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The novel quantum effects induced by the free-electron-photons interaction have attracted increasing interest due to their potential applications in ultrafast quantum information processing. Here, we propose a scheme to generate optical cat states based on the quantum interference of multi-path free-electron-photons interactions that take place simultaneously with strong coupling strength. By performing a projection measurement on the electron, the state of light changes significantly from a coherent state into a non-Gaussian state with either Wigner negativity or squeezing property, both possess metrological power to achieve quantum advantage. More importantly, we show that the Wigner negativity oscillates with the coupling strength, and the optical cat states are successfully generated with high fidelity at all the oscillation peaks. This oscillation reveals the quantum interference effect of the multiple quantum pathways in the interaction of the electron with photons, by that various nonclassical states of light are promising to be fast prepared and manipulated. These findings inspire further exploration of emergent quantum phenomena and advanced quantum technologies with free electrons.

Nonlinear magnonics studies the nonlinear interaction between magnons and other physical platforms (phonon, photon, qubit, spin texture) to generate novel magnon states for information processing. In this tutorial, we first introduce the nonlinear interactions of magnons in pure magnetic systems and hybrid magnon-phonon and magnon-photon systems. Then we show how these nonlinear interactions can generate exotic magnonic phenomena. In the classical regime, we will cover the parametric excitation of magnons, bistability and multistability, and the magnonic frequency comb. In the quantum regime, we will discuss the single magnon state, Schr\"{o}dinger cat state and the entanglement and quantum steering among magnons, photons and phonons. The applications of the hybrid magnonics systems in quantum transducer and sensing will also be presented. Finally, we outlook the future development direction of nonlinear magnonics., Comment: 50 pages, 26 figures

We expand the toolbox for studying Bell correlations in multipartite systems by introducing permutationally invariant Bell inequalities (PIBIs) involving few-body correlators. First, we present around twenty families of PIBIs with up to three- or four-body correlators, that are valid for arbitrary number of particles. Compared to known inequalities, these show higher noise robustenss, or the capability to detect Bell correlations in highly non-Gaussian spin states. We then focus on finding PIBIs that are of practical experimental implementation, in the sense that the associated operators require collective spin measurements along only a few directions. To this end, we formulate this search problem as a semidefinite program that embeds the constraints required to look for PIBIs of the desired form.

Entanglement in bipartite systems has been applied for the generation of secure random numbers, which are playing an important role in cryptography or scientific numerical simulations. Here, we propose to use multipartite entanglement distributed between trusted and untrusted parties for generating randomness of arbitrary dimensional systems. We show that the distributed structure of several parties leads to additional protection against possible attacks by an eavesdropper, resulting in more secure randomness generated than in the corresponding bipartite scenario. Especially, randomness can be certified in the group of untrusted parties, even there is no randomness exists in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when two measurement settings are performed on the untrusted parties. However, the sufficiency no longer holds with more measurement settings. Finally, we apply our analysis to some experimentally realized states and show that more randomness can be extracted in comparison to the existing analysis., Comment: 14 pages, 5 figures

Non-Gaussian states (NGSs) with higher-order correlation properties have wide-range applications in quantum information processing. However, the preparation of such states with high quality still faces practical challenges. Here, we propose a protocol to rapidly generate two types of mechanical NGSs, Schr\"{o}dinger cat states and Fock states, in dissipative optomechanical systems, even when the cooperativity is smaller than one ($g^2/\kappa\gamma, Comment: 7 pages, 4 figures

High-dimensional entanglement has been identified as an important resource in quantum information processing, and also as a main obstacle for simulating quantum systems. Its certification is often difficult, and most widely used methods for experiment are based on fidelity measurements with respect to highly entangled states. Here, instead, we consider covariances of collective observables, as in the well-known Covariance Matrix Criterion (CMC) [1] and present a generalization of the CMC criterion for determining the Schmidt number of a bipartite system. This is potentially particularly advantageous in many-body systems, such as cold atoms, where the set of practical measurements is very limited and only variances of collective operators can typically be estimated. To show the practical relevance of our results, we derive simpler Schmidt-number criteria that require similar information as the fidelity-based witnesses, yet can detect a wider set of states. We also consider case-study criteria based on three orthogonal local spin covariances, which would unlock experimentally feasible detection of high-dimensional entanglement in cold atom systems. In that case, we are able to derive criteria that are valid for mixtures of states with the same Schmidt bases., Comment: 8 pages

