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Quantum state tomography (QST) via local measurements on reduced density matrices (LQST) is a promising approach but becomes impractical for large systems. To tackle this challenge, we developed an efficient quantum state tomography method inspired by quantum overlapping tomography [Phys. Rev. Lett. 124, 100401(2020)], which utilizes parallel measurements (PQST). In contrast to LQST, PQST significantly reduces the number of measurements and offers more robustness against shot noise. Experimentally, we demonstrate the feasibility of PQST in a tree-like superconducting qubit chip by designing high-efficiency circuits, preparing W states, ground states of Hamiltonians and random states, and then reconstructing these density matrices using full quantum state tomography (FQST), LQST, and PQST. Our results show that PQST reduces measurement cost, achieving fidelities of 98.68\% and 95.07\% after measuring 75 and 99 observables for 6-qubit and 9-qubit W states, respectively. Furthermore, the reconstruction of the largest density matrix of the 12-qubit W state is achieved with the similarity of 89.23\% after just measuring $243$ parallel observables, while $3^{12}=531441$ complete observables are needed for FQST. Consequently, PQST will be a useful tool for future tasks such as the reconstruction, characterization, benchmarking, and properties learning of states.

Previous studies in quantum information have recognized that specific types of noise can encode information in certain applications. However, the role of noise in Quantum Hypothesis Testing (QHT), traditionally assumed to undermine performance and reduce success probability, has not been thoroughly explored. Our study bridges this gap by establishing sufficient conditions for noisy dynamics that can surpass the success probabilities achievable under noiseless (unitary) dynamics within certain time intervals. We then devise and experimentally implement a noise-assisted QHT protocol in the setting of ultralow-field nuclear magnetic resonance spin systems. Our experimental results demonstrate that the success probability of QHT under the noisy dynamics can indeed surpass the ceiling set by unitary evolution alone. Moreover, we have shown that in cases where noise initially hampers the performance, strategic application of coherent controls on the system can transform these previously detrimental noises into advantageous factors. This transformative approach demonstrates the potential to harness and leverage noise in QHT, which pushes the boundaries of QHT and general quantum information processing.

Kibble-Zurek (KZ) mechanism describes the scaling behavior when driving a system across a continuous symmetry-breaking transition. Previous studies have shown that the KZ-like scaling behavior also lies in the topological transitions in the Qi-Wu-Zhang model (2D) and the Su-Schrieffer-Heeger model (1D), although symmetry breaking does not exist here. Both models with linear band crossings give that $\nu=1$ and $z=1$. We wonder whether different critical exponents can be acquired in topological transitions beyond linear band crossing. In this work, we look into the KZ behavior in a topological 2D checkerboard lattice with a quadratic band crossing. We investigate from dual perspectives: momentum distribution of the Berry curvature in clean systems for simplicity, and real-space analysis of domain-like local Chern marker configurations in disordered systems, which is a more intuitive analog to conventional KZ description. In equilibrium, we find the correlation length diverges with a power $\nu\simeq 1/2$. Then, by slowly quenching the system across the topological phase transition, we find that the freeze-out time $t_\mathrm{f}$ and the unfrozen length scale $\xi(t_\mathrm{f})$ both satisfy the KZ scaling, verifying $z\simeq 2$. We subsequently explore KZ behavior in topological phase transitions with other higher-order band crossing and find the relationship between the critical exponents and the order. Our results extend the understanding of the KZ mechanism and non-equilibrium topological phase transitions.

We propose a quantum analog of the Vicsek model, consisting of an ensemble of overdamped spin$-1/2$ particles with ferromagnetic couplings, driven by a uniformly polarized magnetic field. The spontaneous magnetization of the spin components breaks the $SO(3)$ (or $SO(2)$) symmetry, inducing an ordered phase of flocking. We derive the hydrodynamic equations, similar to those formulated by Toner and Tu, by applying a mean-field approximation to the quantum analog model up to the next leading order. Our investigation not only establishes a microscopic connection between the Vicsek model and the Toner-Tu hydrodynamics for active matter, but also aims to inspire further studies of active matter in the quantum regime.

