Faithful and efficient hyperentanglement purification for spatial-polarization-time-bin photon system

We present a faithful and efficient hyperentanglement purification protocol(hyper-EPP)for nonlocal two-photon systems in spatial-polarization-time-bin hyperentangled Bell states.As the single-photon detectors can detect and herald the undesirable properties caused by side leakage and finite coupling strength,the parity-check gates and swap gates of our hyper-EPP in the spatial,polarization and time-bin mode degrees of freedom(DoFs)work faithfully.The qubit-flip errors in photon systems in three DoFs can be corrected effectively with the faithful parity-check gates and the photon pairs can be reused to distill high-fidelity ones by introducing the faithful swap gates,which greatly increases the efficiency of our hyper-EPP.Further,the maximal hyperentanglement can be obtained in principle by operating multiple rounds of the hyper-EPP.

Complete hyperentangled Greenberger–Horne–Zeilinger state analysis for polarization and time-bin hyperentanglement

We present an efficient scheme for the complete analysis of hyperentangled Greenberger–Horne–Zeilinger(GHZ)state in polarization and time-bin degrees of freedom with two steps. Firstly, the polarization GHZ state is distinguished completely and nondestructively, resorting to the controlled phase flip(CPF) gate constructed by the cavity-assisted interaction. Subsequently, the time-bin GHZ state is analyzed by using the preserved polarization entanglement. With the help of CPF gate and self-assisted mechanism, our scheme can be directly generalized to the complete N-photon hyperentangled GHZ state analysis, and it may have potential applications in the hyperentanglement-based quantum communication.

A two-step quantum secure direct communication protocol with hyperentanglement

We propose a two-step quantum secure direct communication （QSDC） protocol with hyperentanglement in both the spatial-mode and the polarization degrees of freedom of photon pairs which can in principle be produced with a beta barium borate crystal. The secret message can be encoded on the photon pairs with unitary operations in these two degrees of freedom independently. This QSDC protocol has a higher capacity than the original two-step QSDC protocol as each photon pair can carry 4 bits of information. Compared with the QSDC protocol based on hyperdense coding, this QSDC protocol has the immunity to Trojan horse attack strategies with the process for determining the number of the photons in each quantum signal as it is a one-way quantum communication protocol.

Quantum Secure Direct Communication by Using Three-Dimensional Hyperentanglement

We propose two schemes for realizing quantum secure direct communication (QSDC)by using a set ofordered two-photon three-dimensional hyperentangled states entangled in two degrees of freedom (DOFs)as quantuminformation channels.In the first scheme,the photons from Bob to Alice are transmitted only once.After insuring thesecurity of the quantum channels,Bob encodes the secret message on his photons.Then Alice performs single-photontwo-DOF Bell bases measurements on her photons.This scheme has better security than former QSDC protocols.In thesecond scheme,Bob transmits photons to Alice twice.After insuring the security of the quantum channels,Bob encodesthe secret message on his photons.Then Alice performs two-photon Bell bases measurements on each DOF.The schemehas more information capacity than former QSDC protocols.

Bidirectional Quantum Secure Direct Communication Network Protocol with Hyperentanglement

We propose a bidirectional quantum secure direct communication(QSDC) network protocol with the hyperentanglment in both the spatial-mode ad the polarization degrees of freedom of photon pairs which can in principle be produced with a beta barium borate crystal.The secret message can be encoded on the photon pairs with unitary operations in these two degrees of freedom independently.Compared with other QSDC network protocols,our QSDC network protocol has a higher capacity as each photon pair can carry 4 bits of information.Also,we discuss the security of our QSDC network protocol and its feasibility with current techniques.

Faithful deterministic secure quantum communication and authentication protocol based on hyperentanglement against collective noise

Higher channel capacity and security are difficult to reach in a noisy channel. The loss of photons and the distortion of the qubit state are caused by noise. To solve these problems, in our study, a hyperentangled Bell state is used to design faithful deterministic secure quantum communication and authentication protocol over collective-rotation and collective-dephasing noisy channel, which doubles the channel capacity compared with using an ordinary Bell state as a carrier; a logical hyperentangled Bell state immune to collective-rotation and collective-dephasing noise is constructed. The secret message is divided into several parts to transmit, however the identity strings of Alice and Bob are reused. Unitary operations are not used.

Deterministic nondestructive state analysis for polarization-spatial-time-bin hyperentanglement with cross-Kerr nonlinearity

We present a deterministic nondestructive hyperentangled Bell state analysis protocol for photons entangled in three degrees of freedom(DOFs),including polarization,spatial-mode,and time-bin DOFs.The polarization Bell state analyzer and spatial-mode Bell state analyzer are constructed by polarization parity-check quantum nondemolition detector(P-QND)and spatial-mode parity-check quantum nondemolition detector(S-QND)using cross-Kerr nonlinearity,respectively.The time-bin Bell state analyzer is constructed by the swap gate for polarization state and time-bin state of a photon(P-T swap gate)and P-QND.The Bell states analyzer for one DOF will not destruct the Bell states of other two DOFs,so the polarization-spatial-time-bin hyperentangled Bell states can be determinately distinguished without destruction.This deterministic nondestructive state analysis method has useful applications in quantum information protocols.

