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Neural networks have emerged as a promising paradigm for quantum information processing, yet they confront the challenge of generating training datasets with sufficient size and rich diversity, which is particularly acute when dealing with multipartite quantum systems. For instance, in the task of classifying different structures of multipartite entanglement in continuous variable systems, it is necessary to simulate a large number of infinite-dimension state data that can cover as many types of non-Gaussian states as possible. Here, we develop a data-augmented neural network to complete this task with homodyne measurement data. A quantum data augmentation method based on classical data processing techniques and quantum physical principles is proposed to efficiently enhance the network performance. By testing on randomly generated tripartite and quadripartite states, we demonstrate that the network can indicate the entanglement structure among the various partitions and the accuracies are significantly improved with data augmentation. Our approach allows us to further extend the use of data-driven machine learning techniques to more complex tasks of learning quantum systems encoded in a large Hilbert space.

Multipartite entanglement is an essential resource for quantum information tasks, but characterizing entanglement structures in continuous variable systems remains challenging, especially in multimode non-Gaussian scenarios. In this work, we introduce a method for detecting multipartite entanglement structures in continuous variable states. By leveraging the quantum Fisher information, we propose a systematic approach to identify feasible operators that capture quantum correlations in multimode non-Gaussian states. We demonstrate the effectiveness of our method on over $10^5$ randomly generated multimode-entangled quantum states, achieving a high success rate in entanglement detection. Additionally, our method exhibits enhanced robustness against losses by expanding the set of accessible operators. This work provides a general framework for characterizing entanglement structures in diverse continuous variable systems, enabling a number of experimentally relevant applications.

A noteworthy discovery is that the minimal evolution time is smaller for parity-time ($\mathcal{PT}$) symmetric systems compared to Hermitian setups. Moreover, there is a significant acceleration of two-qubit quantum entanglement preparation near the exceptional point (EP), or spectral coalescence, within such system. Nevertheless, an important problem often overlooked for quantum EP-based devices is their fidelity, greatly affected by the process of dissipation or post-selection, creating an inherent trade-off relation between the degree of entanglement and fidelity. Our study demonstrates that this limitation can be effectively overcome by harnessing an active $\mathcal{PT}$-symmetric system, which possesses balanced gain and loss, enabling maximal entanglement with rapid speed, high fidelity, and greater resilience to non-resonant errors. This new approach can efficiently prepare multi-qubit entanglement and use not only bipartite but also tripartite entanglement, as illustrative examples, even when the precise gain-loss balance is not strictly maintained. Our analytical findings are in excellent agreement with numerical simulations, confirming the potential of truly $\mathcal{PT}$-devices as a powerful tool for creating and engineering diverse quantum resources for applications in quantum information technology

We propose a quantum Rabi square model where both the nearest-neighbor and the next-nearest-neighbor photon hopping are allowed among four quantum Rabi systems located at the vertices of a square. By tuning the next-nearest hopping strength, we realize a first-order phase transition between the antiferromagnetic superradiant phase and the frustrated superradiant phase, as well as a second-order phase transition between the normal and the superradiant phases. To understand the emergence of such phases, we show analytically that the effect induced by next-nearest hopping is equivalent to that of an artificial gauge phase. Our findings suggest that the next-nearest-neighbor hopping can serve as an alternative for the gauge phase to realize quantum control in applications of quantum simulation and quantum materials, and that our model represents a basic building block for the frustrated $J_1$-$J_2$ quantum spin model on square lattices.

Optical Schrodinger's cat (SC) is highly anticipated because of the potential of realizing fault-tolerant quantum computing, but the practical merit is only shown when the amplitude is larger than 2. However, such high-amplitude cats have not been prepared due to the limitations rooted in the existing method. Here, we demonstrate a principle that a large SC-like state can be generated by the superposition of two kittens in which two nearby coherent states interfere and grow to an enlarged coherent-like state. Further, we propose a scheme to breed the cat beyond the limitation in the former works with a high probability by realizing the superposition of two SCs in coupled waveguides. The principle and scheme demonstrated here provide a new perspective on understanding quantum superposition in phase space and a better solution for the efficient generation of SCs on chips.