Nonlocal correlation represents the key feature of quantum mechanics, and is an exploitable resource in quantum information processing. However, the loophole issues and the associated applicability compromises hamper the practical applications. We report the first detection-loophole-free demonstration of steering nonlocality in a fully chip-fiber telecommunication system, with an ultra-fast measurement switching rate (2.5 GHz). In this endeavor, we propose the phase-encoding measurement scheme to adapt the system to the GHz-level modulation rate. We design and fabricate a low-loss silicon chip for efficient entanglement generation, and devise an asymmetric paradigm to mimic the measurement implementation at the steering party thus avoiding the phase-encoding loss. Consequently, we build a fiber-optic setup that can overcome the detection efficiency that is required by conclusive quantum steering with actively switched multiple measurement settings. Our setup presents an immediate platform for exploring applications based on steering nonlocality, especially for quantum communication.

We derive the theoretical limit of single-photon purity of heralded single-photon sources, and accordingly demonstrate a bright, gigahertz-pulsed heralded source with the purity saturating the limit. Based on spontaneous four-wave mixing in a silicon spiral waveguide, this on-chip source is measured to have a coincidence rate exceeding 1.5 MHz at a coincidence to accidental (CAR) ratio of 16.77. The single-photon purity, quantified by the auto-correlation function $g^{(2)}_h(0)$, reaches the theoretical limit with the lowest value of $0.00094 \pm 0.00002$ obtained at a coincidence rate of 0.8 kHz. We attribute our results to effective spectral filtering as well as the coherent pump condition helped by optical injection locking.

Squeezing a quantum state along a specific direction has long been recognized as a crucial technique for enhancing the precision of quantum metrology by reducing parameter uncertainty. However, practical quantum metrology often involves the simultaneous estimation of multiple parameters, necessitating the use of high-quality squeezed states along multiple orthogonal axes to surpass the standard quantum limit for all relevant parameters. In addition, a temporally stabilized squeezed state can provide an event-ready probe for parameters, regardless of the initial state, and robust to the timing of the state preparation process once stabilized. In this work, we generate and stabilize a two-mode squeezed state along two secular motional modes in a vibrating trapped ion with reservoir engineering, despite starting from a thermal state of the motion. Leveraging this resource, we demonstrate an estimation of two simultaneous collective displacements along the squeezed axes, achieving improvements surpassing the classical limit by up to 6.9(3) and 7.0(3) decibels (dB), respectively. Our demonstration can be readily scaled to squeezed states with even more modes. The practical implications of our findings span a wide range of applications, including quantum sensing, quantum imaging, and various fields that demand precise measurements of multiple parameters.

The range and speed of a moving object can be ascertained using the sensing technique known as light detection and ranging (LiDAR). It has recently been suggested that quantum LiDAR, which uses entangled states of light, can enhance the capabilities of LiDAR. Entangled pulsed light is used in prior quantum LiDAR approaches to assess both range and velocity at the same time using the pulses' time of flight and Doppler shift. The entangled pulsed light generation and detection, which are crucial for pulsed quantum LiDAR, are often inefficient. Here, we study a quantum LiDAR that operates on a frequency-modulated continuous wave (FMCW), as opposed to pulses. We first outline the design of the quantum FMCW LiDAR using entangled frequency-modulated photons in a Mach-Zehnder interferometer, and we demonstrate how it can increase accuracy and resolution for range and velocity measurements by $\sqrt{n}$ and $n$, respectively, with $n$ entangled photons. We also demonstrate that quantum FMCW LiDAR may perform simultaneous measurements of the range and velocity without the need for quantum pulsed compression, which is necessary in pulsed quantum LiDAR. Since the generation of entangled photons is the only inefficient nonlinear optical process needed, the quantum FMCW LiDAR is better suited for practical implementations. Additionally, most measurements in the quantum FMCW LiDAR can be carried out electronically by down-converting optical signal to microwave region.

