Quantum entanglement and quantum nonlocality for N-photon entangled states

Quantum entanglement and quantum nonlocality of N-photon entangled states ｜ψNm） m Cm [cos γ｜N - m） 1 ｜m）2 ＋ e^iθm sinγ｜m）1｜N- m）2] and their superpositions are studied. We point out that the relative phase θm affects the quantum nonlocality but not the quantum entanglement for the state ｜ψNm）. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of ｜ψNm）, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on ｜ψNm） can increase the amount of entanglement, and give more ways to reach the maximal violation of the Bell inequality.

Quantum nonlocality of generic family of four-qubit entangled pure states

We directly introduce a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states ｜Gabcd〉[Phys. Rev. A 65 052112（2002）] and several canonical four-qubit entangled states. It has been demonstrated that the inequality is maximally violated by the so called ＂four-qubit the maximally entangled state ｜Gm〉＂ and it is also violated by four-qubit W state and a special family of states ｜Gab00〉. Moreover, a useful entanglement-nonlocality relationship for the family of states ｜Gab00〉is derived. Finally, we present a scheme of preparation of the state ｜Gm〉with linear optics and cross-Kerr nonlinearities.

Effects of photon addition on the quantum nonlocality of squeezed entangled coherent states

Effects of photon addition on the quantum nonlocality of squeezed entangled coherent states for Bell-inequality tests are studied theoretically. By utilizing the method of photon-parity measurement, it is found that photon addition can always increase the degrees of Bell violations within a certain parameter range. A possible scheme for generating photon-added squeezed entangled coherent states is proposed.

The quantification of quantum nonlocality by characteristic function

We propose a way to measure the strength of quantum nonlocal correlation (QNC) based on the characteristic function, which is defined as a response function under the local quantum measurement in a composite system. It is found that the strength of QNC based on the characteristic function is a half-positive-definite function and does not change under any LU operation. Generally, we give a new definition for quantum entanglement using the strength function. Furthermore, we also give a separability-criterion for 2×m-dimensional mixed real matrix. This paper proposes an alternative way for QNC further research.

Simultaneous observation of quantum contextuality and quantum nonlocality

Quantum nonlocality and quantum contextuality are the most curious properties that change our understanding of nature, and were observed independently in recent decades. One important question is whether both properties can be observed simultaneously. In this paper, we show that in a qutrit-qutrit system we can observe quantum nonlocality and quantum contextuality at the same time. From the perspective of quantum information, our experiment proves in principle that the two resources, quantum nonlocality and quantum contextuality, can be utilized simultaneously.

Experimental observation of quantum nonlocality in general networks with different topologies

Nonlocal correlation plays an important role in device independent quantum information processing.The stan-dard Bell nonlocality has been well studied with single local hidden variables,however the nonlocal correlations in general networks with several independent quantum sources and distant observers have been far less explored.Here,by using three independent entangled photon sources and recently constructed nonlinear Bell inequalities,we experimentally test the nonlocal correlations in the network scenario with different topologies.The violation of the inequalities can be obtained simply with separate measurements,which is much more favourable from the practical point of view.Our experiment results show a violation as 0.7779±0.0093 for the star network,and 0.7303±0.0024 for the chain network.Furthermore,we demonstrate that more measurement settings for each observer can bound more information against an eavesdropper.

Connecting Quantum Contextuality and Genuine Multipartite Nonlocality with the Quantumness Witness

The Clauser Horne--Shimony-Holt-type noncontextuality inequality and the Svetliehny inequality are derived from the Alicki-van Ryn quantumness witness. Thus connections between quantumness and quantum contextuality, and between quantumness and genuine multipartite nonlocality are established.

Quantum discord dynamics of two qubits in single-mode cavities

The dynamics of quantum discord for two identical qubits in two independent single-mode cavities and a common single-mode cavity are discussed. For the initial Bell state with correlated spins, while the entanglement sudden death can occur, the quantum discord vanishes only at discrete moments in the independent cavities and never vanishes in the common cavity. Interestingly, quantum discord and entanglement show opposite behavior in the common cavity, unlike in the independent cavities. For the initial Bell state with anti-correlated spins, quantum discord and entanglement behave in the same way for both independent cavities and a common cavity. It is found that the detunings always stabilize the quantum discord.

Relativistic motion on Gaussian quantum steering for two-mode localized Gaussian states

Realistic quantum systems always exhibit gravitational and relativistic features.In this paper,we investigate the properties of Gaussian steering and its asymmetry by the localized two-mode Gaussian quantum states,instead of the traditional single-mode approximation method in the relativistic setting.We find that the one-side Gaussian quantum steering will monotonically decrease with increasing observers of acceleration.Meanwhile,our results also reveal the interesting behavior of the Gaussian steering asymmetry,which increases for a specific range of accelerated parameter and then gradually approaches to a finite value.Such finding is well consistent and explained by the well-known Unruh effect,which could significantly destroy the one-side Gaussian quantum steering.Finally,our results could also be applied to the dynamical studies of Gaussian steering between the Earth and satellites,since the effects of acceleration are equal to the effects of gravity according to the equivalence principle.