Genuine multipartite entanglement (GME) is not only fundamental interesting for the study of quantum-to-classical transition, but also is essential for realizing universal quantum computing and quantum networks. Here we investigate the multipartite entanglement (ME) dynamics in a linear chain of N LC resonators interacting optomechanically with a common thermal acoustic reservoir. By presenting the exact analytical solutions of system evolution, we predict the periodic generation of non-Gaussian ME, including the discrete and continuous variables entanglement. Interestingly, the GME is obtained even though the system is in a heat bath. The mechanism relies on the special acoustic environment featuring frequency comb structure. More importantly, our proposed model also allows the periodic generation of entangled multipartite cat states (MCSs), i.e., a typical GHZ state, with high fidelity. This work fundamentally broadens the fields of ME, and have wide applications in implementing thermal-noise-resistant quantum information processing and many-body quantum simulation.

We study the squeezing dynamics in a Kerr-nonlinear oscillator, and quantify the metrological usefulness of the resulting states. Even if the nonlinearity limits the attainable squeezing by making the evolution non-Gaussian, the states obtained still have a high quantum Fisher information for sensing displacements. However, contrary to the Gaussian case, the amplitude of the displacement cannot be estimated by simple quadrature measurements. Therefore, we propose the use of a measurement-after-interaction protocol where a linear quadrature measurement is preceded by an additional nonlinear evolution, and show the significant sensitivity enhancement that can be obtained. Our results are robust when considering realistic imperfections such as energy relaxation, and can be implemented in state-of-the-art experimental setups.

As a precious global resource in quantum information, genuine tripartite nonlocality(GTN) can be quantified by violating Svetlichny inequality. However, there is still no analytical expression for the general three-qubit states due to the difficulty of theoretical calculations. In this paper, we achieve highly accurate quantization of GTN for arbitrary three-qubit quantum states numerically. As an example, we study the dynamics of GTN and genuine tripartite entanglement(GTE) for the W state. Moreover, the complementarity of GTN is verified by examining the nonlocality between the tripartite and the bipartite. Finally, we also find a useful strategy to protect the correlation of GTN and GTE under decoherence by utilizing the Zeno effect.

The exotic phase transitions and multistabilities in atom-cavity coupled systems have attracted tremendous interests recently. In this work, we investigate the effect of photon hopping between two Dicke cavities, which induces rich quantum phases for steady states and dynamic process. Starting from a generic dimer system where the two cavities are not necessarily identical, we analytically prove all possible steady-state phases, which are confirmed by numerical calculations. We then focus on the special case with two identical cavities, where all the steady states are confirmed by exact solutions. We show that photon hopping is a convenient and powerful tool to manipulate the quantum phases and induce multistable behavior in this system.

Understanding entanglement of potentially high-dimensional multipartite quantum systems is crucial across different disciplines in quantum sciences. We take inspiration from covariance matrix based techniques to derive a nonlinear criterion that can be used to lower bound the dimensionality vector of mixed quantum states, revealing both the level of multipartiteness and the dimensionality of the entanglement in the quantum states. The technique is based on a system of inequalities that has to be satisfied by all quantum states with a given entanglement dimensionality vector, which can be checked via linear programming. We test our condition on paradigmatic classes of high-dimensional multipartite entangled states like imperfect Greenberger-Horne-Zeilinger (GHZ) states and find that, in comparison with other available criteria our method provides a significant advantage, which is enhanced especially in the case that the dimensions of the individual particles are different from each other.

We propose a novel and experimentally feasible approach to achieve high-efficiency ground-state cooling of a mechanical oscillator in an optomechanical system under the deeply unresolved sideband condition with the assistance of both intracavity and extracavity squeezing. In the scheme, a degenerate optical parametric amplifier is placed inside the optical cavity, generating the intracavity squeezing; besides, the optical cavity is driven by externally generated squeezing light, namely the extracavity squeezing. The quantum interference effect generated by intracavity squeezing and extracavity squeezing can completely suppress the non-resonant Stokes heating process while greatly enhancing the anti-Stokes cooling process. Therefore, the joint-squeezing scheme is capable of cooling the mechanical oscillators to their quantum ground state in a regime far away from the resolved sideband condition. Compared with other traditional optomechanical cooling schemes, the single-photon cooling rate in this joint-squeezing scheme can be tremendously enlarged by nearly three orders of magnitude. At the same time, the coupling strength required to achieve ground-state cooling can be significantly reduced. This scheme is promising for cooling large-mass and low-frequency mechanical oscillators, which provides a prerequisite for preparing and manipulating non-classical states in macroscopic quantum systems and lays a significant foundation for quantum manipulation.