Precise control of hyperfine matterwaves via Raman excitations is instrumental to a class of atom-based quantum technology. We investigate the Raman spinor control technique for alkaline atoms in an intermediate regime of single-photon detuning where a choice can be made to balance the Raman excitation power efficiency with the control speed, excited-state adiabatic elimination, and spontaneous emission suppression requirements. Within the regime, rotations of atomic spinors by the Raman coupling are biased by substantial light shifts. Taking advantage of the fixed bias angle, we show that composite biased rotations can be optimized to enable precise ensemble spinor matterwave control within nanoseconds, even for multiple Zeeman pseudo-spins defined on the hyperfine ground states and when the laser illumination is strongly inhomogeneous. Our scheme fills a technical gap in light pulse atom interferometry, for achieving high speed Raman spinor matterwave control with moderate laser power.

Quantum entanglement has become an essential resource in quantum information processing. Existing works employ entangled quantum states to perform various tasks, while little attention is paid to the control of the resource. In this work, we propose a simple protocol to upgrade an entanglement source with access control through phase randomization at the optical pump. The enhanced source can effectively control all users in utilizing the entanglement resource to implement quantum cryptography. In addition, we show this control can act as a practical countermeasure against memory attack on device-independent quantum key distribution at a negligible cost. To demonstrate the feasibility of our protocol, we implement an experimental setup using just off-the-shelf components and characterize its performance accordingly.

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 Floquet engineering opens the way to create new topological states without counterparts in static systems. Here, we report the experimental realization and characterization of new anomalous topological states with high-precision Floquet engineering for ultracold atoms trapped in a shaking optical Raman lattice. The Floquet band topology is manipulated by tuning the driving-induced band crossings referred to as band inversion surfaces (BISs), whose configurations fully characterize the topology of the underlying states. We uncover various exotic anomalous topological states by measuring the configurations of BISs which correspond to the bulk Floquet topology. In particular, we identify an unprecedented anomalous Floquet valley-Hall state that possesses anomalous helicallike edge modes protected by valleys and a chiral state with high Chern number.

There has been a recent upsurge of interest in the quantum properties of magnons for quantum information processing. An important issue is to examine the stability of quantum states of magnons against various relaxation and dephasing channels. Since the interaction of magnons in magnetic systems may fall in the ultra-strong and even deep-strong coupling regimes, the relaxation process of magnon states is quite different from the more common quantum optical systems. Here we study the relaxation and dephasing of magnons based on the Lindblad formalism and derive a generalized master equation that describes the quantum dynamics of magnons. Employing this master equation, we identify two distinct dissipation channels for squeezed magnons, i.e., the local dissipation and collective dissipation, which play a role for both ferromagnets and antiferromagnets. The local dissipation is caused by the independent exchange of angular momentum between the magnonic system and the environment, while the collective dissipation is dressed by the parametric interactions of magnons and it enhances the quantumness and thermal stability of squeezed magnons. Further, we show how this formalism can be applied to study the pure dephasing of magnons caused by four-magnon scattering and magnon-phonon interactions. Our results provide the theoretical tools to study the decoherence of magnons within a full quantum-mechanical framework and further benefit the use of quantum states of magnons for information processing.

Within the quantum computing, there are two ways to encode a normalized vector $\{ \alpha_i \}$. They are one-hot encoding and binary coding. The one-hot encoding state is denoted as $\left | \psi_O^{(N)} \right \rangle=\sum_{i=0}^{N-1} \alpha_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle \left |0 \right \rangle ^{\otimes i}$ and the binary encoding state is denoted as $\left | \psi_B^{(N)} \right \rangle=\sum_{i=0}^{N-1} \alpha_i \left |b_i \right \rangle$, where $b_i$ is interpreted in binary of $i$ as the tensor product sequence of qubit states. In this paper, we present a method converting between the one-hot encoding state and the binary encoding state by taking the Edick state as the transition state, where the Edick state is defined as $\left | \psi_E^{(N)} \right \rangle=\sum_{i=0}^{N-1} \alpha_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle ^{\otimes i}$. Compared with the early work, our circuit achieves the exponential speedup with $O(\log^2 N)$ depth and $O(N)$ size.