Steering quantum nonlocalities of quantum dot system suffering from decoherence

The important applications of quantum dot system are to implement logic operations and achieve universal quantum computing based on different quantum nonlocalities.Here,we characterize the quantum steering,Bell nonlocality,and nonlocal advantage of quantum coherence(NAQC)of quantum dot system suffering nonunital and unital channels.The results reveal that quantum steering,Bell nonlocality,and NAQC can display the traits of dissipation,enhancement,and freezing.One can achieve the detections of quantum steering,Bell nonlocality,and NAQC of quantum dot system in different situations.Among these quantum nonlocalities,NAQC is the most fragile,and it is most easily influenced by different system parameters.Furthermore,considering quantum dot system coupling with amplitude damping channel and phase damping channel,these quantum nonlocalities degenerate with the enlargement of the channel parameters t andΓ.Remarkably,measurement reversal can effectively control and enhance quantum steering,Bell nonlocality,and NAQC of quantum dot system suffering from decoherence,especially in the scenarios of the amplitude damping channel and strong operation strength.

Distributed quantum information processing via quantum dot spins

We propose a scheme to engineer a non-local two-qubit phase gate between two remote quantum-dot spins. Along with one-qubit local operations, one can in principal perform various types of distributed quantum information processing. The scheme employs a photon with linearly polarisation interacting one after the other with two remote quantum-dot spins in cavities. Due to the optical spin selection rule, the photon obtains a Faraday rotation after the interaction process. By measuring the polarisation of the final output photon, a non-local two-qubit phase gate between the two remote quantum-dot spins is constituted. Our scheme may has very important applications in the distributed quantum information processing.

Direct measurement of nonlocal quantum states without approximation

Efficient acquiring information from a quantum state is important for research in fundamental quantum physics and quantum information applications. Instead of using standard quantum state tomography method with reconstruction algorithm, weak values were proposed to directly measure density matrix elements of quantum state. Recently, similar to the concept of weak value, modular values were introduced to extend the direct measurement scheme to nonlocal quantum wavefunction. However, this method still involves approximations, which leads to inherent low precision. Here, we propose a new scheme which enables direct measurement for ideal value of the nonlocal density matrix element without taking approximations. Our scheme allows more accurate characterization of nonlocal quantum states, and therefore has greater advantages in practical measurement scenarios.

Remote interactions between two d-dimensional distributed quantum systems： nonlocal generalized quantum control-NOT gate and entanglement swapping

We present a systematic simple method to implement a generalized quantum control-NOT （CNOT） gate on two d-dimensional distributed systems. First, we show how the nonlocal generalized quantum CNOT gate can be implemented with unity fidelity and unity probability by using a maximally entangled pair of qudits as a quantum channel. We also put forward a scheme for probabilistically implementing the nonlocal operation with unity fidelity by employing a partially entangled qudit pair as a quantum channel. Analysis of the scheme indicates that the use of partially entangled quantum channel for implementing the nonlocal generalized quantum CNOT gate leads to the problem of ＇the general optimal information extraction＇. We also point out that the nonlocal generalized quantum CNOT gate can be used in the entanglement swapping between particles belonging to distant users in a communication network and distributed quantum computer.

Demonstration of controlled high-dimensional quantum teleportation

Controlled quantum teleportation(CQT), which is regarded as the prelude and backbone for a genuine quantum internet, reveals the cooperation, supervision, and control relationship among the sender, receiver, and controller in the quantum network within the simplest unit. Compared with low-dimensional counterparts, high-dimensional CQT can exhibit larger information transmission capacity and higher superiority of the controller's authority. In this article, we report a proof-of-principle experimental realization of three-dimensional(3D) CQT with a fidelity of 97.4% ± 0.2%. To reduce the complexity of the circuit, we simulate a standard 4-qutrit CQT protocol in a 9×9-dimensional two-photon system with high-quality operations. The corresponding control powers are 48.1% ± 0.2% for teleporting a qutrit and 52.8% ± 0.3% for teleporting a qubit in the experiment, which are both higher than the theoretical value of control power in 2-dimensional CQT protocol(33%). The results fully demonstrate the advantages of high-dimensional multi-partite entangled networks and provide new avenues for constructing complex quantum networks.