We study the transport properties of a driven-dissipative quantum network, where multiple bosonic cavities such as photonic microcavities are coupled through a nonreciprocal bus with unidirectional transmission. For short-range coupling between the cavities, the occurrence of nonreciprocal amplification can be linked to a topological phase transition of the underlying dynamic Hamiltonian. However, for long-range coupling, we find that the nonreciprocal amplification transition deviates drastically from the topological phase transition. Nonetheless, we show that the nonreciprocal amplification transition can be connected to the emergence of zero-energy edge states of an auxiliary Hamiltonian with chiral symmetry even in the long-range coupling limit. We also investigate the stability, the crossover from short to long-range coupling, and the bandwidth of the nonreciprocal amplification. Our work has potential application in signal transmission and amplification, and also opens a window to non-Hermitian systems with long-range coupling and nontrivial boundary effects., Comment: 5 pages, 4 figures

Whether the observables of a physical system admit real values is of fundamental importance to a deep understanding of nature. In this work, we report a device-independent experiment to confirm that the joint reality of two observables on a single two-level system is incompatible with the assumption of operational completeness, which is strictly weaker than that of preparation noncontextuality. We implement two observables on a trapped $^{171}{\rm Yb}^{+}$ ion to test this incompatibility via violation of certain inequalities derived from both linear and nonlinear criteria. Moreover, by introducing a highly controllable dephasing channel, we show that the nonlinear criterion is more robust against noise. Our results push the fundamental limit to delineate the quantum-classical boundary and pave the way for exploring relevant problems in other scenarios., Comment: 6 pages, 3 figures

Einstein-Rosen-Podolsky (EPR) steering or quantum steering describes the "spooky-action-at-a-distance" that one party is able to remotely alter the states of the other if they share a certain entangled state. Generally, it admits an operational interpretation as the task of verifying entanglement without trust in the steering party's devices, making it lying intermediate between Bell nonlocality and entanglement. Together with the asymmetrical nature, quantum steering has attracted a considerable interest from theoretical and experimental sides over past decades. In this Perspective, we present a brief overview of the EPR steering with emphasis on recent progress, discuss current challenges, opportunities and propose various future directions. We look to the future which directs research to a larger-scale level beyond massless and microscopic systems to reveal steering of higher dimensionality, and to build up steered networks composed of multiple parties., Comment: PRX Quantum accepted

We present an experimentally practical method to reveal Einstein-Podolsky-Rosen steering in non-Gaussian spin states by exploiting a connection to quantum metrology. Our criterion is based on the quantum Fisher information, and uses bounds derived from generalized spin-squeezing parameters that involve measurements of higher-order moments. This leads us to introduce the concept of conditional spin-squeezing parameters, which quantify the metrological advantage provided by conditional states, as well as detect the presence of an EPR paradox.

Magnon cat state represents a macroscopic quantum superposition of collective magnetic excitations of large number spins that not only provides fundamental tests of macroscopic quantum effects but also finds applications in quantum metrology and quantum computation. In particular, remote generation and manipulation of Schr��dinger cat states are particularly interesting for the development of long-distance and large-scale quantum information processing. Here, we propose an approach to remotely prepare magnon even/odd cat states by performing local non-Gaussian operations on the optical mode that is entangled with magnon mode through pulsed optomagnonic interaction. By evaluating key properties of the resulting cat states, we show that for experimentally feasible parameters they are generated with both high fidelity and nonclassicality, and with a size large enough to be useful for quantum technologies. Furthermore, the effects of experimental imperfections such as the error of projective measurements and dark count when performing single-photon operations have been discussed, where the lifetime of the created magnon cat states is expected to be $t\sim1\,��$s., 14 pages, 10 figures

Schr\"odinger held that a local quantum system has some objectively real quantum state and no other (hidden) properties. He therefore took the Einstein-Podolsky-Rosen (EPR) phenomenon, which he generalized and called `steering', to require nonlocal wavefunction collapse. Because this would entail faster-than-light (FTL) information transmission, he doubted that it would be seen experimentally. Here we report a demonstration of EPR steering with entangled photon pairs that puts--in Schr\"odinger's interpretation--a non-zero lower bound on the amount of FTL information transmission. We develop a family of $n$-setting loss-tolerant EPR-steering inequalities allowing for a size-$d$ classical message sent from Alice's laboratory to Bob's. For the case $n=3$ and $d=2$ (one bit) we observe a statistically significant violation. Our experiment closes the efficiency and locality loopholes, and we address the freedom-of-choice loophole by using quantum random number generators to independently choose Alice's and Bob's measurement basis settings. To close the efficiency and locality loopholes simultaneously, we introduce methods for quickly switching between three mutually unbiased measurement bases and for accurately characterizing the efficiency of detectors. From the space-time arrangement of our experiment, we can conclude that if the mechanism for the observed bipartite correlations is that Alice's measurement induces wave-function collapse of Bob's particle, then more than one bit of information must travel from Alice to Bob at more than three times the speed of light., Comment: 10 pages plus 9 pages of supplemental material. v2 includes changes to text explaining Eq. (2), in section V.1., and in first paragraph of section VI