For a wide range of nonclassical magnonic states that have been proposed and demonstrated recently, a new time scale besides the magnon lifetime - the magnon dephasing time - becomes important, but this time scale is rarely studied. Considering exchange interaction and spin-phonon coupling, we evaluate the pure magnon dephasing time and find it to be smaller than the magnon lifetime at temperatures of a few Kelvins. By examining a magnonic cat state as an example, we show how pure dephasing of magnons destroys and limits the survival of quantum superpositions. Thus it will be critical to perform quantum operations within the pure dephasing time. We further derive the master equation for the density matrix describing such magnonic quantum states taking into account the role of pure dephasing, whose methodology can be generalized to include additional dephasing channels that experiments are likely to encounter in the future. Our findings enable one to design and manipulate robust quantum states of magnons for information processing.

We analyze theoretically the single-photon excitation and transmission spectra of a strong-coupling hybrid optomechanics, where a two-level system (TLS) is coupled to the mechanical resonator (MR), generating the Jaynes-Cummings-type polariton doublets. In our model, both the optomichanical coupling and the TLS-MR coupling are strong. In this parameter region, the polaron-assisted excitation and reemission processes can strongly affect the single-photon excitation and output spectra of the cavity. We find that the fine structure around each sideband can be used to characterize the TLS-MR and the effective TLS-photon couplings, even at single-quantum level. Thus, the spectrum structures may make it possible to sensitively probe the quantum nature of a macroscopic mechanical element. We further provide a possible approach for tomographic reconstruction of the state of a TLS, utilizing the single-photon transmission spectra.

We studied the effect of delocalized single-photon addition (DPA) on two input modes containing four cases: two independent coherent states (CSs), two independent thermal states (TSs), two independent single-mode squeezed vacuums (SVs), and an entangled two-mode squeezed vacuum (TMSV). In essence, four types of new non-Gaussian entangled light states are generated. We studied three different resources (including entanglement, discorrelation and Wigner negativity) for each two-mode light state. The output states after DPA are entangled, with more parameters and complex structures, characterizing more Wigner negativity or even discorrelation. In contrast, the CSs case is the most tunable protocol, because its negativity under partial transposition, discorrelation, and Wigner logarithmic negativity are more sensitive to superposition phase than those in TSs, SVs and TMSV cases.

Spintronics and quantum information science are two promising candidates for innovating information processing technologies. The combination of these two fields enables us to build solid-state platforms for studying quantum phenomena and for realizing multi-functional quantum tasks. For a long time, however, the intersection of these two fields was limited. This situation has changed significantly over the last few years because of the remarkable progress in coding and processing information using magnons. On the other hand, significant advances in understanding the entanglement of quasi-particles and in designing high-quality qubits and photonic cavities for quantum information processing provide physical platforms to integrate magnons with quantum systems. From these endeavours, the highly interdisciplinary field of quantum magnonics emerges, which combines spintronics, quantum optics and quantum information science.Here, we give an overview of the recent developments concerning the quantum states of magnons and their hybridization with mature quantum platforms. First, we review the basic concepts of magnons and quantum entanglement and discuss the generation and manipulation of quantum states of magnons, such as single-magnon states, squeezed states and quantum many-body states including Bose-Einstein condensation and the resulting spin superfluidity. We discuss how magnonic systems can be integrated and entangled with quantum platforms including cavity photons, superconducting qubits, nitrogen-vacancy centers, and phonons for coherent information transfer and collaborative information processing. The implications of these hybrid quantum systems for non-Hermitian physics and parity-time symmetry are highlighted, together with applications in quantum memories and high-precision measurements. Finally, we present an outlook on the opportunities in quantum magnonics.

