Continuous-Variable Quantum Network Coding Based on Quantum Discord

Establishing entanglement is an essential task of quantum communication technology.Beyond entanglement,quantum discord,as a measure of quantum correlation,is a necessary prerequisite to the success of entanglement distribution.To realize efficient quantum communication based on quantum discord,in this paper,we consider the practical advantages of continuous variables and propose a feasible continuous-variable quantum network coding scheme based on quantum discord.By means of entanglement distribution by separable states,it can achieve quantum entanglement distribution from sources to targets in a butterfly network.Compared with the representative discrete-variable quantum network coding schemes,the proposed continuous-variable quantum network coding scheme has a higher probability of entanglement distribution and defends against eavesdropping and forgery attacks.Particularly,the deduced relationship indicates that the increase in entanglement is less than or equal to quantum discord.

A Practical Quantum Network Coding Protocol Based on Non-Maximally Entangled State

In many earlier works,perfect quantum state transmission over the butterfly network can be achieved via quantum network coding protocols with the assist of maximally entangled states.However,in actual quantum networks,a maximally entangled state as auxiliary resource is hard to be obtained or easily turned into a non-maximally entangled state subject to all kinds of environmental noises.Therefore,we propose a more practical quantum network coding scheme with the assist of non-maximally entangled states.In this paper,a practical quantum network coding protocol over grail network is proposed,in which the non-maximally entangled resource is assisted and even the desired quantum state can be perfectly transmitted.The achievable rate region,security and practicability of the proposed protocol are discussed and analyzed.This practical quantum network coding protocol proposed over the grail network can be regarded as a useful attempt to help move the theory of quantum network coding towards practicability.

A quantum network for implementation of the optimal quantum cloning

This paper presents a quantum network to implement the optimal 1→2 quantum cloning in 2 dimensions, including the optimal asymmetric universal, the optimal symmetric phase-covariant, and the asymmetric real state cloning. By only choosing different angles of the single-qubit rotations, the quantum network can implement three optimal quantum cloning.

An Alternative Scheme for Transferring Quantum States and Preparing a Quantum Network in Cavity QED

An alternative scheme is proposed to transfer quantum states and prepare a quantum network in cavity QED. It is based on the interaction of a two-mode cavity field with a three-level V-type atom. In the scheme, the atom-cavity field interaction is resonant, thus the time required to complete the quantum state transfer process is greatly shortened, which is very important in view of decoherence. Moreover, the present scheme does not require one mode of the cavities to be initially prepared in one-photon state, thus it is more experimentally feasible than the previous ones.

Controlled Quantum Network Coding Without Loss of Information

Quantum network coding is used to solve the congestion problem in quantum communication,which will promote the transmission efficiency of quantum information and the total throughput of quantum network.We propose a novel controlled quantum network coding without information loss.The effective transmission of quantum states on the butterfly network requires the consent form a third-party controller Charlie.Firstly,two pairs of threeparticle non-maximum entangled states are pre-shared between senders and controller.By adding auxiliary particles and local operations,the senders can predict whether a certain quantum state can be successfully transmitted within the butterfly network based on the Z-{10>,|1>}basis.Secondly,when trans-mission fails upon prediction,the quantum state will not be lost,and it will sill be held by the sender.Subsequently,the controller Charlie re-prepares another three-particle non-maximum entangled state to start a new round.When the predicted transmission is successful,the quantum state can be transmitted successfully within the butterfly network.If the receiver wants to receive the effective quantum state,the quantum measurements from Charlie are needed.Thirdly,when the transmission fails,Charlie does not need to integrate the X-{1+>,1->}basis to measure its own particles,by which quantum resources are saved.Charlie not only controls the effective transmission of quantum states,but also the usage of classical and quantum channels.Finally,the implementation of the quantum circuits,as well as a flow chart and safety analysis of our scheme,is proposed.

