Out-of-time-ordered correlation functions (OTOCs) play a crucial role in the study of thermalization, entanglement, and quantum chaos, as they quantify the scrambling of quantum information due to complex interactions. As a consequence of their out-of-time-ordered nature, OTOCs are difficult to measure experimentally. Here we propose an OTOC measurement protocol that does not rely on the reversal of time evolution and is easy to implement in a range of experimental settings. The protocol accounts for both pure and mixed initial states, and is applicable to systems that interact with environmental degrees of freedom. We demonstrate the application of our protocol by the characterization of scrambling in a periodically driven spin that exhibits quantum chaos.

We study the bound states of $N$ identical bosons that are described by a multiband Bose-Hubbard model with generic hoppings and an attractive on-site interaction. Using a variational approach, we first derive exact integral equations for the dimers, trimers, tetramers, and other multimers, and then apply them to a one-dimensional sawtooth model that features two bands. In particular we reveal the presence of not only the off-site dimer states which consist of two monomers on different sites even in the strong-coupling limit but also the off-site trimer states which consist of either a dimer on one site and a monomer on another site or three monomers on three different sites. Our variational calculations for the ground states of on-site dimers, on-site trimers and off-site trimers benchmark perfectly well with the density matrix renormalization group (DMRG) simulations. We also present DMRG results for the ground states of on-site tetramers, off-site tetramers, on-site pentamers, off-site pentamers, and other multimers.

We investigate the ground-state phase diagram of the one-dimensional attractive Fermi-Hubbard model with spin-dependent hoppings and an on-site Rabi coupling using the density matrix renormalization group method. In particular, we show that even in the limit of one component being immobile the pair superfluidity can be resonantly enhanced when the Rabi coupling is on the order of the interaction strength just before the system starts to strongly polarize. We derive an effective spin-1/2 XXZ model in order to understand the ground-state properties in the strong attraction limit.

We investigate the effect of the continuous spontaneous localization (CSL) model on light-pulse atom interferometry. Using a path-integral approach with an additional stochastic potential accounting for CSL, we derive an exponential loss of the contrast that scales linearly with the interferometer time $T$ if both interferometer arms are spatially separated. We compare our theoretical results with measurements from a cold rubidium atom interferometer based on counterpropagating two-photon transitions with pulse separation times up to $T=260\mathrm{ms}$ and obtain the corresponding bounds on the CSL parameters.

We present a concrete theoretical proposal for detecting topological phase transitions in double kicked atom-optics kicked rotors with internal spin-1/2 degree of freedom. The implementation utilizes a kicked Bose-Einstein condensate evolving in one-dimensional momentum space. To reduce the influence of atom loss and phase decoherence, we aim to keep experimental durations short while maintaining a resonant experimental protocol. Experimental limitations induced by phase noise, quasimomentum distributions, symmetries, and the ac-Stark shift are considered. Our results thus suggest a feasible and optimized procedure for observing topological phase transitions in quantum kicked rotors.

We propose a multichannel version of quantum electro-optic sampling involving monochromatic field modes. It allows for multiple simultaneous measurements of arbitrarily many $\widehat{X}$ and $\widehat{Y}$ field quadratures for a single quantum-state copy, while independently tuning the interaction strengths at each channel. In contrast to standard electro-optic sampling, the sampled midinfrared (MIR) mode undergoes a nonlinear interaction with multiple near-infrared pump beams. We present a complete positive operator-valued measure description for quantum states in the MIR mode. The probability distribution of the electro-optic signal outcomes is shown to be related to an $s$-parametrized phase-space quasiprobability distribution of the indirectly measured MIR state, with the parameter $s$ depending solely on the quantities characterizing the nonlinear interaction. Furthermore, we show that the quasiprobability distributions for the sampled and postmeasurement states are related to each other through a renormalization and a change in the parametrization. This result is then used to demonstrate that two consecutive measurements of both $\widehat{X}$ and $\widehat{Y}$ quadratures can outperform eight-port homodyne detection.

The Krylov subspace method is a traditional approach to approximate quantum evolution, allowing us to treat systems with large Hilbert spaces. Despite its popularity, current bounds typically overestimate the error, which translates into more expensive simulation routines. In this paper, we tackle this problem by realizing that the error can be understood as a Loschmidt echo in a one-dimensional (1D) noninteracting tight-binding Hamiltonian. We show that the different time regimes of the approximation can be understood using simple physical ideas. More importantly, we obtain computationally cheap error bounds that describe with high precision the actual error in the approximation.