Quantum secure direct communication network with hyperentanglement

We propose a quantum secure direct communication protocol with entanglement swapping and hyperentanglement. Any two users, Alice and Bob, can communicate with each other in a quantum network, even though there is no direct quantum channel between them. The trust center, Trent, who provides a quantum channel to link them by performing entanglement swapping, cannot eavesdrop on their communication. This protocol provides a high channel capacity because it uses hyperentanglement, which can be generated using a beta barium borate crystal.

Quantum superdense coding based on hyperentanglement

We present a scheme for quantum superdense coding with hyperentanglement, in which the sender can transfer four bits of classical information by sending only one photon. The important device in the scheme is the hyperentangled Bell-state analyzer in both polarization and frequency degrees of freedom, which is also constructed in the paper by using a quantum nondemolition detector assisted by cross-Kerr nonlinearity. Our scheme can transfer more informationwith less resources than the existing schemes and is nearly deterministic and nondestructive.

One-step quantum dialogue

Quantum dialogue(QD)enables two communication parties to directly exchange secret messages simultaneously.In conventional QD protocols,photons need to transmit in the quantum channel for two rounds.In this paper,we propose a one-step QD protocol based on the hyperentanglement.With the help of the non-local hyperentanglement-assisted Bell state measurement(BSM),the photons only need to transmit in the quantum channel once.We prove that our one-step QD protocol is secure in theory and numerically simulate its secret message capacity under practical experimental condition.Compared with previous QD protocols,the one-step QD protocol can effectively simplify the experiment operations and reduce the message loss caused by the photon transmission loss.Meanwhile,the non-local hyperentanglement-assisted BSM has a success probability of 100%and is feasible with linear optical elements.Moreover,combined with the hyperentanglement heralded amplification and purification,our protocol is possible to realize long-distance one-step QD.

General hyperentanglement concentration for polarization- spatial-time-bin multi-photon systems with linear optics

Hyperentanglement has attracted considerable attention recently because of its high-capacity for long- distance quantum communication. In this study, we present a hyperentanglement concentration pro- tocol （hyper-ECP） for nonlocal three-photon systems in the polarization, spatial-mode, and time- bin partially hyperentangled Greenberger-Horne-Zeilinger （GHZ） states using the Schmidt projection method. In our hyper-ECP, the three distant parties must perform the parity-check measurements on the polarization, spatial-mode, and time-bin degrees of freedom, respectively, using linear optical ele- ments and Pockels cells, and only two identical nonlocal photon systems are required. This hyper-ECP can be directly extended to the N-photon hyperentangled GHZ states, and the success probability of this general hyper-ECP for a nonlocal N-photon system is the optimal one, regardless of the photon number N.

Quantum hyperentanglement and its applications in quantum information processing

Hyperentanglement is a promising resource in quantum information processing with its high capacity character, defined as the entanglement in multiple degrees of freedom(DOFs) of a quantum system, such as polarization, spatial-mode, orbit-angular-momentum, time-bin and frequency DOFs of photons.Recently, hyperentanglement attracts much attention as all the multiple DOFs can be used to carry information in quantum information processing fully. In this review, we present an overview of the progress achieved so far in the field of hyperentanglement in photon systems and some of its important applications in quantum information processing, including hyperentanglement generation, complete hyperentangled-Bell-state analysis, hyperentanglement concentration, and hyperentanglement purification for high-capacity long-distance quantum communication. Also, a scheme for hyper-controlled-not gate is introduced for hyperparallel photonic quantum computation, which can perform two controlled-not gate operations on both the polarization and spatial-mode DOFs and depress the resources consumed and the photonic dissipation.

Compact generation scheme of path–frequency hyperentangled photons using 2D periodical nonlinear photonic crystal

Hyperentanglement is a promising resource for achieving high capacity quantum communication.Here,we propose a compact scheme for the generation of path-frequency hyperentangled photon pairs via spontaneous parametric down-conversion(SPDC)processes,where six different paths and two different frequencies are covered.A two-dimensional periodicalχ^((2))nonlinear photonic crystal(NPC)is designed to satisfy type-Ⅰquasi-phase-matching conditions in the plane perpendicular to the incident pump beam,and a perfect phase match is achieved along the pump beam's direction to ensure high conversion efficiency,with theoretically estimated photon flux up to 2.068×10^(5) pairs·s^(-1)·mm^(-2).We theoretically calculate the joint-spectral amplitude(JSA)of the generated photon pair and perform Schmidt decomposition on it,where the resulting entropy S of entanglement and effective Schmidt rank K reach 3.2789 and 6.4675,respectively.Our hyperentangled photon source scheme could provide new avenues for high-dimensional quantum communication and high-speed quantum information processing.