Enhanced electron–positron pair production by frequency chirping in one-and two-color laser pulse fields

Enhanced electron–positron pair production by frequency chirping in one- and two-color laser pulse fields is investigated by solving the quantum Vlasov equation. A small frequency chirp shifts the momentum spectrum along the momentum axis. The positive and negative frequency chirp parameters play the same role in increasing the pair number density. The sign change of the frequency chirp parameter at the moment t = 0 leads the pulse shape and momentum spectrum to be symmetric, and the number density to be increased. The number density of produced pairs in the two-color pulse field is much higher than that in the one-color pulse field and the larger frequency chirp pulse field dominates more strongly. In the two-color pulse fields, the relation between the frequency ratio of two colors and the number density is not sensitive to the parameters of small frequency chirp added in either a low frequency strong field or a high frequency weak field but sensitive to the parameters of large frequency chirp added in a high frequency weak field.

Enhanced electron positron pair creation by the frequency chirped laser pulse

Based on the quantum Vlasov equation, the effect of frequency chirp on electron-positron pair production is investigated. The cycle parameter, which characterizes the laser field cycle degree within the pulse, is also considered. In both supercycle and subcycle laser pulses the frequency chirp can greatly enhance the momentum distribution function of created pairs and the pair number density. The pair number density created by a supercycle laser pulse is larger than that by a subcycle pulse under the same laser frequency and chirping. There exists an optimal cycle parameter corresponding to the maximum value of the created pair number density for different chirp rates. It is found that the pair number density is sensitive/insensitive to chirping rate when the cycle parameter lies below/above the optimal one.

Entanglement and nonlocality in multi-particle systems

Entanglement, the Einstein-Podolsky Rosen （EPR） paradox and Bell＇s failure of local-hidden- variable （LHV） theories are three historically famous forms of ＂quantum nonlocality＂. We give experimental criteria for these three forms of nonlocality in multi-particle systems, with the aim of better understanding the transition from microscopic to macroscopic nonlocality. We examine the nonlocality of N separated spin J systems. First, we obtain multipartite Bell inequalities that address the correlation between spin values measured at each site, and then we review spin squeezing inequal- ities that address the degree of reduction in the variance of collective spins. The latter have been particularly useful as a tool for investigating entanglement in Bose Einstein eondensates （BEC）. We present solutions for two topical quantum states： multi-qubit Greenberger-Horne Zeilinger （GHZ） states, and the ground state of a two-well BEC.

Device-independent characterization of entanglement based on bell nonlocality

Quantum entanglement,has been acknowledged as a precious resource due to its inherent nonclassical correla-tions between subsystems.These quantum correlations have the potential for many quantum processes,includ-ing canonical ones:quantum cryptography,quantum teleportation,and dense coding.To exploit the advantages of quantum entanglement,two essential premises are required,i.e.,to prepare high-quality entanglement and characterize quality level of prepared entanglement.Thus far,quantum entanglement can be produced in various quantum systems;however,it appears that this new resource is complex and difficult to characterize.The standard methods to characterize multipartite entanglement,e.g.,entanglement witness,state tomography,or quantum state verification,require full knowledge of the Hilbert space dimension and precise calibration of measurement devices,which are usually difficult to acquire in experiment.The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the exper-iment,namely,device-independent characterization of entanglement.This article reviews the recently developed device-independent methods to characterize entanglement,including self-testing and device-independent certi-fication of entanglement.These approaches can be widely applied in kinds of quantum information processing,especially for those with security demands.

A nonlocal quantum simulator and simulation of superluminality

With the support by the National Natural Science Foundation of China and the Chinese Academy of Sciences(CAS),the research team led by Prof.Li Chuanfeng(李传锋)at the CAS Key Lab of Quantum Information,University of Science and Technology of China,developed a nonlocal quantum simulator and simulated the superluminality phenomenon in parity-time(PT)world.This study for the first time exhib-

Experimentally testing Bell's theorem based on Hardy's nonlocal ladder proofs

Bell＇s theorem argues the existence of quantum nonlocality which goes basically against the hidden variable theory （HVT）. Many experiments have been done via testing the violations of Bell＇s inequalities to statistically verify the Bell＇s theorem. Alternatively, by testing the Hardy＇s ladder proofs we experimentally demonstrate the deterministic violation of HVT and thus confirm the quantum nonlocality. Our tests are implemented with non-maximal entangled photon pairs generated by spontaneous parametric down conversions （SPDCs）. We show that the degree freedom of photon entanglement could be significantly enhanced by using interference filters. As a consequence, the Hardy＇s ladder proofs could be tested and Bell＇s theorem is verified robustly. The probability of violating the locality reach to 41.9%, which is close to the expectably ideal value 46.4% for the photon pairs with degree of entanglement e = 0.93. The higher violating probability is possible by further optimizing the experimental parameters.