Anti-Noise Quantum Network Coding Protocol Based on Bell States and Butterfly Network Model

How to establish a secure and efficient quantum network coding algorithm isone of important research topics of quantum secure communications. Based on thebutterfly network model and the characteristics of easy preparation of Bell states, a novelanti-noise quantum network coding protocol is proposed in this paper. The new protocolencodes and transmits classical information by virtue of Bell states. It can guarantee thetransparency of the intermediate nodes during information, so that the eavesdropper Evedisables to get any information even if he intercepts the transmitted quantum states. Inview of the inevitability of quantum noise in quantum channel used, this paper analyzesthe influence of four kinds of noises on the new protocol in detail further, and verifies theefficiency of the protocol under different noise by mathematical calculation and analysis.In addition, based on the detailed mathematical analysis, the protocol has functioned wellnot only on improving the efficiency of information transmission, throughput and linkutilization in the quantum network, but also on enhancing reliability and antieavesdroppingattacks.

Characterization of the pairwise correlations in different quantum networks consisting of four-wave mixers and beamsplitters

We investigate the performances of the pairwise correlations（PCs） in different quantum networks consisting of fourwave mixers（FWMs） and beamsplitters（BSs）. PCs with quantum correlation in different quantum networks can be verified by calculating the degree of relative intensity squeezing for any pair of all the output fields. More interestingly, the quantum correlation recovery and enhancement are present in the FWM＋BS network and the repulsion effect phenomena（signal（idler）-frequency mode cannot be quantum correlated with the other two idler（signal）-frequency modes simultaneously）between the PCs with quantum correlation are predicted in the FWM ＋ FWM and FWM ＋ FWM ＋ FWM networks. Our results presented here pave the way for the manipulation of the quantum correlation in quantum networks.

A full quantum network scheme

We present a full quantum network scheme using a modified BB84 protocol. Unlike other quantum network schemes, it allows quantum keys to be distributed between two arbitrary users with the help of an intermediary detecting user. Moreover, it has good expansibility and prevents all potential attacks using loopholes in a detector, so it is more practical to apply. Because the fiber birefringence effects are automatically compensated, the scheme is distinctly stable in principle and in experiment. The simple components for every user make our scheme easier for many applications. The experimental results demonstrate the stability and feasibility of this scheme.

Criterion of Quantum Entanglement and the Covariance Correlation Tensor in the Theory of Quantum Network

This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.

Separability of Pure States and Mixed States of the Quantum Network of Two Nodes

This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum network theory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor is equal to zero for all possible and .

Transferring Multi-Dimensional Quantum States and Preparing Quantum Networks in Cavity QED

In this paper we propose a scheme for transferring quantum states and preparing quantum networks. Compared with the previous schemes, this scheme is more efficient, since three or four-dimensional quantum states can be transferred with a single step and information interchange of three-dimensional quantum states can be realized, which is a significant improvement. It is based on the resonant interaction of a three-mode cavity field with an atom. As a consequence, the interaction time is shortened greatly. Furthermore, we give some discussions about the feasibility of the scheme.

Quantum Remote State Preparation Based on Quantum Network Coding

As an innovative theory and technology,quantum network coding has become the research hotspot in quantum network communications.In this paper,a quantum remote state preparation scheme based on quantum network coding is proposed.Comparing with the general quantum remote state preparation schemes,our proposed scheme brings an arbitrary unknown quantum state finally prepared remotely through the quantum network,by designing the appropriate encoding and decoding steps for quantum network coding.What is worth mentioning,from the network model,this scheme is built on the quantum k-pair network which is the expansion of the typical bottleneck network—butterfly network.Accordingly,it can be treated as an efficient quantum network preparation scheme due to the characteristics of network coding,and it also makes the proposed scheme more applicable to the large-scale quantum networks.In addition,the fact of an arbitrary unknown quantum state remotely prepared means that the senders do not need to know the desired quantum state.Thus,the security of the proposed scheme is higher.Moreover,this scheme can always achieve the success probability of 1 and 1-max flow of value k.Thus,the communication efficiency of the proposed scheme is higher.Therefore,the proposed scheme turns out to be practicable,secure and efficient,which helps to effectively enrich the theory of quantum remote state preparation.

