Improvement and security analysis of multi-ring discrete modulation continuous variable quantum secret sharing scheme

In order to avoid the complexity of Gaussian modulation and the problem that the traditional point-to-point communication DM-CVQKD protocol cannot meet the demand for multi-user key sharing at the same time, we propose a multi-ring discrete modulation continuous variable quantum key sharing scheme(MR-DM-CVQSS). In this paper, we primarily compare single-ring and multi-ring M-symbol amplitude and phase-shift keying modulations. We analyze their asymptotic key rates against collective attacks and consider the security key rates under finite-size effects. Leveraging the characteristics of discrete modulation, we improve the quantum secret sharing scheme. Non-dealer participants only require simple phase shifters to complete quantum secret sharing. We also provide the general design of the MR-DM-CVQSS protocol.We conduct a comprehensive analysis of the improved protocol's performance, confirming that the enhancement through multi-ring M-PSK allows for longer-distance quantum key distribution. Additionally, it reduces the deployment complexity of the system, thereby increasing the practical value.

Quantum computation and error correction based on continuous variable cluster states

Measurement-based quantum computation with continuous variables,which realizes computation by performing measurement and feedforward of measurement results on a large scale Gaussian cluster state,provides a feasible way to implement quantum computation.Quantum error correction is an essential procedure to protect quantum information in quantum computation and quantum communication.In this review,we briefly introduce the progress of measurement-based quantum computation and quantum error correction with continuous variables based on Gaussian cluster states.We also discuss the challenges in the fault-tolerant measurement-based quantum computation with continuous variables.

Continuous variable quantum key distribution

Quantum key distribution enables unconditionally secure key distribution between two legitimate users.The information-theoretic security is guaranteed by the fundamental laws of quantum physics.Initially,the quantum key distribution protocol was proposed based on the qubits.Later on,it was found that quantum continuous variables can also be exploited for this target.The continuous variable quantum key distribution can build upon standard telecommunication technology and exhibits a higher secret key rate per pulse at a relatively short distance due to the possibility of encoding more than 1 bit per pulse.In this article,we review the current status of the continuous variable quantum key distribution research,including its basic principle,experimental implementations,security and future directions;the experimental progress in this field made by our group is also presented.

Effect of excess noise on continuous variable entanglement sudden death and Gaussian quantum discord

A symmetric two-mode Gaussian entangled state is used to investigate the effect of excess noise on entanglement sudden death and Gaussian quantum discord with continuous variables. The results show that the excess noise in the channel can lead to entanglement sudden death of a symmetric two-mode Gaussian entangled state, while Gaussian quantum discord never vanishes. As a practical application, the security of a quantum key distribution （QKD） scheme based on a symmetric two-mode Gaussian entangled state against collective Gaussian attacks is analyzed. The calculation results show that the secret key cannot be distilled when entanglement vanishes and only quantum discord exists in such a QKD scheme.

Application of Bipartite and Tripartite Entangled State Representations in Quantum Teleportation of Continuous Variables

We mostly investigate two schemes. One is to teleport a multi-mode W-type entangled coherent state using a peculiar bipartite entangled state as the quantum channel different from other proposals. Based on our formalism,teleporting multi-mode coherent state or squeezed state is also possible. Another is that the tripartite entangled state is used as the quantum channel of controlled teleportation of an arbitrary and unknown continuous variable in the case of three participators.

Teleportation of a Kind of Three-Mode Entangled States of Continuous Variables

A quantum teleportation scheme to teleport a kind of tripartite entangled states of continuous variables by using a quantum channel composed of three bipartite entangled states is proposed. The joint Bell measurement is feasible because the bipartite entangled states are complete and the squeezed state has a natural representation in the entangled state basis. The calculation is greatly simplified by using the Schmidt decomposition of the entangled states.

Implementing Classical Hadamard Transform Algorithm by Continuous Variable Cluster State

Measurement-based one-way quantum computation, which uses cluster states as resources, provides an efficient model to perforrn computation. However, few of the continuous variable （CV） quantum algorithms and classical algorithms based on one-way quantum computation were proposed. In this work, we propose a method to implement the classical Hadamard transform algorithm utilizing the CV cluster state. Compared with classical computation, only half operations are required when it is operated in the one-way CV quantum computer. As an example, we present a concrete scheme of four-mode classical Hadamard transform algorithm with a four-partite CV cluster state. This method connects the quantum computer and the classical algorithms, which shows the feasibility of running classical algorithms in a quantum computer efficiently.

