Efficient Entanglement Concentration of Nonlocal Two-Photon Polarization-Time-Bin Hyperentangled States

We present two different hyperentanglement concentration protocols (hyper-ECPs) for two-photon systems in nonlocal polarization-time-bin hyperentangled states with known parameters, including Bell-like and cluster-like states, resorting to the parameter splitting method. They require only one of two parties in quantum communication to operate her photon in the process of entanglement concentration, not two, and they have the maximal success probability. They work with linear optical elements and have good feasibility in experiment, especially in the case that there are a big number of quantum data exchanged as the parties can obtain the information about the parameters of the nonlocal hyperentangled states by sampling a subset of nonlocal hyperentangled two-photon systems and measuring them. As the quantum state of photons in the time-bin degree of freedom suffers from less noise in an optical-fiber channel, these hyper-ECPs may have good applications in practical long-distance quantum communication in the future.     

Experiments of quantum nonlocality with polarization-momentum entangled photon pairs

We present the results of some experimental tests of quantum nonlocality performed by two-photon states, entangled both in polarization and momentum, namely hyperentangled states and two-photon four-qubit linear cluster states. These states, which double the number of available qubits with respect to the standard two-photon entangled states, are engineered by a simple experimental method, which adopts linear optics and a single type I nonlinear crystal. The tests of local realism performed with these states represent a generalization of the Greenberger, Home, and Zeilinger (GHZ) theorem to the case of two entangled particles.     

Enhancing the violation of the einstein-podolsky-rosen local realism by quantum hyperentanglement

Mermin's observation [Phys. Rev. Lett. 65, 1838 (1990)] that the magnitude of the violation of local realism, defined as the ratio between the quantum prediction and the classical bound, can grow exponentially with the size of the system is demonstrated using two-photon hyperentangled states entangled in polarization and path degrees of freedom, and local measurements of polarization and path simultaneously.     

Quantum Secure Direct Communication by Using Three-Dimensional Hyperentanglement

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

An improved quantum repeater protocol using hyperentangled state purification

This article indicates an improved protocol of quantum repeaters through the scheme of nest entanglement purification [Phys. Rev. Lett. 81, 5932 (1998)]. The hyperentangled photon pairs are utilized to overcome the limitations of long distance quantum communication via noisy channels. In addition, it is mentioned that if there are imperfect quantum operations and noises in realistic communication, the fidelities of hyperentangled quantum channels will be improved compared with the traditional entangled states.     

Refined hyperentanglement purification of two-photon systems for high-capacity quantum communication with cavity-assisted interaction

Hyperentanglement, defined as the entanglement in multiple degrees of freedom (DOFs) of a photonic quantum system, has attracted much attention recently as it can improve the channel capacity of quantum communication largely. Here we present a refined hyperentanglement purification protocol (hyper-EPP) for two-photon systems in mixed hyperentangled states in both the spatial-mode and polarization DOFs, assisted by cavity quantum electrodynamics. By means of the spatial (polarization) quantum state transfer process, the quantum states that are discarded in the previous hyper-EPPs can be preserved. That is, the spatial (polarization) state of a four-photon system with high fidelity can be transformed into another four-photon system with low fidelity, not disturbing its polarization (spatial) state, which makes this hyper-EPP take the advantage of possessing a higher efficiency.     

Hyperconcentration Based on Projection Measurements

We propose an efficient hyperconcentration protocol for distilling maximally hyperentangled state from partially entangled pure state, resorting to the projection measurement on an auxiliary photon. In our scheme, two photons simultaneously entangled in polarization states and spatial modes are considered. One party performs quantum nondemolition detections on his photon and an additional photon to produce three photon hyperentangled state, then he projects the assistant photon into an orthogonal basis composed of both the polarization and spatial degree of freedom. Then the state of the left two photons collapses into maximally hyperentangled state with a certain probability. In the rest cases, some less-entangled states are obtained, which can be used as resource for the next round concentration. By repeating the concentration process for several rounds, a higher success probability can be obtained, which makes our scheme useful in practical quantum information applications.     

光子两自由度超并行量子计算与超纠缠态操控

光子系统在量子信息处理和传输过程中有非常重要的应用. 譬如, 利用光子与原子(或人工原子)之间的相互作用, 可以完成信息的安全传输、存储和快速的并行计算处理等任务. 光子系统具有多个自由度, 如极化、空间模式、轨道角动量、时间-能量、频率等自由度. 光子系统的多个自由度可以同时应用于量子信息处理过程. 超并行量子计算利用光子系统多个自由度的光量子态同时进行量子并行计算, 使量子计算具有更强的并行性, 且需要的量子资源少, 更能抵抗光子数损耗等噪声的影响. 多个自由度同时存在纠缠的光子系统量子态称为超纠缠态, 它能够提高量子通信的容量与安全性, 辅助完成一些重要的量子通信任务. 在本综述中, 我们简要介绍了光子系统两自由度量子态在量子信息中的一些新应用, 包括超并行量子计算、超纠缠态分析、超纠缠浓缩和纯化三个部分.     