We investigate the amplification of the genuine tripartite nonlocality(GTN) and the genuine tripartite entanglement(GTE) of Dirac particles in the background of a Schwarzschild black hole by a local filtering operation under decoherence. It is shown that the physically accessible GTN will be completely destroyed by decoherence, which means that the physically accessible GTN will not exist in the system. Particularly, the local filtering operation can make the physically accessible GTN appear within a certain range of Hawking temperature, namely, the local filtering operation can cause the physically accessible GTN to be generated in the system coupled with the environment, which is not discovered before and is benefit for the quantum information processing. Furthermore, we also find that the physically accessible GTE approaches a stable value in the limit of infinite Hawking temperature for most cases, but if the decoherence parameter $p$ is less than 1, the ``sudden death'' of GTE will take place when the decoherence strength is large enough. It is worth noting that the nonzero stable value of GTE can be increased by performing the local filtering operation, even in the presence of decoherence. Finally, we explore the generation of physically inaccessible GTN and GTE of other tripartite subsystems under decoherence, it is shown that the physically inaccessible GTN cannot be produced, but the physically inaccessible GTE can be produced. In addition, we can see that the generated physically inaccessible GTE can be increased by applying the local filtering operation.

Entanglement in continuous-variable non-Gaussian states provides irreplaceable advantages in many quantum information tasks. However, the sheer amount of information in such states grows exponentially and makes a full characterization impossible. Here, we develop a neural network that allows us to use correlation patterns to effectively detect continuous-variable entanglement through homodyne detection. Using a recently defined stellar hierarchy to rank the states used for training, our algorithm works not only on any kind of Gaussian state but also on a whole class of experimentally achievable non-Gaussian states, including photon-subtracted states. With the same limited amount of data, our method provides higher accuracy than usual methods to detect entanglement based on maximum-likelihood tomography. Moreover, in order to visualize the effect of the neural network, we employ a dimension reduction algorithm on the patterns. This shows that a clear boundary appears between the entangled states and others after the neural network processing. In addition, these techniques allow us to compare different entanglement witnesses and understand their working. Our findings provide a new approach for experimental detection of continuous-variable quantum correlations without resorting to a full tomography of the state and confirm the exciting potential of neural networks in quantum information processing.

We analyse the conditional states in which one part of a split spin-squeezed state is left, upon performing a collective spin measurement on the other part. For appropriate measurement directions and outcomes, we see the possibility of obtaining states with high quantum Fisher information, even reaching the Heisenberg limit. This allows us to propose a metrological protocol that can outperform standard approaches, for example in a situation where the number of particles in the probe is bounded. The robustness of this protocol is investigated by considering realistic forms of noise present in cold-atom experiments, such as particle number fluctuations and imperfect detection. Ultimately, we show how this measurement-based state preparation approach can allow for the conditional (\ie heralded) preparation of spin Schrödinger's cat states even when the initial state before splitting is only mildly squeezed.

Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein-Podolsky-Rosen (EPR) steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.

Continuous U(1) gauge symmetry, which guarantees the conservation of the total excitations in linear bosonic systems, will be broken when it comes to the strong-coupling regime where the rotation wave approximation (RWA) fails. Here we develop analytic solutions for multi-mode bosonic systems with XX-type couplings beyond RWA, and proposed a novel scheme to implement high-fidelity quantum state transfer (QST) and entanglement preparation (EP) with high speed. The scheme can be realized with designated coupling strength and pulse duration with which the excitation number keeps unchanged regardless of the breakdown of the global U(1) symmetry. In the QST tasks, we consider several typical quantum states and demonstrate that this method is robust against thermal noise and imperfections of experimental sequence. In the EP tasks, the scheme is successfully implemented for the preparation of Bell states and W-type states, within a shortest preparation time.

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.