In this work, a burst eddy current testing technique based on the employment of a diamond nitrogen vacancy (NV) center magnetometer with the Hahn echo (HE) sequence is demonstrated. With the confocal experiment apparatus, the HE-based NV magnetometer attained a magnetic sensitivity of $4.3 ~ \mathrm{nT} / \sqrt{\mathrm{Hz}}$ and a volume-normalized sensitivity of $3.6 ~ \mathrm{pT} / \sqrt{\mathrm{Hz} \cdot \mathrm{mm}^{-3}}$, which are 5 times better than the already existing method under the same conditions. Based on the proposed magnetometer configuration, a burst eddy current (BEC) testing prototype achieves a minimum detectable sample smaller than ${300~{\mu} \mathrm{m}}$ and measurement accuracy of $9.85~\mathrm{\mu} \mathrm{m}$., which is employed to image different metallic specimens and detect the layered internal structures. Since our prototype comprises superb high sensitivity, it exhibits various potential applications in the fields of deformation monitoring, security screening, and quality control. Moreover, its biocompatibility and promising nanoscale resolution paves the way for electromagnetic testing in the fields of biomaterials.

Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to the external force in a lattice, where the system possessing single- or multipleparticles could exhibit distinct oscillation behaviors. In particular, it has been pointed out that quantum statistics could dramatically affected the Bloch oscillation even in the absence of particle interactions, where the oscillation frequency of two pseudofermions with the anyonic statistical angle being pi becomes half of that for two bosons. However, these statisticdependent Bloch oscillations have never been observed in experiments up to now. Here, we report the first experimental simulation of anyonic Bloch oscillations using electric circuits. By mapping eigenstates of two anyons to modes of designed circuit simulators, the Bloch oscillation of two bosons and two pseudofermions are verified by measuring the voltage dynamics. It is found that the oscillation period in the two-boson simulator is almost twice of that in the two-pseudofermion simulator, which is consistent with the theoretical prediction. Our proposal provides a flexible platform to investigate and visualize many interesting phenomena related to particle statistics, and could have potential applications in the field of the novelty signal control.

The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation. In this paper, we have given the generalized Hamilton principle, which can describe the open system (mass or energy exchange systems) and nonconservative force systems or dissipative systems. On this basis, we have given the generalized Lagrange function, it has to do with the kinetic energy, potential energy and the work of nonconservative forces to do. With the Feynman path integration, we have given the non-Hermitian quantum theory of the nonconservative force systems. Otherwise, we have given the generalized Hamiltonian function for the particle exchanging heat with the outside world, which is the sum of kinetic energy, potential energy and thermal energy, and further given the equation of quantum thermodynamics.

Non-Hermiticity greatly expands existing physical laws beyond the Hermitian framework, revealing various novel phenomena with unique properties. Up to now, most exotic nonHermitian effects, such as exceptional points and non-Hermitian skin effects, are discovered in single-particle systems. The interplay between non-Hermitian and manybody correlation is expected to be a more fascinating but much less explored area. Due to the complexity of the problem, current researches in this field mainly stay at the theoretical level. The experimental observation of predicted non-Hermitian manybody phases is still a great challenging. Here, we report the first experimental simulation of strongly correlated non-Hermitian many-body system, and reveal a new type of nonHermitian many-body skin states toward effective boundaries in Hilbert space. Such an interaction-induced non-Hermitian many-body skin effect represents the aggregation of bosonic clusters with non-identical occupations in the periodic lattice. In particular, by mapping eigen-states of three correlated bosons to modes of the designed threedimensional electric circuit, non-Hermitian many-body skin effects in Hilbert space is verified by measuring the spatial impedance response. Our finding not only discloses a new physical effect in the non-Hermitian many-body system, but also suggests a flexible platform to further investigate other non-Hermitian correlated phases in experiments.

