay, but still a relevant relaxation pathway. For heavy atoms the excess energy is enormous and by consulting the usual asymptotic equation for the ICD rate one can only conclude the deep core-level ICD to be negligible. Retardation effects due to the finite speed of light strongly change the asymptotic behavior of the ICD rate, in particular for deep core levels. The impact of retardation is investigated in detail for deep core-level ICD. Several examples of heavy atoms undergoing ICD with heavy neighbors are explicitly studied and general conclusions are drawn.

Supersolidity, characterized by superfluidity and crystallization, is an exotic state of matter. The spin-orbit- (SO-) coupled Bose-Einstein condensates (BECs) provide an ideal paradigm for exploring this quantum state. Here, we present a theoretical analysis of the ground-state phases and collective modes of supersolid SO-coupled BECs in a harmonic trap. The phase diagram of three ground-state phases (i.e., the supersolid phase, plane-wave phase, and zero-momentum phase) is obtained analytically under the condition $\omega \ll k_0$ (here, $\omega$ is harmonic trap frequency, $k_0$ is SO-coupling strength), showing the spin polarization, the phase diagram, and the contrast of the supersolid stripes can be effectively manipulated by trapping potential. An efficient scheme to manipulate the supersolid phase is provided. Furthermore, with particular discussion of the supersolid phase, the collective modes in all three phases are obtained with a unified approach, and softening of both dipole and breathing modes with divergence of effective mass at phase transition point is explained analytically and well confirmed by direct numerical simulations. The impact of SO coupling on local currents during the breathing mode is discussed. The anharmonic collective modes are also revealed with the appearance of the flat band in the single-particle dispersion, especially when SO-coupling strength is comparable with trapping potential. Our theoretical method provides a clear physical picture that collective modes of SO-coupled BECs can be regarded as classical harmonic oscillators with an effective mass containing the SO coupling.

The quantum regression theorem is a powerful tool for calculating the multitime correlators of operators of open quantum systems whose dynamics can be described in Markovian approximation. However, the scope of the quantum regression theorem is limited by a particular time order of the operators in multitime correlators and does not include out-of-time-ordered correlators. In this work, we obtain an adjoint master equation for multitime correlators that applies to out-of-time-ordered correlators. We show that this equation can be derived for various approaches to the description of the dynamics of open quantum systems, such as the global or local approach. We show that the adjoint master equation for multitime correlators is self-consistent. Namely, the final equation does not depend on how the operators are grouped inside the correlator and it coincides with the quantum regression theorem for the particular time ordering of the operators.

Given that contextuality and coherence are significant resources in quantum physics, exploring the intricate interplay between these two factors presents a compelling avenue for research. Here, an experiment is presented to investigate the nuanced relationship between contextual robustness and coherence in a scenario of state discrimination. Specifically, two types of noises—depolarizing and dephasing—are introduced in the measurement procedure to assess the robustness of contextuality. By varying the overlap between the states to be discriminated, we explore the variations in contextual robustness across different levels of coherence. Importantly, our findings demonstrate that contextuality can persist under any degree of coherence. Notably, when coherence approaches zero (while remaining nonzero), contextuality can still endure under arbitrary amounts of partial dephasing. These results underscore the pivotal role of coherence in contextual phenomena, offering significant insights into the intricate interplay between coherence and contextuality.

We formulate the O(3) nonlinear sigma model in $1+1$ dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous-variable (CV) approach to quantum computing. We construct the ground state and excited states using the coupled-cluster Ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates and obtain numerical results using a photonic quantum simulator. We expect that the methods developed in this paper will be useful for exploring interesting dynamics for a wide class of sigma models and gauge theories, as well as for simulating scattering events on quantum hardware in the coming decades.

The quantification of state-based quantum “resources” such as entanglement, coherence, and nonstabilizer states lies at the heart of quantum science and technology, providing potential advantages over classical methods. In a realistic scenario, due to the imperfections and uncertainties in physical devices, we are unable to perfectly prepare or detect the true quantum states. Consequently, it is necessary to study the quantification of quantum resources under such circumstances. In this work, by focusing on the state-based quantum resource theory, we introduce a family of resource measures called $\epsilon$ measure that relies on a precision parameter to address this issue. This family of resource measures inherits the fundamental properties of the original resource measure, such as weak monotonicity, convexity, monogamy, and so forth. Furthermore, the $\epsilon$ measure remains continuous irrespective of whether the original measure is continuous or not. We also investigate the $\epsilon$ measure of distance-based resource quantifiers, and some interesting properties are presented. As part of the applications, we derived several formulas for the $\epsilon$ measure of coherence, nonstabilizerness, asymmetry, nonuniformity, and imaginarity. Additionally, we offered an upper bound for the $\epsilon$ measure of the resource rank. Finally, we outline how this work can be extended to channel-based resources among others.