Remote state preparation enables one to prepare and manipulate quantum state non-locally. As an essential quantum resource, optical cat state is usually prepared locally by subtracting photons from a squeezed vacuum state. For remote quantum information processing, it is essential to prepare and manipulate optical cat states remotely based on Gaussian entanglement, which remains a challenge. Here, we present experimental preparation of optical cat states based on a remotely distributed two-mode Gaussian entangled state in a lossy channel. By performing photon subtraction and homodyne projective measurement at Alice's station, an optical cat state is prepared remotely at Bob's station. Furthermore, the prepared cat state is rotated by changing Alice's measurement basis of homodyne detection, which demonstrates the remote manipulation of it. By distributing two modes of the two-mode Gaussian entangled state in lossy channels, we demonstrate that the remotely prepared cat state can tolerate much more loss in Alice's channel than that in Bob's channel. We also show that cat states with amplitudes larger than 2 can be prepared by increasing the squeezing level and subtracting photon numbers. Our results make a crucial step toward remote hybrid quantum information processing involving discrete- and continuous-variable techniques.

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, Schrödinger 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.

The quantum internet -- in synergy with the internet that we use today -- promises an enabling platform for next-generation information processing, including exponentially speed-up distributed computation, secure communication, and high-precision metrology. The key ingredients for realizing such a global network are the distribution and storage of quantum entanglement. As ground-based quantum networks are likely to be based on existing fiber networks, telecom-wavelength entangled photons and corresponding quantum memories are of central interest. Recently, $\rm^{167}Er^{3+}$ ions have been identified as a promising candidate for an efficient, broadband quantum memory at telecom wavelength. However, to date, no storage of entangled photons, the crucial step of quantum memory using these promising ions, $\rm^{167}Er^{3+}$, has been reported. Here, we demonstrate the storage and recall of the entangled state of two telecom photons generated from an integrated photonic chip based on a silicon nitride micro-ring resonator. Combining the natural narrow linewidth of the entangled photons and long storage time of $\rm^{167}Er^{3+}$ ions, we achieve storage time of 1.936 $\mu$s, more than 387 times longer than in previous works. Successful storage of entanglement in the crystal is certified by a violation of an entanglement witness with more than 23 standard deviations (-0.234 $\pm$ 0.010) at 1.936 $\mu$s storage time. These results pave the way for realizing quantum networks based on solid-state devices.

Non-Gaussian states (NGSs) with higher-order correlation properties have wide-range applications in quantum information processing. However, the generation of such states with high quality still faces practical challenges. Here, we propose a protocol to faithfully generate two types of mechanical NGSs, i.e., Schrödinger cat states and Fock states, in open optomechanical systems, even when the cooperativity is smaller than one ($g^2/\kappa\gamma<1$). In contrast to the usual scheme, a short squeezed field is pumped to rapidly entangle with a mechanical resonator via a beam-splitter-like optomechanical interaction, effectively reducing the mechanical decoherence. Furthermore, by performing an additional amplifier and a following multi photon subtraction on the entangled optical field, one can selectively obtain the high-fidelity mechanical cat and Fock states. This protocol is robust to various imperfections, allowing it to be implemented with state-of-the-art experimental systems with close to unit fidelity. Moreover, it can be extended to generate a four-component cat state and provide possibilities for future quantum applications of NGSs.

Quantum entanglement plays a key role in both understanding the fundamental aspects of quantum physics and realizing various quantum devices for practical applications. Here we propose how to achieve coherent switch of optomechanical entanglement in an optical whispering-gallery-mode resonator, by tuning the phase difference of the driving lasers. We find that the optomechanical entanglement and the associated two-mode quantum squeezing can be well tuned in a highly asymmetric way, providing an efficient way to protect and enhance quantum entanglement against optical backscattering, in comparison with conventional symmetric devices. Our findings shed a new light on improving the performance of various quantum devices in practical noisy environment, which is crucial in such a wide range of applications as noise-tolerant quantum processing and the backscattering-immune quantum metrology.