The optical bistability have been studied theoretically in a multi-mode optomechanical system with two mechanical oscillators independently coupled to two cavities in addition to direct tunnel coupling between cavities. It is proved that the bistable behavior of mean intracavity photon number in the right cavity can be tuned by adjusting the strength of the pump laser beam driving the left cavity. And the mean intracavity photon number is relatively larger in the red sideband regime than that in the blue sideband regime. Moreover, we have shown that the double optical bistability of intracavity photon in the right cavity and the two steady-state positions of mechanical resonators can be observed when the control field power is increased to a critical value. Besides, the critical values for observing bistability and double bistability can be tuned by adjusting the coupling coefficient between two cavities and the coupling rates between cavities mode and mechanical mode.

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.

Two dimensional layered van der Waals (vdW) magnets have demonstrated their potential to study both fundamental and applied physics due to their remarkable electronic properties. However, the connection of vdW magnets to spintronics as well as quantum information science is not clear. In particular, it remains elusive whether there are novel magnetic phenomena only belonging to vdW magnets, but absent in the widely studied crystalline magnets. Here we consider the quantum correlations of magnons in a layered vdW magnet and identify an entanglement channel of magnons across the magnetic layers, which can be effectively tuned and even deterministically switched on and off by both magnetic and electric means. This is a unique feature of vdW magnets in which the underlying physics is well understood in terms of the competing roles of exchange and anisotropy fields that contribute to the magnon excitation. Furthermore, we show that such a tunable entanglement channel can mediate the electrically controllable entanglement of two distant qubits, which also provides a protocol to indirectly measure the entanglement of magnons. Our findings provide a novel avenue to electrically manipulate the qubits and further open up new opportunities to utilize vdW magnets for quantum information science.

In conventional quantum mechanics, quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned, respectively. Here, we investigate the quantum deleting and cloning in a pseudo-unitary system. We first present a pseudo-Hermitian Hamiltonian with real eigenvalues in a two-qubit system. By using the pseudo-unitary operators generated from this pseudo-Hermitian Hamiltonian, we show that it is possible to delete and clone a class of two different and nonorthogonal states, and it can be generalized to arbitrary two different and nonorthogonal pure qubit states. Furthermore, state discrimination, which is strongly related to quantum no-cloning theorem, is also discussed. Last but not least, we simulate the pseudo-unitary operators in conventional quantum mechanics with post-selection, and obtain the success probability of simulations. Pseudo-unitary operators are implemented with a limited efficiency due to the post-selections. Thus, the success probabilities of deleting and cloning in the simulation by conventional quantum mechanics are less than unity, which maintain the quantum no-deleting and no-cloning theorems.

The critical quantum metrology, which exploits the quantum phase transition for high precision measurement, has gained increasing attention recently. The critical quantum metrology with the continuous quantum phase transition, however, is experimentally very challenging since the continuous quantum phase transition only exists at the thermal dynamical limit. Here, we propose an adiabatic scheme on a perturbed Ising spin model with the first order quantum phase transition. By employing the Landau-Zener anticrossing, we can not only encode the unknown parameter in the ground state but also tune the energy gap to control the evolution time of the adiabatic passage. We experimentally implement the adiabatic scheme on the nuclear magnetic resonance and show that the achieved precision attains the Heisenberg scaling. The advantages of the scheme-easy implementation, robust against the decay, tunable energy gap-are critical for practical applications of quantum metrology.

This article proposes a scheme for nitrogen-vacancy (NV) center magnetometry that combines the advantages of lock-in detection and pulse-type scheme. The optimal conditions, optimal sensitivity, and noise-suppression capability of the proposed method are compared with those of the conventional methods from both theoretical and simulation points of view. Through experimental measurements, a four-time improvement in sensitivity and 60-times improvement in minimum resolvable magnetic field (MRMF) was obtained. By using a confocal experiment setup, proposed scheme achieves a sensitivity of 3 nT/Hz1/2 and a MRMF of 100 pT.