Projected squeezed (PS) states are multipartite entangled states generated by unitary spin squeezing, followed by a collective quantum measurement and postselection. They can lead to an appreciable decrease in the state preparation time of the maximally entangled $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state when compared to deterministic preparation by unitary transformations in physical systems where spin squeezing can be realized, such as ion, neutral atom, and superconducting qubits. Here we simulate the generation of PS states in nonideal experimental conditions with relevant decoherence channels. By employing the Kraus operator method and quantum trajectory method to reduce the computational complexity, we assess the quantum Fisher information and overlap fidelity with an ideal GHZ state. Our findings highlight PS states as useful metrological resources, demonstrating a robustness against environmental effects with increasing qubit number $N$.

We apply the Kubo-Anderson stochastic theory of molecular spectral line shapes to the case of polaritons formed in the collective strong-coupling regime. We investigate both the fast and slow limits of the random frequency modulation of the emitter as well as the intermediate regime and show how the interplay between the characteristic timescales of the cavity and the molecular disorder is expressed in the observed polaritons line shapes. The analytical solution obtained for the slow limit is valid for any ratio between the inhomogeneous broadening of the molecules and the Rabi splitting, which is especially relevant for molecular polaritons where these two quantities can be of the same order of magnitude.

Using rare-gas ions as the interacting medium, phase-matched high-order harmonic generation up to 1-keV hard x ray can be achieved by balancing the negative plasma dispersion and Gouy phase shift with the positive, intensity-dependent, intrinsic dipole phase variation. The time-dependent phase-matching condition automatically gates the harmonic output to an isolated attosecond pulse. The estimated pulse duration is as short as 120 as.

Phase estimation has attracted much attention in the field of sensing, where weak measurement has become an effective solution for the study of small physical quantities because of its anomalous amplification property. However, it is difficult for weak measurement to cope with large low-frequency noise signals in the environment due to its extremely narrow linear range, which makes the extension of weak measurement to practical applications a challenging task. In order to solve this issue, we propose and experimentally verify a phase demodulation scheme based on weak measurement, which solves the problem of working point offset caused by the noise through artificially introducing a high-frequency carrier and performing demodulation operations on the output light. The experimental results show that the scheme can improve the signal-to-noise ratio by 17 dB compared to standard weak measurement and ensures low distortion in phase demodulation. Moreover, the scheme is not limited to a specific modulation depth, which greatly improves the robustness of the scheme.

We propose a scheme to dissipatively stabilize superpositions of squeezed coherent states for single- and two-resonator modes in superconducting circuits, where a superconducting qubit is coupled to a single or two parametrically driven transmission-line resonators with different circuit designs. A modulated magnetic flux applied to the qubit can periodically break the inversion symmetry of the qubit and induce both the parametrically enhanced transverse and longitudinal couplings to the resonators, resulting in strong nonlinear two-photon interactions between the qubit and the resonators and enabling the scheme to be implemented in a relatively weak coupling regime. With an additional microwave drive applied to the qubit, the dissipation of the qubit used as a resource can help drive the resonators into the desired superpositions of squeezed coherent states at a steady state with high speed. Numerical simulations show that the target states with high fidelity and highly nonlinear properties can be created for a long time even in the presence of photon leakage out of the resonators. The scheme can be generalized to other quantum platforms and may have potential applications in the field of quantum information processing and the improvement of estimation precision in quantum metrology.

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture prior information on the statistics of noise, smoothness of the functions, and training data uncertainty. However, their computational complexity quickly becomes intractable as the size of the data set grows. We propose a Hilbert-space approximation-based quantum algorithm for Gaussian process regression to overcome this limitation. Our method consists of a combination of classical basis function expansion with quantum computing techniques of quantum principal component analysis, conditional rotations, and Hadamard and swap tests. The quantum principal component analysis is used to estimate the eigenvalues, while the conditional rotations and the Hadamard and swap tests are employed to evaluate the posterior mean and variance of the Gaussian process. Our method provides polynomial computational complexity reduction over the classical method.

Quantum illumination uses quantum correlations to improve the detection of objects in the presence of background noise. A simple and common practical approach to quantum illumination is to use threshold detectors to measure the idler mode. We investigate the optimization of these direct measurement protocols. Surprisingly, we find that there can be an advantage to having a signal detector whose quantum efficiency is significantly less than perfect, one that does not vanish for low object reflectivities or signal strengths. We also show that decreasing the separation between pulses, while keeping the rate of photons transmitted per second fixed, can improve the performance, under appropriate conditions. We further show that postselecting on the idler detector firing is less efficient at object detection than not postselecting.