Optical downconversion is a key resource for generating nonclassical states. Very recently, direct nondegenerate triple-photon spontaneous downconversion (NTPSD) with bright photon triplets and strong third-order correlations has been demonstrated in a superconducting device (2020 Phys. Rev. X 10 011011). Besides, linear and nonlinear tripartite entanglement in this process have also been predicted (2018 Phys. Rev. Lett. 120 043601; 2020 Phys. Rev. Lett. 125 020502). In this paper, we consider the generation of nonclassical optical quantum superpositions and investigate nonlinear quantum steering effects in NTPSD.We find that large-size Schrödinger cat states of one downconverted mode can be achieved when the other two modes are subjected to homodyne detection. Also, a two-photon Bell entangled state can be generated when only one mode is homodyned.We further reveal that such ability of remote state steering originates from nonlinear quantum steerable correlations among the triplets. This is specifically embodied by the seeming violation of the Heisenberg uncertainty relation for the inferred variances of two noncommutating higher-order quadratures of downconverted modes, based on the outcomes of homodyne detection on the other mode, i.e., nonlinear quantum steering, compared to original EPR steering. Our results demonstrate non-Gaussian nonclassical features in NTPSD and would be useful for the fundamental tests of quantum physics and implementations of optical quantum technologies.

Very recently, strongly non-Gaussian states have been observed via a direct three-mode spontaneous parametric down-conversion in a superconducting cavity [Phys. Rev. X 10, 011011 (2020)]. The created multi-photon non-Gaussian correlations are attractive and useful for various quantum information tasks. However, how to detect and classify multipartite non-Gaussian entanglement has not yet been completely understood. Here, we present an experimentally practical method to characterize continuous-variable multipartite non-Gaussian entanglement, by introducing a class of nonlinear squeezing parameters involving accessible higher-order moments of phase-space quadratures. As these parameters can depend on arbitrary operators, we consider their analytical optimization over a set of practical measurements, in order to detect different classes of multipartite non-Gaussian entanglement ranging from fully separable to fully inseparable. We demonstrate that the nonlinear squeezing parameters act as an excellent approximation to the quantum Fisher information within accessible third-order moments. The level of the nonlinear squeezing quantifies the metrological advantage provided by those entangled states. Moreover, by analyzing the above mentioned experiment, we show that our method can be readily used to confirm fully inseparable tripartite non-Gaussian entangled states by performing a limited number of measurements without requiring full knowledge of the quantum state.

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.

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.

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 Schrödinger 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 $t\sim1\,\mu$s.

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.

Non-local point-to-point correlations between two photons have been used to produce "ghost" images without placing the camera towards the object. Here we theoretically demonstrated and analyzed the advantage of non-Gaussian quantum light in improving the image quality of ghost imaging system over traditional Gaussian light source. For any squeezing degree, the signal-to-noise ratio (SNR) of the ghost image can be enhanced by the non-Gaussian operations of photon addition and subtraction on the two-mode squeezed light source. We find striking evidence that using non-Gaussian coherent operations, the SNR can be promoted to a high level even within the extremely weak squeezing regime. The resulting insight provides new experimental recipes of quantum imaging using non-Gaussian light for illumination.

Schrödinger 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 Schrödinger'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.

Famous double-slit or double-path experiments, implemented in a Young's or Mach-Zehnder interferometer, have confirmed the dual nature of quantum matter, When a stream of photons, neutrons, atoms, or molecules, passes through two slits, either wave-like interference fringes build up on a screen, or particle-like which-path distribution can be ascertained. These quantum objects exhibit both wave and particle properties but exclusively, depending on the way they are measured. In an equivalent Mach-Zehnder configuration, the object displays either wave or particle nature in the presence or absence of a beamsplitter, respectively, that represents the choice of which-measurement. Wheeler further proposed a gedanken experiment, in which the choice of which-measurement is delayed, i.e. determined after the object has already entered the interferometer, so as to exclude the possibility of predicting which-measurement it will confront. The delayed-choice experiments have enabled significant demonstrations of genuine two-path duality of different quantum objects. Recently, a quantum controlled version of delayed-choice was proposed by Ionicioiu and Terno, by introducing a quantum-controlled beamsplitter that is in a coherent superposition of presence and absence. It represents a controllable experiment platform that can not only reveal wave and particle characters, but also their superposition. Moreover, a quantitative description of two-slit duality relation was initialized in Wootters and Zurek's seminal work and formalized by Greenberger,et. al. as D2+V2<=1, where D is the distinguishability of whichpath information, and V is the contrast visibility of interference. In this regard, getting which-path information exclusively reduces the interference visibility, and vice versa. This double-path duality relation has been tested in pioneer experiments and recently in delayed-choice measurements.