Diamond nitrogen-vacancy (NV) center magnetometry has recently received considerable interest from researchers in the fields of applied physics and sensors. The purpose of this review is to analyze the principle, sensitivity, technical development potential, and application prospect of the diamond NV center magnetometry. This review briefly introduces the physical characteristics of NV centers, summarizes basic principles of the NV center magnetometer, analyzes the theoretical sensitivity, and discusses the impact of technical noise on the NV center magnetometer. Furthermore, the most critical technologies that affect the performance of the NV center magnetometer are described: diamond sample preparation, microwave manipulation, fluorescence collection, and laser excitation. The theoretical and technical crucial problems, potential solutions and research technical route are discussed. In addition, this review discusses the influence of technical noise under the conventional technical conditions and the actual sensitivity which is determined by the theoretical sensitivity and the technical noise. It is envisaged that the sensitivity that can be achieved through an optimized design is in the order of 10 fT/Hz^1/2. Finally, the roadmap of applications of the diamond NV center magnetometer are presented.

By employing Pauli measurements, we present some nonlinear steering criteria applicable for arbitrary two-qubit quantum systems and optimized ones for symmetric quantum states. These criteria provide sufficient conditions to witness steering, which can recover the previous elegant results for some well-known states. Compared with the existing linear steering criterion and entropic criterion, ours can certify more steerable states without selecting measurement settings or correlation weights, which can also be used to verify entanglement as all steerable quantum states are entangled.

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 ability that one system immediately affects another one by using local measurements is regarded as quantum steering, which can be detected by various steering criteria. Recently, Mondal et al. [Phys. Rev. A 98, 052330 (2018)] derived the complementarity relations of coherence steering criteria, and revealed that the quantum steering of system can be observed through the average coherence of subsystem. Here, we experimentally verify the complementarity relations between quantum steering criteria by employing two-photon Bell-like states and three Pauli operators. The results demonstrate that if prepared quantum states can violate two setting coherence steering criteria and turn out to be steerable states, then it cannot violate the complementary settings criteria. Three measurement settings inequality, which establish a complementarity relation between these two coherence steering criteria, always holds in experiment. Besides, we experimentally certify that the strengths of coherence steering criteria dependent on the choice of coherence measure. In comparison with two setting coherence steering criteria based on l1 norm of coherence and relative entropy of coherence, our experimental results show that the steering criterion based on skew information of coherence is more stronger in detecting the steerability of quantum states. Thus, our experimental demonstrations can deepen the understanding of the relation between the quantum steering and quantum coherence.

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 precise measurement of a magnetic field is one of the most fundamental and important tasks in quantum metrology. Although extensive studies on quantum magnetometry have been carried out over past decades, the ultimate precision that can be achieved for the estimation of all three components of a magnetic field with entangled probe states under the parallel scheme remains unknown. Here we present the ultimate lower bound for the sum of arbitrarily weighted variances in the estimation of all three components of a magnetic field under the parallel scheme and show that this lower bound can be achieved for sufficiently large N. The optimal entangled probe state that achieves the ultimate precision is also explicitly constructed. The obtained precision sets the ultimate limit for the multi-parameter quantum magnetometry under the parallel scheme, which is of fundamental interest and importance in quantum metrology. Our approach also provides a way to characterize the tradeoff among the precisions of multiple parameters that arise from the constraints on the probe states.

The input-output formalism is the basis to study the response of an optical cavity to the external stimulations. The existing theories usually handle cavity systems with only one internal mode. However, there is growing interest in more complex systems, especially the hybrid cavity-matter systems, which contains at least two internal modes, one or more from the optical cavity and the matter, respectively. Here we propose a graphical loop theory to calculate and visualize the reflection and transmission spectrum of such multi-mode cavity, resembling the role of Feynman diagrams in the quantum field theory. This loop theory gives a unified picture to interpret the experimental observations on a hybrid magnet-light system, and is extremely easy to apply to arbitrary complicated problems without any calculations.