Deterministic Quantum Secure Direct Communication with Dense Coding and Continuous Variable Operations

We propose a deterministic quantum secure direct two check photon sequences are used to check the securities of the communication protocol by using dense coding. The channels between the message sender and the receiver. The continuous variable operations instead of the usual discrete unitary operations are performed on the travel photons so that the security of the present protocol can be enhanced. Therefore some specific attacks such as denial-of-service attack, intercept-measure-resend attack and invisible photon attack can be prevented in ideal quantum channel. In addition, the scheme is still secure in noise channel. Furthurmore, this protocol has the advantage of high capacity and can be realized in the experiment.

Controlled Entanglement Swapping for Continuous Variables

We propose a scheme for controlled entanglement swapping of continuous variable, where an EPR pair shared by two parties （Alice and Debbie） and a GHZ entangled state shared by three parties （Alice, Bob and Claire） are required. One optical beams of the EPR state will be entangled with the output mode displaced by Bob with the help of Claire. It is shown that the entanglement swapping can occur controlled by the third party （Claire）

Continuous variable entanglement generation in coupled cavities

We investigate continuous variable entanglement produced in two distant coupled cavities, in which two four-level atoms are driven by classical fields respectively. Under the large detuning condition, an effective Hamiltonian containing the square of the creation （annihilation） operator of the cavity field is derived. Due to the nonlinearity, entanglement formally created by the beam splitter type interaction is transformed into the nondegenerate parametric down conversion type. Employing the operator algebraic method, we study the time evolution of the entanglement condition, and show that the system provides us an advantage in achieving a larger photon number with better entanglement. We also discuss the dissipation of the cavities affecting the entanglement.

Analysis of atmospheric effects on the continuous variable quantum key distribution

Atmospheric effects have significant influence on the performance of a free-space optical continuous variable quantum key distribution(CVQKD)system.In this paper,we investigate how the transmittance,excess noise and interruption probability caused by atmospheric effects affect the secret-key rate(SKR)of the CVQKD.Three signal wavelengths,two weather conditions,two detection schemes,and two types of attacks are considered in our investigation.An expression aims at calculating the interruption probability is proposed based on the Kolmogorov spectrum model.The results show that a signal using long working wavelength can propagate much further than that of using short wavelength.Moreover,as the wavelength increases,the influence of interruption probability on the SKR becomes more significant,especially within a certain transmission distance.Therefore,interruption probability must be considered for CVQKD by using long-signal wavelengths.Furthermore,different detection schemes used by the receiver will result in different transmission distances when subjected to individual attacks and collective attacks,respectively.

Proposed Entanglement Swapping in Continuous Variable Systems via Braiding

We study entanglement swapping in continuous variable systems by using braiding transformations.It isfound that entanglement swapping in two-mode squeezed vacuum states and squeezed coherent states can be realizedbased on the braiding operators.

Entanglement swapping of continuous variable using squeezed vacuum states

We present a realistic scheme for the entanglement swapping of continuous variable, in which a two-mode squeezed vacuum state serves as a quantum channel. The position sum and momentum difference of two local modes are measured. By taking the input entangled state also as a two-mode squeezed vacuum state, we investigate the average fidelity and the yon Neumann entropy of the output state. The results show that the perfect teleportation can be achieved by increasing the squeezing of the quantum channel and that any nonzero squeezing in both the quantum channel and the input entangled state is sufficient to swap the entanglement.

Oscillation of Nonlinear Partial Difference Equations with Continuous Variables

This paper is concerned with the oscillation of nonlinear partial difference equations with continuous variables and the corresponding dual equations. Several sufficientconditions are obtained for the oscillation of these equations.

THE CONSTRUCTION METHOD OF STABILIZER CODES FOR CONTINUOUS VARIABLES

The paper analyzes the basic principles of stabilizer codes, focusing on how to construct stabilizer codes for achieving the continuous-variable quantum error correction. Stabilizer codes can be used in the reconciliation of continuous-variable quantum key distribution system. The construction method of stabilizer codes is very important and it can be turned into finding the check matrix for stabilizer codes. In this paper, a new algorithm called region elimination algorithm for finding the check matrix of stabilizer codes was presented which can seek the voluntary check matrix for continu-ous-variable stabilizer codes within 8 bit code length quickly and effectively, and it was simulated by Visual C++. The algorithm is mainly realized by initializing search region, reducing the search region and then keeping searching till finding all the commuting generators. The finding of check matrix of stabilizer codes lays important foundations for the further development of stabilizer codes in the con-tinuous-variable quantum key distribution.