Effect of the Spin-Orbit Interaction (Heisenberg XYZ Model) on Partial Entangled Quantum Network

Dzyaloshiniskii-Moriya (DM) interaction in three directions (Dx, Dy and Dz) is used to generate entangled network from partially entangled states in the presence of the spin-orbit coupling. The effect of the spin coupling on the entanglement between any two nodes of the network is investigated. The entanglement is quantified using Woottores concurrence method. It is shown that the entanglement decays as the coupling increases. For larger values of the spin coupling, the entanglement oscillates within finite bounds. For the initially entangled channels, the upper bound does not exceed its initial value, whereas the entanglement reaches its maximum value for the channels generated via indirect interaction.

Quantum Secret Broadcast for Wireless Quantum Networks

In wireless quantum networks, nodes communicate by means of pre-distribution for entangled pairs and relay path establishment for quantum teleportation. However, simple point-to-point communication seriously restricts the efficiency of quantum communication. Inspired by sharing idea of quantum secret sharing (QSS), which is based on three collaborative nodes with pre-shared GHZ (Greenberger-Horne-Zeilinger) states, we propose a quantum secret broadcast scheme to improve network performance. In a cluster net-work cored on three parties of QSS, three cluster heads with pre-shared GHZ states are senders, while cluster members are receivers. One cluster head encodes secret messages on auxiliary particles by performing certain operations on them with GHZ particles, then three cluster heads measure their own par-ticles and broadcast measurement results honestly. Based on the specific correlation of measurement results and secret messages, all receivers can re-cover the secret messages. Furthermore, to prevent eavesdropping, cluster heads can update an encoding key periodically. Analysis shows the proposed scheme is more efficient than previous schemes in wireless quantum net-works, especially when the number of receivers is larger. Besides, in the proposed scheme, attacks on quantum channel based on GHZ state can be detected, and eavesdroppers cannot recover messages correctly for lack of suitable decoding key.

Quantum correlations in a chain-type quantum network

A quantum network concerns several independent entangled resources and can create strong quantum correlations by performing joint measurements on some observers.In this paper,we discuss an n-partite chain network with each of two neighboring observers sharing an arbitrary Bell state and all intermediate observers performing some positive-operator-valued measurements with parameterλ.The expressions of all post-measurement states between any two observers are obtained,and their quantifications of Bell nonlocality,Einstein-Podolsky-Rosen steering and entanglement with different ranges ofλare respectively detected and analyzed.

Verification of quantum networks using the GHZ paradox

The Greenberger–Horne–Zeilinger(GHZ)paradox shows that it is possible to create a multipartite state involving three or more particles in which the measurement outcomes of the particles are correlated in a way that cannot be explained by classical physics.We extend it to witness quantum networks.We first extend the GHZ paradox to simultaneously verify the GHZ state and Einstein–Podolsky–Rosen states on triangle networks.We then extend the GHZ paradox to witness the entanglement of chain networks consisting of multiple GHZ states.All the present results are robust against the noise.

HQNN-SFOP:Hybrid Quantum Neural Networks with Signal Feature Overlay Projection for Drone Detection Using Radar Return Signals-A Simulation