Entangled two-qubit states are the core building blocks for constructing quantum communication networks. Their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. In this work we study the self-testing of two-qubit entangled states via steering inequalities, with robustness analysis against noise. More precisely, steering inequalities are constructed from the tilted Clauser-Horne-Shimony-Holt inequality and its general form, to verify the general two-qubit entangled states. The study provides a good robustness bound, using both local extraction map and numerical semidefinite-programming methods. In particular, optimal local extraction maps are constructed in the analytical method, which yields the theoretical optimal robustness bound. To further improve the robustness of one-sided self-testing, we propose a family of three measurement settings steering inequalities. The result shows that three-setting steering inequality demonstrates an advantage over two-setting steering inequality on robust self-testing with noise. Moreover, to construct a practical verification protocol, we clarify the sample efficiency of our protocols in the one-sided device-independent scenario.

We consider the application of the entanglement criteria derived by Hillery and Zubairy [Phys. Rev. Lett. 96, 050503 (2006)] to the detection of entanglement in $N$-qubit systems. For $N=2$ qubits we show that, with the natural choice of operators, one of the criteria never detects entanglement; we also derive conditions for the other criterion to work and for it to have a simple relation to the negativity when it does. For general angular momenta we show the Hillery-Zubairy relations can always detect the entanglement of the (pure) states of well-defined total (J, $J_z$) if the “test” operators are chosen appropriately. We then show how this may be used, in particular, to develop useful criteria to detect entanglement in a system of $N$ two-level atoms interacting with a field initially in a number state (the Tavis-Cummings model).

Ground states of quantum many-body systems are both entangled and possess a kind of quantum complexity, as their preparation requires universal resources that go beyond the Clifford group and stabilizer states. These resources—sometimes described as magic—are also the crucial ingredient for quantum advantage. We study the behavior of the stabilizer Rényi entropy in the integrable transverse field Ising spin chain. We show that the locality of interactions results in a localized stabilizer Rényi entropy in the gapped phase, thus making this quantity computable in terms of local quantities in the gapped phase, while measurements involving $L$ spins are necessary at the critical point to obtain an error scaling with $O\left(L^{-1}\right)$.

An intriguing spin-orbital angular momentum interaction, called the geometric spin Hall effect of light (GSHEL), has aroused much interest and manifests itself as a transverse shift. The GSHEL of the classical optical field is independent of the beam size. In this paper the GSHELs of the vortex vector continuous wave (VVCW) and vortex ultrashort pulsed beam (VUPB) are systematically analyzed beyond the paraxial approximation. The analytical expression of the transverse shift of the VVCW is obtained. Evidently, the magnitude of the transverse shift depends on the ratio of the beam waist to the wavelength. The transverse shift can be effectively enlarged by narrowing the beam waist even to the order of more than $10\mu \text{m}$. This intriguing phenomenon is caused by the stronger spin-orbital interaction induced energy flow in the nonparaxial regime. Furthermore, the GSHEL of the VUPB is also explored. The pulse duration time strongly affects the distribution of the phase. The singularities play a crucial role in altering the orientation of the electric field. As a result, the VUPBs with different pulse duration time have different magnitudes of the GSHEL. These results may find significant applications in the investigation of the particle manipulation, microscopic imaging, and ultrashort optics.

The exceptional points (EPs) of non-Hermitian Hamiltonians (NHHs) are spectral degeneracies associated with coalescing eigenvalues and eigenvectors, which are associated with remarkable dynamical properties. These EPs can be generated experimentally in open quantum systems, evolving under a Lindblad equation, by postselecting on trajectories that present no quantum jumps, such that the dynamics is ruled by a NHH. Interestingly, changing the way the information used for postselection is collected leads to different unravelings, i.e., different set of trajectories, which average to the same Lindblad equation, but are associated with a different NHH. Here, we exploit this mechanism to create and control EPs solely by changing the measurement we postselect on. Our scheme is based on a realistic homodyne reading of the emitted leaking photons with a weak-intensity laser (a process that we call $\beta$-dyne), which we show generates a tunable NHH, that can exhibit EPs even though the system does have any in the absence of the laser. We consider a few illustrative examples pointing out the dramatic effects that different postselections can have on the spectral features of the NHH, paving the road towards engineering of EPs in simple quantum systems.

We present a detailed analysis of the capture and acceleration of a nonrelativistic charged vortex particle (electron, positron, proton, etc.) with an orbital angular momentum in the field of an axisymmetric electromagnetic lens, typical for a linear accelerator. We account for the acceleration and the inhomogeneity of both electric and magnetic fields that may arise from real-life imperfections. We establish the conditions for this wave packet to be captured and successfully transported through the lens. We describe the transition process and explain how a free Laguerre-Gaussian packet can be captured into the Landau state of the lens and how its structure is preserved for all moments in time. We illustrate the developed formalism with several representative examples.

We analyze and compare different measures for the degree of non-Markovianity in the dynamics of open quantum systems. These measures are based on the distinguishability of quantum states, which is quantified, on the one hand, by the trace distance or, more generally, by the trace norm of the Helstrom matrix and, on the other hand, by entropic quantifiers: the Jensen-Shannon divergence and the Holevo or quantum skew divergence. We explicitly construct a qubit dynamics for which the trace-norm-based non-Markovianity measure is nonzero, while all the entropic measures turn out to be zero. This leads to the surprising conclusion that the non-Markovianity measure which employs the trace norm of the Helstrom matrix is strictly stronger than all entropic non-Markovianity measures.