Continuous Variable Quantum Teleportation in Beam-Wandering Modeled Atmosphere Channel

We investigate the continuous variable quomtum teleportation in atmosphere channels. The beam-wandering mode/is employed to analyze the teleportation of the unknown single-mode coherent state. Two methods, one is deterministic by increasing the aperture size of the detecting device and one is probabilistic by entanglement distillation, are proposed to improve the teleportation fidelity in the presence of atmosphere noises.

Continuous Variable Quantum MNIST Classifiers—Classical-Quantum Hybrid Quantum Neural Networks

In this paper, classical and continuous variable (CV) quantum neural network hybrid multi-classifiers are presented using the MNIST dataset. Currently available classifiers can classify only up to two classes. The proposed architecture allows networks to classify classes up to nm classes, where n represents cutoff dimension and m the number of qumodes on photonic quantum computers. The combination of cutoff dimension and probability measurement method in the CV model allows a quantum circuit to produce output vectors of size nm. They are then interpreted as one-hot encoded labels, padded with nm - 10 zeros. The total of seven different classifiers is built using 2, 3, …, 6, and 8-qumodes on photonic quantum computing simulators, based on the binary classifier architecture proposed in “Continuous variable quantum neural networks” [1]. They are composed of a classical feed-forward neural network, a quantum data encoding circuit, and a CV quantum neural network circuit. On a truncated MNIST dataset of 600 samples, a 4-qumode hybrid classifier achieves 100% training accuracy.

Combined-Type Continuous Variable Transmission with Quadric Crank Chains and One-Way Clutches

The conventional Continuously Variable Transmission （CVT） has been classified as belt-type or toroidal CVTs. Each CVT is fundamentally composed of several components to transmit the frictional force or torque generated by the driving force. Since the conventional CVTs use friction force, their energy （force or torque） transfer efficiency might be inferior due to slippage and pressure between the transmission components. Consequently, we propose a new type of structural CVT. The CVT we proposed in this paper means a combined-type transmission with quadric crank chains and one-way clutches.

Non-adiabatic holonomic quantum operations in continuous variable systems

Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to their potential robustness.When a system in a non-degenerate eigenstate undergoes an adiabatically cyclic evolution dominated by its Hamiltonian,it will get a geometric phase,referred to as the Berry Phase.While a non-adiabatically cyclic evolution produces an Aharonov-Anandan geometric phase.The two types of Abelian geometric phases are extended to the non-Abelian cases,where the phase factors become matrix-valued and the transformations associated with different loops are non-commutable.Abelian and non-Abelian(holonomic)operations are prevalent in discrete variable systems,whose limited(say,two)energy levels,form the qubit.While their developments in continuous systems have also been investigated,mainly due to that,bosonic modes(in,such as,cat states)with large Hilbert spaces,provide potential advantages in fault-tolerant quantum computation.Here we propose a feasible scheme to realize non-adiabatic holonomic quantum logic operations in continuous variable systems with cat codes.We construct arbitrary single-qubit(two-qubit)gates with the combination of single-and two-photon drivings applied to a Kerr Parametric Oscillator(KPO)(the coupled KPOs).Our scheme relaxes the requirements of the previously proposed quantum geometric operation strategies in continuous variable systems,providing an effective way for quantum control.

Large-scale particle trapping by acoustic vortices with a continuously variable topological charge

Strengthened directivity with higher-order side lobes can be generated by the transducer with a larger radius at a higher frequency. The multi-annular pressure distributions are displayed in the cross-section of the acoustic vortices(AVs)which are formed by side lobes. In the near field, particles can be trapped in the valley region between the two annuli of the pressure peak, and cannot be moved to the vortex center. In this paper, a trapping method based on a sector transducer array is proposed, which is characterized by the continuously variable topological charge(CVTC). This acoustic field can not only enlarge the range of particle trapping but also improve the aggregation degree of the trapped particles. In the experiments, polyethylene particles with a diameter of 0.2 mm are trapped into the multi-annular valleys by the AV with a fixed topological charge. Nevertheless, by applying the CVTC, particles outside the radius of the AV can cross the pressure peak successfully and move to the vortex center. Theoretical studies are also verified by the experimental particles trapping using the AV with the continuous variation of three topological charges, and suggest the potential application of large-scale particle trapping in biomedical engineering.