Wigner negativity, as a well-known indicator of nonclassicality, plays an essential role in quantum computing and simulation using continuous-variable systems. Recently, it has been proven that Einstein-Podolsky-Rosen steering is a prerequisite to generate Wigner negativity between two remote modes. Motivated by the demand of real-world quantum network, here we investigate the shareability of generated Wigner negativity in the multipartite scenario from a quantitative perspective. By establishing a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality, we show that the amount of Wigner negativity cannot be freely distributed among different modes. Moreover, for photon subtraction -- one of the main experimentally realized non-Gaussian operations -- we provide a general method to quantify the remotely generated Wigner negativity. With this method, we find that there is no direct quantitative relation between the Gaussian steerability and the amount of generated Wigner negativity. Our results pave the way for exploiting Wigner negativity as a valuable resource for numerous quantum information protocols based on non-Gaussian scenario.

As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and steering play important roles in quantum-enhanced communication protocols. Distributing such quantum resources among multiple remote users in a network is a crucial precondition underlying various quantum tasks. We experimentally demonstrate the deterministic distribution of two- and three-mode Gaussian entanglement and steering by transmitting separable states in a network consisting of a quantum server and multiple users. In our experiment, entangled states are not prepared solely by the quantum server, but are created among independent users during the distribution process. More specifically, the quantum server prepares separable squeezed states and applies classical displacements on them before spreading out, and users simply perform local beam-splitter operations and homodyne measurements after they receive separable states. We show that the distributed Gaussian entanglement and steerability are robust against channel loss. Furthermore, one-way Gaussian steering is achieved among users that is useful for further directional or highly asymmetric quantum information processing.

It is widely recognized that a physical system can only respond to a periodic driving significantly when the driving frequency matches the normal mode frequency of the system, which leads to resonance. Off-resonant phenomena are rarely considered because of the difficulty to realize strong coupling between physical systems and off-resonant waves. Here we examine the response of a magnetic system to squeezed light and surprisingly find that the magnons are maximally excited when the effective driving frequency is several orders of magnitude larger than the resonant frequency. The generated magnons are squeezed which brings the advantage of tunable squeezing through an external magnetic field. Furthermore, we demonstrate that such off-resonant quasi-particle excitation is universal in all the hybrid systems in which the coherent and parametric interaction of bosons exists and that it is purely a quantum effect, which is rooted in the quantum fluctuations of particles in the squeezed vacuum. Our findings may provide an unconventional route to study off-resonant phenomena and may further benefit the use of hybrid matter-light systems in continuous variable quantum information.

The generation and manipulation of strong entanglement and Einstein-Podolsky-Rosen (EPR) steering in macroscopic systems are outstanding challenges in modern physics. Especially, the observation of asymmetric EPR steering is important for both its fundamental role in interpreting the nature of quantum mechanics and its application as resource for the tasks where the levels of trust at different parties are highly asymmetric. Here, we study the entanglement and EPR steering between two macroscopic magnons in a hybrid ferrimagnet-light system. In the absence of light, the two types of magnons on the two sublattices can be entangled, but no quantum steering occurs when they are damped with the same rates. In the presence of the cavity field, the entanglement can be significantly enhanced, and strong two-way asymmetric quantum steering appears between two magnons with equal dispassion. This is very different from the conventional protocols to produce asymmetric steering by imposing additional unbalanced losses or noises on the two parties at the cost of reducing steerability. The essential physics is well understood by the unbalanced population of acoustic and optical magnons under the cooling effect of cavity photons. Our finding may provide a novel platform to manipulate the quantum steering and the detection of bi-party steering provides a knob to probe the magnetic damping on each sublattice of a magnet.

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, quantum noise of the KK receiver keeps the radical fluctuation of measuring the minimum-phase signal, the same as the balanced heterodyne detection does, while compressing the tangential fluctuation to 1/3 times the radical one using information provided by the Hilbert transform. 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. This further provides a feasible scheme for compressing the quantum fluctuation of measuring the coherent state in a specific direction to 1/6, which is even lower than 1/4 of measuring directly in the same direction. Our work presents a physical insight of the KK receiver and a further step of deep understanding of electromagnetic noise in quantum optical measurement.