With the wide application of drone technology,there is an increasing demand for the detection of radar return signals from drones.Existing detection methods mainly rely on time-frequency domain feature extraction and classical machine learning algorithms for image recognition.This method suffers from the problem of large dimensionality of image features,which leads to large input data size and noise affecting learning.Therefore,this paper proposes to extract signal time-domain statistical features for radar return signals from drones and reduce the feature dimension from 512×4 to 16 dimensions.However,the downscaled feature data makes the accuracy of traditional machine learning algorithms decrease,so we propose a new hybrid quantum neural network with signal feature overlay projection(HQNN-SFOP),which reduces the dimensionality of the signal by extracting the statistical features in the time domain of the signal,introduces the signal feature overlay projection to enhance the expression ability of quantum computation on the signal features,and introduces the quantum circuits to improve the neural network’s ability to obtain the inline relationship of features,thus improving the accuracy and migration generalization ability of drone detection.In order to validate the effectiveness of the proposed method,we experimented with the method using the MM model that combines the real parameters of five commercial drones and random drones parameters to generate data to simulate a realistic environment.The results show that the method based on statistical features in the time domain of the signal is able to extract features at smaller scales and obtain higher accuracy on a dataset with an SNR of 10 dB.On the time-domain feature data set,HQNNSFOP obtains the highest accuracy compared to other conventional methods.In addition,HQNN-SFOP has good migration generalization ability on five commercial drones and random drones data at different SNR conditions.Our method verifies the feasibility and effectiveness of signal detection methods based on quantum computation and experimentally demonstrates that the advantages of quantum computation for information processing are still valid in the field of signal processing,it provides a highly efficient method for the drone detection using radar return signals.

Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism

Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NISQ)computing.In this paper,we use the bit-flip averaging(BFA)method to mitigate frequent readout errors in quantum generative adversarial networks(QGAN)for image generation,which simplifies the response matrix structure by averaging the qubits for each random bit-flip in advance,successfully solving problems with high cost of measurement for traditional error mitigation methods.Our experiments were simulated in Qiskit using the handwritten digit image recognition dataset under the BFA-based method,the Kullback-Leibler(KL)divergence of the generated images converges to 0.04,0.05,and 0.1 for readout error probabilities of p=0.01,p=0.05,and p=0.1,respectively.Additionally,by evaluating the fidelity of the quantum states representing the images,we observe average fidelity values of 0.97,0.96,and 0.95 for the three readout error probabilities,respectively.These results demonstrate the robustness of the model in mitigating readout errors and provide a highly fault tolerant mechanism for image generation models.

Design of a novel hybrid quantum deep neural network in INEQR images classification

We redesign the parameterized quantum circuit in the quantum deep neural network, construct a three-layer structure as the hidden layer, and then use classical optimization algorithms to train the parameterized quantum circuit, thereby propose a novel hybrid quantum deep neural network(HQDNN) used for image classification. After bilinear interpolation reduces the original image to a suitable size, an improved novel enhanced quantum representation(INEQR) is used to encode it into quantum states as the input of the HQDNN. Multi-layer parameterized quantum circuits are used as the main structure to implement feature extraction and classification. The output results of parameterized quantum circuits are converted into classical data through quantum measurements and then optimized on a classical computer. To verify the performance of the HQDNN, we conduct binary classification and three classification experiments on the MNIST(Modified National Institute of Standards and Technology) data set. In the first binary classification, the accuracy of 0 and 4 exceeds98%. Then we compare the performance of three classification with other algorithms, the results on two datasets show that the classification accuracy is higher than that of quantum deep neural network and general quantum convolutional neural network.

Deep learning framework for time series classification based on multiple imaging and hybrid quantum neural networks

Time series classification(TSC)has attracted a lot of attention for time series data mining tasks and has been applied in various fields.With the success of deep learning(DL)in computer vision recognition,people are starting to use deep learning to tackle TSC tasks.Quantum neural networks(QNN)have recently demonstrated their superiority over traditional machine learning in methods such as image processing and natural language processing,but research using quantum neural networks to handle TSC tasks has not received enough attention.Therefore,we proposed a learning framework based on multiple imaging and hybrid QNN(MIHQNN)for TSC tasks.We investigate the possibility of converting 1D time series to 2D images and classifying the converted images using hybrid QNN.We explored the differences between MIHQNN based on single time series imaging and MIHQNN based on the fusion of multiple time series imaging.Four quantum circuits were also selected and designed to study the impact of quantum circuits on TSC tasks.We tested our method on several standard datasets and achieved significant results compared to several current TSC methods,demonstrating the effectiveness of MIHQNN.This research highlights the potential of applying quantum computing to TSC and provides the theoretical and experimental background for future research.