Measurement-Based Hyperentanglement Distillation for Lossy and Distortion Photon State

The information content of a photon system can be extended by hyperentanglement, but the quality of hyperentanglement will be decreased by the complicated transmission loss and channel noise in quantum information processing. Here, an efficient measurement-based hyperentanglement distillation protocol (MB-HDP) is presented for depressing the effects of complicated transmission loss and channel noise on hyperentanglement. In the MB-HDP, the nonlocal lossy and distortion photon states are coupled to local hyperentangled Greenberger–Horne–Zeilinger (GHZ) states using parity measurement and qubit amplification device, and the decoherence caused by bit-flip (phase-flip) error, diverse transmission coefficients and transmission loss can be depressed by the successful measurement results, which can increase the quality of nonlocal hyperentangled photon state. This MB-HDP broadens the application scope of hyperentanglement distillation to nonlocal lossy and distortion photon state with a lower degree of entanglement. In addition, the MB-HDP can further improve the quality of nonlocal hyperentangled photon state by coupling multiple copies of lossy and distortion hyperentangled photon state with local hyperentangled GHZ states. This work demonstrates the ability of measurement-based method for ensuring the quality of nonlocal hyperentanglement, which can improve the integrity and capacity of long-distance quantum information processing.     

Generation of hyperentangled photon pairs

We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric down-conversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode, and time energy. We also produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2 x 2 x 3 x 3 system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.     

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.     

High-Capacity Quantum Secret Sharing with Hyperdense Coding Assisted by Hyperentangled Photon Pairs

We presents a high-capacity three-party quantum secret sharing (QSS) protocol with a sequence of photon pairs in hyperentangled Bell states in both the polarization and the spatial-mode degrees of freedom. In our scheme, the boss Alice prepares a sequence of photon pairs in hyperentangled Bell states and divides them into two photon sequences which are sent the two agents, respectively. Alice exploits four subsets of decoy photons to assure the security of the photon transmission between her and her agents. The present QSS scheme has the advantage of having a high channel capacity as each photon pair can carry 4 bits of secret message in principle, two times of that by Deng et al. (Phys. Lett. A 372: 1957, 2008). We give out the setups for the preparation of the photon pairs in hyperentangled Bell states with a beta barium borate crystal and the manipulation of the photons with linear optical elements. It will be shown that our QSS protocol is feasible with current experimental technology.     

六光子超纠缠态制备方案

自发参量下转换对应于一种非线性光学过程, 实验上作为一种标准方法, 人们利用自发参量下转换源产生纠缠光子对. 本文考虑由自发参量下转换源产生三对纠缠光子的情况. 通过使用由几组偏振光 束分束器、分束器和半波片等线性光学器件组成的量子线路演化三对光子, 给出了一个高效制备 包含偏振纠缠和空间纠缠的六光子超纠缠态方案. 因为方案中包含了参量下转换源产生三对纠缠光子 的所有可能情况, 所以本方案有很高的效率. 基于弱非线性介质构建了一个量子非破坏性测量装置, 用于区分光子在两指定的空间模中的两种分布情况. 特别地, 方案中可以通过合理约束在量子非破坏性测量过程中引入的非线性强度来达到实际实验所限定的数量级, 因此, 该方案易于在实验上实现.     

Efficient Superdense Coding with W States

Superdense coding is a distinct property of quantum entanglement. In this paper, we show that the bipartite three-particle W state can transmit 3 bits by sending two qubits using single qubit operations. This has justified previous conjecture (Agrawal and Pati, Phys. Rev. A 74(6), 062320 2006). Similar result holds for hyperentangled W states.     

Two-Photon Spin States and Entanglement States

In this paper, we have given the spin states of two-photon, which are expressed by the quadratic combination of two single-photon spin states, and given all entanglement states of two-photon from the spin states of two-photon. The new expression of two-photon entanglement states should be used in quantum computation and quantum communication.     

Generation of a two-photon KLM quantum channel

As demonstrated by E. Knill et al. [Nature 409, 46 (2001)], quantum teleportation and quantum logic gates with a success probability close to one can be implemented using only linear optical elements, additional photons, and post-selection. To do this, it is desirable to have special quantum channels in sight before quantum teleportation performance. Here, we propose an experimental arrangement to generate a two-photon KLM state different from the well-known Bell states. This two-photon KLM state can be used to enhance the success probability of the quantum teleportation of a one-mode quantum qubit from 0.5 up to 2/3.     

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 hyperentanglement-assisted 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 about 354 km. Our MDI one-step QSDC protocols may have potential applications in the future quantum secure communication field.     

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

Hyperentanglement has attracted considerable attention recently because of its high-capacity for longdistance quantum communication. In this study, we present a hyperentanglement concentration protocol (hyper-ECP) for nonlocal three-photon systems in the polarization, spatial-mode, and timebin 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 elements 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.     

Bipartite bell inequalities for hyperentangled states

We show that bipartite Bell inequalities based on the Einstein-Podolsky-Rosen criterion for elements of reality and derived from the properties of some hyperentangled states allow feasible experimental verification of the fact that quantum nonlocality grows exponentially with the size of the subsystems, and Bell loophole-free tests with currently available photodetection efficiencies.     

The Linear Optical Unambiguous Discrimination of Hyperentangled Bell States Assisted by Time Bin

A linear optical unambiguous discrimination of hyperentangled Bell states is proposed for two‐photon systems entangled in both the polarization and momentum degrees of freedom (DOFs) assisted by time bin. This unambiguous discrimination scheme can completely identify 16 orthogonal hyperentangled Bell states using only linear optical elements, where the function of the auxiliary entangled Bell state is replaced by time bin. Moreover, the possibility of extending this scheme for distinguishing hyperentangled Bell states in n DOFs is discussed, and it shows that $2^{n+k+1}$ hyperentangled Bell states in n ( $n\ge 2$) DOFs can be distinguished with k ( $k<n$) auxiliary entangled states of additional DOFs by introducing a time delay, which decreases the auxiliary entanglement resource required for unambiguous discrimination of hyperentangled Bell state. Therefore, this scheme provides a new way for distinguishing hyperentangled states with current technology, which will extend the application of discrimination of hyperentangled states via linear optics to other quantum information protocols besides hyperdense coding schemes in the future.