Generation of hyperentangled photon pairs based on lithium niobate waveguide

Generation of hyperentangled photon pairs is investigated based on the lithium niobate straight waveguide.We propose to use the nonlinear optical process of spontaneous parametric down-conversion(SPDC)and a well-designed lithium niobate waveguide structure to generate a hyperentangled(in the polarization dimension and the energy-time dimension)two-photon state.By performing numerical simulations of the waveguide structure and calculating the possible polarization states,joint spectral amplitudes(JSA),and joint temporal amplitudes(JTA)of the generated photon pair,we show that the generated photon pair is indeed hyperentangled in both the polarization dimension and the energy-time dimension.

Measurement-device-independent one-step quantum secure direct communication

The one-step quantum secure direct communication(QSDC)(Sci.Bull.67,367(2022))can effectively simplify QSDC’s operation and reduce message loss.For enhancing its security under practical experimental condition,we propose two measurement-device-independent(MDI)one-step QSDC protocols,which can resist all possible attacks from imperfect measurement devices.In both protocols,the communication parties prepare identical polarization-spatial-mode two-photon hyperentangled states and construct the hyperentanglement channel by hyperentanglement swapping.The first MDI one-step QSDC protocol adopts the nonlinear-optical complete hyperentanglement Bell state measurement(HBSM)to construct the hyperentanglement channel,while the second protocol adopts the linear-optical partial HBSM.Then,the parties encode the photons in the polarization degree of freedom and send them to the third party for the hyperentanglementassisted complete polarization Bell state measurement.Both protocols are unconditionally secure in theory.The simulation results show the MDI one-step QSDC protocol with complete HBSM attains the maximal communication distance of about354 km.Our MDI one-step QSDC protocols may have potential applications in the future quantum secure communication field.

Complete hyperentangled state analysis and generation of multi-particle entanglement based on charge detection

We propose the schemes for implementing hyperentangled state analysis and generating four-electron high entan-gled states （including cluster state, ｜X） state, and symmetric Dicke state） based on the charge detection of free electrons. These schemes are deterministic and rely only on charge detection and single-spin rotations. This method, which uses noninteracting electrons, is not only efficient but also saves on quantum resources.

Generation of hyperentangled four-photon cluster state via cross-Kerr nonlinearity

We propose a scheme for generating a hyperentangled four-photon cluster state that is simultaneously entangled in polarization modes and spatial modes. This scheme is based on linear optical elements, weak cross-Kerr nonlinearity, and homodyne detection. Therefore, it is feasible with current experimental technology.

New Quantum Private Comparison Using Hyperentangled GHZ State

In this paper,we propose a new protocol designed for quantum private comparison(QPC).This new protocol utilizes the hyperentanglement as the quantum resource and introduces a semi-honest third party(TP)to achieve the objective.This protocol’s quantum carrier is a hyperentangled three-photon GHZ state in 2 degrees of freedom(DOF),which could have 64 combinations.The TP can decide which combination to use based on the shared key information provided from a quantum key distribution(QKD)protocol.By doing so,the security of the protocol can be improved further.Decoy photon technology is also used as another means of security and checks if the transmission in the quantum channel is secure or not before sending the quantum carrier.The proposed protocol is proved to be able to fend off various kinds of eavesdropping attacks.In addition,the new QPC protocol also can compare secret inputs securely and efficiently.

High-capacity device-independent quantum secure direct communication based on hyper-encoding

Quantum secure direct communication(QSDC)can directly transmit secret messages through quantum channel without keys.Device-independent(DI)QSDC guarantees the message security relying only on the observation of the Bell-inequality violation,but not on any detailed description or trust of the devices'inner workings.Compared with conventional QSDC,DI-QSDC has relatively low secret message capacity.To increase DI-QSDC's secret messages capacity,we propose a high-capacity DI-QSDC protocol based on the hyper-encoding technique.The total message leakage rate of our DI-QSDC protocol only relies on the most robust degree of freedom.We provide the numerical simulation of its secret message capacity altered with the communication distance.Our work serves as an important step toward thefurther development of DI-QSDC systems.

Generation of hyperentangled state encoded in three degrees of freedom

Hyperentanglement, the simultaneous entanglement in more than one degree of freedom(DOF), plays an important role in quantum communication and quantum information processing for it can effectively increase the channel capacity. Existing hyperentanglement sources mainly focus on the generation of the hyperentanglement in two DOFs. In this paper, we design the generation protocols for three kinds of hyperentanglement encoded in three DOFs with the practical coherent pulses sources, including the polarization-frequency-space hyperentanglement, the polarization-frequency-time-bin hyperentanglement, and the polarizationspace-time-bin hyperentanglement. These protocols exploit the spontaneous parametric down-conversion(SPDC) process and the Sagnac interferometer. The three protocols are all based on feasible experimental condition and may have potential applications in future hyperentanglement-based quantum communication and quantum information processing protocols.