We use the uncertainty relation between the operators associated to the total number of particles and to the relative phase of two bosonic modes to construct entanglement and Einstein-Podolsky-Rosen steering criteria. These can be tested experimentally in a variety of systems, such as optical fields, Bose-Einstein condensates or mechanical oscillators. While known entanglement criteria involving the phase observable typically require to perform interference measurements by recombining the two systems, our criteria can be tested through local measurements at two spatially distinct positions, to investigate the nonlocal nature of quantum correlations. We present simple examples where our criteria are violated, and show their robustness to noise. Apart from being useful for state characterization, they might find application in quantum information protocols, for example based on number-phase teleportation.

Multipartite Einstein-Podolsky-Rosen steering is an essential resource for quantum communication networks where the reliability of equipment at all of the nodes cannot be fully trusted. Here, we present experimental generation of a highly versatile and flexible repository of multipartite steering using an optical frequency comb and ultrafast pulse shaping. Simply modulating the optical spectral resolution of the detection system using the pulse shaper, this scheme is able to produce on-demand 4, 8 and 16-mode Gaussian steering without changing the photonics architecture. We find that the steerability increases with higher spectral resolution. For 16-mode state, we identify as many as 65534 possible bipartition steering existing in this intrinsic multimode quantum resource, and demonstrate that the prepared state steerability is robust to mode losses. Moreover, we verify four types of monogamy relations of Gaussian steering and demonstrate strong violation for one of them. Our method offers a powerful foundation for constructing quantum networks in real-world scenario.

A cat-state is formed as the steady-state solution for the signal mode of an ideal, degenerate parametric oscillator, in the limit of negligible single-photon signal loss. In the presence of the signal loss, this is no longer true over timescales much longer than the damping time. However, for sufficient parametric nonlinearity, a cat-state can exist as a transient state. In this paper, we study the dynamics of the creation and decoherence of cat-states in degenerate parametric oscillation, both with and without the effect of a Kerr nonlinearity that applies to recent superconducting-circuit experiments generating cat-states in microwave cavities. We determine the time of formation and the lifetime of a cat-state in terms of three dimensionless parameters $\lambda$, $g$ and $\chi$. These relate to the driving strength, the parametric nonlinearity, and the Kerr nonlinearity, respectively. We find that the Kerr nonlinearity has little effect on the threshold parametric nonlinearity ($g>1$) required for the formation of cat-states, and does not significantly alter the decoherence time of the cat-state, but can reduce the time of formation. The quality of the cat-state increases with the value $g$, and can also improved by the Kerr nonlinearity. To verify the existence and quality of the cat-state, we consider several signatures, including interference fringes and negativity, and show how they can be computed. We simulate a superconducting-circuit experiment using published experimental parameters and found good agreement with experimental results, indicating that a nonclassical cat-like state with a small Wigner negativity is generated in the experiment. A stronger nonlinearity would lead to a cat-state with convincing cat-state signatures. Finally, we explore the feasibility of creating large cat-states with a coherent amplitude of 20, corresponding to 400 photons.

We show that parity-time ($\mathcal{PT}$) symmetry can be spontaneously broken in the recently reported energy level attraction of magnons and cavity photons. In the $\mathcal{PT}$-broken phase, magnon and photon form a high-fidelity Bell state with maximum entanglement. This entanglement is steady and robust against the perturbation of environment, in contrast to the general wisdom that expects instability of the hybridized state when the symmetry is broken. This anomaly is further understood by the compete of non-Hermitian evolution and particle number conservation of the hybridized system. As a comparison, neither $\mathcal{PT}$-symmetry broken nor steady magnon-photon entanglement is observed inside the normal level repulsion case. Our results may open a novel window to utilize magnon-photon entanglement as a resource for quantum technologies.

We discuss general properties of discrete time quantum symmetry breaking in degenerate parametric oscillators. Recent experiments in superconducting quantum circuit with Josephson junction nonlinearities give rise to new properties of strong parametric coupling and nonlinearities. Exact analytic solutions are obtained for the steady-state of this single-mode case of subharmonic generation. We also obtain analytic solutions for the tunneling time over which the time symmetry-breaking is lost above threshold. We find that additional anharmonic terms found in the superconducting case increase the tunneling rate, and can also lead to new regimes of tristability as well as bistability. Our analytic results are confirmed by number state calculations.