Uncertainty relation usually is one of the most important features in quantum mechanics, and is the backbone of quantum theory, which distinguishes from the rule in classical counterpart. Specifically, entropy-based uncertainty relations are of fundamental importance in the region of quantum information theory, offering one nontrivial bound of key rate towards quantum key distribution. In this work, we experimentally demonstrate the entropic uncertainty relations and coherence-based uncertainty relations in an all-optics platform. By means of preparing two kinds of bipartite initial states with high fidelity, i.e., Bell-like states and Bell-like diagonal states, we carry on local projective measurements over a complete set of mutually unbiased bases on the measured subsystem. In terms of quantum tomography, the density matrices of the initial states and the post-measurement states are reconstructed. It shows that our experimental results coincide with the theoretical predictions very well. Additionally, we also verify that the lower bounds of both the entropy-based and coherence-based uncertainty can be tightened by imposing the Holevo quantity and mutual information, and the entropic uncertainty is inversely correlated with the coherence. Our demonstrations might offer an insight into their uncertainty relations and their connection to quantum coherence in quantum information science, which might be applicable to the security analysis of quantum key distributions.

In terms of the characteristic functions of the quantum states, we present a complete operator description of a lossy photon-subtraction scheme. Feeding a single-mode squeezed vacuum into a variable beam splitter and counting the photons in one of the output channels, a broad class of multiphoton-subtracted squeezed vacuum states (MSSVSs) can be generated in other channel. Here the losses are considered in the beginning and the end channels in the circuit. Indeed, this scheme has been discussed in Ref. [Phys. Rev. A 100, 022341 (2019)]. However, different from the above work, we give all the details of the optical fields in all stages. In addition, we present the analytical expressions and numerical simulations for the success probability, the quadrature squeezing effect, photon-number distribution and Wigner function of the MSSVSs. Some interesting results effected by the losses are obtained.

Quantum steering describes the phenomenon that one system can be immediately influenced by another with local measurements. It can be detected by the violation of a powerful and useful steering criterion from general entropic uncertainty relation. This criterion, in principle, can be evaluated straightforwardly and achieved by only probability distributions from a finite set of measurement settings. Herein, we experimentally verify the steering criterion by means of the two-photon Werner-like states and three Pauli measurements. The results indicate that quantum steering can be verified by the criterion in a convenient way. In particular, it is no need to perform the usual quantum state tomography in experiment, which reduces the required experimental resources greatly. Moreover, we demonstrate that the criterion is stronger than the linear one for the detecting quantum steering of the Werner-like states.

This paper focuses on changing Fock matrix elements of two-mode squeezed vacuum state (TMSVS) by employing three quantum operations in one-sided lossy channel. These three quantum operations include one-photon replacement (OPR), one-photon substraction (OPS) and one-photon addition (OPA). Indeed, three conditional quantum states have been generated from the original TMSVS. Using the characteristic function (CF) representation of quantum density operator, we derive the analytical expressions of their Fock matrix elements, which are dependent on the interaction parameters, including the squeezing parameter of the input TMSVS, the loss factor and the transmissivity of the variable beam splitter. For convenience of discussion, we only give the Fock matrices in the subspace span |00>,|01>,|10>,|02>,|11>,|20> for these two-mode states. Obviously, the TMSVS only has the populations in |00> and |11> in such subspace. By comparing the generated states with the TMSVS, we find that: (1) The generated state after OPR will remain the populations in |00> and |11>, and add the populations in |10> and |20>; (2) The generated state after OPS will lost the populations in |00> and |11>, but add the populations in |10> and |20>; (3) The generated state after OPA will remain the population only in |11> and add the population in |01>.

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.