Continuous-variable (CV) systems are attracting increasing attention in the realization of universal quantum computation. Several recent experiments have shown the feasibility of using CV systems to, e.g., encode a qubit into a trapped-ion mechanical oscillator and perform logic gates [Nature 566, 513-517 (2019)]. The essential next step is to protect the encoded qubit from quantum decoherence, e.g., the motional decoherence due to the interaction between a mechanical oscillator and its environment. Here we propose a scheme to suppress quantum decoherence of a single-mode harmonic oscillator used to encode qubits by introducing a nonperturbative leakage elimination operator (LEO) specifically designed for this purpose. Remarkably, our nonperturbative LEO can be used to analytically derive exact equations of motion without approximations. It also allows us to prove that the effectiveness of these LEOs only depends on the integral of the pulse sequence in the time domain, while details of the pulse shape does not make a significant difference when the time period is chosen appropriately. This control method can be applied to a system at an arbitrary temperature and arbitrary system-bath coupling strength which makes it extremely useful for general open quantum systems., 7 pages, 4 figures

The Kramers-Kronig (KK) receiver provides an efficient method to reconstruct the complex-valued optical field by means of intensity detection given a minimum-phase signal. In this paper, we analytically show that for detecting coherent states through measuring the minimum-phase signal, while keeping the radial quantum fluctuation the same as the balanced heterodyne detection does, by adopting the Kramers-Kronig relations to utilize the information of the physically measured radial component on the entire time domain, the KK receiver can indirectly recover the tangential component with fluctuation equivalently reduced to 1/3 times the radial one at the decision time. In consequence, the KK receiver achieves 3/2 times the signal-to-noise ratio of balanced heterodyne detection, while presenting an asymmetric quantum fluctuation distribution depending on the time-varying phase. Therefore, the KK receiver provides a feasible scheme to reduce the quantum fluctuation for obtaining the selected component to 2/ 3 times that of physically measuring the same component of the coherent state. This work provides a physical insight of the KK receiver and should enrich the knowledge of electromagnetic noise in quantum optical measurement.

We discuss general properties of the equilibrium state of parametric down-conversion in superconducting quantum circuits with detunings and Kerr anharmonicities, in the strongly nonlinear regime. By comparing moments of the steady state and those of a Schr��dinger cat, we show that true Schr��dinger cats cannot survive in the steady state if there is any single-photon loss. A delta-function 'cat-like' steady-state distribution can be formed, but this only exists in the limit of an extremely large nonlinearity. The steady state is a mixed state, which is more complex than a mixture or linear combination of delta-functions, and whose purity is reduced by driving. We expect this general behaviour to occur in other driven, dissipative quantum subharmonic non-equilibrium open systems., 10 pages, 4 figures

We study pairing states in an largely imbalanced two-component Fermi gas loaded in an anisotropic two-dimensional optical lattice, where the spin up and spin down fermions filled to the $s$- and $p_x$-orbital bands, respectively. We show that due to the relative inversion of band structures of the $s$ and $p_x$ orbitals, the system favors pairing between two fermions on the same side of the Brillouin zone, leading to a large stable regime for states with finite center-of-mass momentum, i.e., the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In particular, when the two Fermi surfaces are close in momentum space, a nesting effect stabilizes a special kind of $\pi$-FFLO phase with spatial modulation of $\pi$ along the easily tunneled $x$-direction. We map out the zero temperature phase diagrams within mean-field approach for various aspect ratio within the two-dimensional plane, and calculate the Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures $T_{\rm BKT}$ for different phases., Comment: 6 pages, 4 figures

We study multi-partite entanglement, the generation of EPR states and quantum steering in a three-mode optomechanical system composed of an atomic ensemble located inside a single-mode cavity with a movable mirror. The cavity mode is driven by a short laser pulse, has a nonlinear parametric-type interaction with the mirror and a linear beamsplitter-type interaction with the atomic ensemble. There is no direct interaction of the mirror with the atomic ensemble. A threshold effect for the dynamics of the system is found, above which the system works as an amplifier and below which as an attenuator of the output fields. The threshold is determined by the ratio of the coupling strengths of the cavity mode to the mirror and to the atomic ensemble. It is shown that above the threshold the system effectively behaves as a two-mode system in which a perfect bipartite EPR state can be generated, while it is impossible below the threshold. Furthermore, a fully inseparable tripartite entanglement and even further a genuine tripartite entanglement can be produced above and below the threshold. In addition, we consider quantum steering and examine the monogamy relations that quantify the amount of bipartite steering that can be shared between different modes. It is found that the mirror is more capable for steering of entanglement than the cavity mode. The two way steering is found between the mirror and the atomic ensemble despite the fact that they are not directly coupled to each other, while it is impossible between the output of cavity mode and the ensemble which are directly coupled to each other., Comment: 17 pages, 10 figures