Magnon-photon coupling has been experimentally realized inside a cavity and the emerging field known as cavity spintronics has attracted significant attention for its potential docking with quantum information science. However, one seldom knows whether this coupling implies an entanglement state among magnons and photons or not, which is crucial for its usage in quantum information. Here we study the entanglement properties among magnons and photons in an antiferromagnet-light system and find that the entanglement between magnon and photon is nearly zero while the magnon-magnon entanglement is very strong and it can be even further enhanced through the coupling with the cavity photons. The maximum enhancement occurs when the antiferromagnet reaches resonant with the light. The essential physics can be well understood within the picture of cavity induced cooling of magnon-magnon state near its joint vacuum with stronger entanglement. Our results are significant to extend the cavity spintronics to quantum manipulation and further provide an alternate to manipulate the deep strong correlations of continuous variable entanglement with a generic stable condition and easy tunability.

Generation of quantum correlations between separate objects is of significance both in fundamental physics and in quantum networks. One important challenge is to create the directional "spooky action-at-a-distanc" effects that Schrödinger called "steering" between two macroscopic and massive objects. Here, we analyze a generic scheme for generating steering correlations in cascaded hybrid systems in which two distant oscillators with effective masses of opposite signs are coupled to a unidirectional light field, a setup which is known to build up quantum correlations by means of quantum back-action evasion. The unidirectional coupling of the first to the second oscillator via the light field can be engineered to enhance steering in both directions and provides an active method for controlling the asymmetry of steering. We show that the resulting scheme can efficiently generate unconditional steady-state Einstein-Podolsky-Rosen steering between the two subsystems, even in the presence of thermal noise and optical losses. As a scenario of particular technological interest in quantum networks, we use our scheme to engineer enhanced steering from an untrusted node with limited tunability (in terms of interaction strength and type with the light field) to a trusted, highly tunable node, hence offering a path to implementing one-sided device-independent quantum tasks.

The spontaneous formation of lattice structure of quantized vortices is a characteristic feature of superfluidity in closed systems under thermal equilibrium. In exciton-polariton Bose-Einstein condensate, which is a typical example of macroscopic quantum state in open systems, spontaneous vortex lattices have also been proposed by not yet observed. Here, we take into account the finite decay rate of exciton reservoir, and theoretically investigate the vortex structures in circularly pumped polariton Bose-Einstein condensate. Our results show that a decreasing reservoir decay rate can reduce the number of vortices and destabilize the lattice structure, hence is unfavorable to the formation and observation of vortex lattices. These detrimental effects can be prevailed by applying an external angular momentum.

We present a phase control method for a general three-mode system with closed-loop in coupling that drives the system into an entangled steady state and produces directional steering between two completely symmetric modes via quantum interference effects. In the scheme, two modes are coupled with each other both by a direct binary interaction and by an indirect interaction through a third intermediate damping mode, creating interference effects determined by the relative phase between the two physical interaction paths. By calculating the populations and correlations of the two modes, we show that depending on the phase, two modes can be prepared into an entangled steady state with asymmetric and directional steering even if they possess completely symmetric decoherence properties. Meanwhile, entanglement and steering can be significantly enhanced due to constructive interference, and thus more robust to thermal noises. This provides an active method to manipulate the asymmetry of steering instead of adding asymmetric losses or noises on subsystems at the cost of reducing steerability. Moreover, we show that the interference effects can also enhance and control the correlations between other pair of modes in the loop with opposite phase dependent behavior, indicating monogamy constraints for distributing correlations among multipartite. The present model could be applied in cavity optomechanical systems or in antiferromagnets where all components can mutually interact.

The generation of entanglement between disparate physical objects is a key ingredient in the field of quantum technologies, since they can have different functionalities in a quantum network. Here we propose and analyze a generic approach to steady-state entanglement generation between two oscillators with different temperatures and decoherence properties coupled in cascade to a common unidirectional light field. The scheme is based on a combination of coherent noise cancellation and dynamical cooling techniques for two oscillators with effective masses of opposite signs, such as quasi-spin and motional degrees of freedom, respectively. The interference effect provided by the cascaded setup can be tuned to implement additional noise cancellation leading to improved entanglement even in the presence of a hot thermal environment. The unconditional entanglement generation is advantageous since it provides a ready-to-use quantum resource. Remarkably, by comparing to the conditional entanglement achievable in the dynamically stable regime, we find our unconditional scheme to deliver a virtually identical performance when operated optimally.