Neural networks (NNs) representing quantum states are typically trained using Markov chain Monte Carlo based methods. However, unless specifically designed, such samplers only consist of local moves, making the slow-mixing problem prominent even for extremely simple quantum states. Here, we propose to use mode-assisted training that provides global information via the modes of the NN distribution. Applied to quantum state tomography using restricted Boltzmann machines, this method improves the quality of reconstructed quantum states by orders of magnitude. The method is applicable to other types of NNs and may efficiently tackle problems previously unmanageable.

As we are entering the era of constructing practical quantum computers, suppressing the inevitable noise to accomplish reliable computational tasks will be the primary goal. Leakage noise, as the amplitude population leaking outside the qubit subspace, is a particularly damaging source of error that error-correction approaches cannot handle. However, the impact of this noise on the performance of variational quantum algorithms (VQAs), a type of near-term quantum algorithm that is naturally resistant to a variety of noises, is yet unknown. Here, we consider a typical scenario with the widely used hardware-efficient ansatz and the emergence of leakage in two-qubit gates, observing that leakage noise generally reduces the expressive power of VQAs. Furthermore, we benchmark the influence of leakage noise on VQAs in real-world learning tasks. Results show that, for both data fitting and data classification, leakage noise generally has a negative impact on the training process and final outcomes. Our findings give strong evidence that VQAs are vulnerable to leakage noise in most cases, implying that leakage noise must be effectively suppressed in order to achieve practical quantum computing applications, whether for near-term quantum algorithms or for long-term error-correcting quantum computing.

In this paper we extend the resource theory of magic states to the channel domain by considering completely stabilizer-preserving operations (CSPOs) as free. We introduce and characterize the set of CSPO-preserving and completely CSPO-preserving superchannels. We quantify magic channels by extending the generalized robustness and the min-relative entropy defined for magic states to channels and show that they bound the single-shot dynamical magic cost and distillation. We also provide analytical conditions for qubit interconversion under CSPOs and show that it is a linear programming feasibility problem and hence can be efficiently solved. Lastly, we give a classical simulation algorithm whose runtime is related to the generalized robustness of magic channels. Our algorithm depends on some predefined precision, and if there is no bound on the desired precision then it achieves a constant runtime.

We study the phenomenon of localization and delocalization in a circuit-QED network with connectivity varying from finite-range coupling to all-to-all coupling. We find a fascinating interplay between interactions and connectivity. In particular, we consider (i) harmonic, (ii) Jaynes-Cummings, and (iii) Bose-Hubbard networks. We start with the initial condition where one of the nodes in the network is populated and then let it evolve in time. The time dynamics and steady state characterize the features of localization (self-trapping) in these large-scale networks. For the case of harmonic networks, exact analytical results are obtained, and we demonstrate that all-to-all connection shows self-trapping whereas the finite-ranged connectivity shows delocalization. The interacting cases (Jaynes-Cummings and Bose-Hubbard networks) are investigated both via exact quantum dynamics and via a semiclassical approach. We obtain an interesting phase diagram when one varies the range of connectivity and the strength of the interaction. We investigate the consequence of imperfections in the cavity or qubit and the role of inevitable disorder. Our results are relevant especially given recent experimental progress in engineering systems with long-range connectivity.

We present a method for quantum state tomography within a single-excitation subspace of two-qubit states in an open waveguide. The system under investigation consists of three qubits in an open waveguide, separated by a distance comparable to the wavelength of the electromagnetic field. We show that the modulation of the frequency of the central ancillary qubit allows us to obtain unambiguous information about the initial phase difference ${\phi }_1-{\phi }_3$ of the edge qubits via the measurement of the evolution of their probability amplitudes.

The ability to program and control interactions provides the key to implementing large-scale quantum simulation and computation in trapped-ion systems. Adding optical tweezers, which can tune the phonon spectrum and thus modify the phonon-mediated spin-spin interaction, was recently proposed as a way of programing quantum simulators for a broader range of spin models [Arias Espinoza et al., Phys. Rev. A 104, 013302 (2021)]. In this work we study the robustness of our findings in the presence of experimental imperfections: micromotion, local stress, and intensity noise. We show that the effects of micromotion can be easily circumvented when designing and optimizing tweezer patterns to generate a target interaction. Furthermore, while local stress, whereby the tweezers apply small forces on individual ions, may appear to enable further tuning of the spin-spin interactions, any additional flexibility is negligible. We conclude that optical tweezers are a useful method for controlling interactions in trapped-ion quantum simulators in the presence of micromotion and imperfections in the tweezer alignment, but require intensity stabilization on the subpercent level.