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.     

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.     

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 information with less resources than the existing schemes and is nearly deterministic and nondestructive.     

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.     

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.     

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.     

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.     

Error-heralded generation and self-assisted complete analysis of two-photon hyperentangled Bell states through single-sided quantum-dot-cavity systems

Hyperentangled-Bell-state analysis(HBSA) is critical for high-capacity quantum communication. Based on a recent proposal by Wang et al. [Opt. Express 24, 28444(2016)], we design two independent schemes for error-heralded deterministic generation and self-assisted complete HBSA of two-photon systems entangled in both polarization and spatial-mode degrees of freedom(DOFs).Unlike previous programs, we firstly propose an error-heralded block with a singly charged quantum dot inside a single-sided optical microcavity, with which errors due to imperfect interactions between photons and quantum dot systems can be heralded.The error-heralded block, ensures that the fidelity of the two schemes for hyperentangled-Bell-state generation and complete HBSA reaches unity. Moreover, hyperentanglement makes it possible to analyze the polarization state with the assistance of the measured spatial-mode state. The self-assisted mechanism of HBSA greatly simplifies the analytical process and significantly relaxes the requirements of nonlinearities. Therefore, these schemes promise to be implemented more easily in experiments,taking a step closer to long-distance high-capacity quantum communication.     

Logic Bell state concentration with parity check measurement

Logic qubit plays an important role in current quantum communication. In this paper, we propose an efficient entanglement concentration protocol (ECP) for a new kind of logic Bell state, where the logic qubit is the concatenated Greenber–Horne–Zeilinger (C-GHZ) state. Our ECP relies on the nondemolition polarization parity check (PPC) gates constructed with cross-Kerr nonlinearity, and can distill one pair of maximally entangled logic Bell state from two same pairs of less-entangled logic Bell states. Benefit from the nondemolition PPC gates, the concentrated maximally entangled logic Bell state can be remained for further application. Moreover, our ECP can be repeated to further concentrate the less-entangled logic Bell state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in future long-distance quantum communication.     

An Arbitrated Proxy Blind Signature Based on Hyper Entanglement Analysis

Motivated by the hyperentangled Bell states analysis, an arbitrated quantum proxy blind signature (QPBS) scheme is developed. Four participants accomplish the task of signing and verifying via exchanging the entanglement of polarization and spatial-mode degrees of freedom. Alice blinds message and sends it to a proxy signatory David who is delegated by the original signatory Charlie. David generates a signature using the delegating code while Bob verifies the signing with the help of an arbitrator Trent. Unlike previous schemes, the verifying phase is no longer executed only by a recipient. Analysis shows that when the even numbers of blinding string always equal 1, the scheme protects the proxy blind signature against forgery and disavow while maintaining the properties of verifiability and identifiability.     

Quantum-Error-Rejection for Hyperentanglement Transmission without Calibrated Reference Frames

In quantum communication, the channel noise and the misalignment of the reference frames between the communication parties will lead to the failure of quantum state transmission. Here an alignment-free spatial-polarization hyperentanglement transmission scheme is provided for hyperentangled photons. In this scheme, before the spatial-polarization hyperentanglement is transmitted through the fiber channel, it is first encoded as a time-bin entanglement with the same polarization. After the photons pass through the noise channel, the polarization errors caused by reference frames misalignment and channel noise can be corrected by time-bin entanglement. In principle, by implementing this scheme, the communication parties can share the original hyperentangled state, and the success probability can approach unity. The scheme is robust to random channel noise and reference frames misalignment, and the decoherence effect caused by the misalignment of the reference frames between the communication parties can be completely suppressed by implementing this scheme.     

Nonlocal hyperconcentration on entangled photons using photonic module system

Entanglement distribution will inevitably be affected by the channel and environment noise. Thus distillation of maximal entanglement nonlocally becomes a crucial goal in quantum information. Here we illustrate that maximal hyperentanglement on nonlocal photons could be distilled using the photonic module and cavity quantum electrodynamics, where the photons are simultaneously entangled in polarization and spatial-mode degrees of freedom. The construction of the photonic module in a photonic band-gap structure is presented, and the operation of the module is utilized to implement the photonic nondestructive parity checks on the two degrees of freedom. We first propose a hyperconcentration protocol using two identical partially hyperentangled initial states with unknown coefficients to distill a maximally hyperentangled state probabilistically, and further propose a protocol by the assistance of an ancillary single photon prepared according to the known coefficients of the initial state. In the two protocols, the total success probability can be improved greatly by introducing the iteration mechanism, and only one of the remote parties is required to perform the parity checks in each round of iteration. Estimates on the system requirements and recent experimental results indicate that our proposal is realizable with existing or near-further technologies.     

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.     

Deterministic and complete hyperentangled Bell states analysis assisted by frequency and time interval degrees of freedom

Hyperentangled Bell states analysis (HBSA) is an essential building block for certain hyper-parallel quantum information processing. We propose a complete and deterministic HBSA scheme encoded in spatial and polarization degrees of freedom (DOFs) of two-photon system assisted by a fixed frequency-based entanglement and a time interval DOF. The parity information the spatial-based and polarization-based hyper-entanglement can be distinguished by the distinct time intervals of the photon pairs, and the phase information can be distinguished by the detection signature. Compared with previous schemes, the number of the auxiliary entanglements is reduced from two to one by introducing time interval DOF. Moreover, the additional frequency and time interval DOFs suffer less from the collective channel noise.     

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.     

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.     

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.     

Teleportation of a Photonic Qubit with Non-maximally Entangled State by Using Weak Cross-Kerr Nonlinearities

We present a scheme for teleporting an unknown single-photon polarization state by using the partially entangled state as the quantum channel. Based on weak cross-Kerr nonlinearity, in this scheme the sender utilizes the quantum parity-check detector (PCD) instead of the usual Bell state measurement. After getting the sender’s measurement result, the receiver of the scheme exploits another PCD to retrieve the original state with some additional photons being introduced. We work out the success probability of the scheme and show that the scheme is feasible with the current technology.     

Heralded entanglement purification protocol using high-fidelity parity-check gate based on nitrogen-vacancy center in optical cavity

The decoherence of entangled states caused by the noisy channel is a salient problem for reducing the fidelity of quantum communication. Here we present a heralded two-photon entanglement purification protocol(EPP) using heralded high-fidelity parity-check gate(HH-PCG), which can increase the entanglement of nonlocal two-photon polarization mixed state. The HH-PCG is constructed by the input-output process of nitrogen-vacancy(NV) center in diamond embedded in a single-sided optical cavity, where the errors caused by the imperfect interaction between the NV center-cavity system and the photon can be heralded by the photon detector. As the unwanted components can be filtrated due to the heralded function, the fidelity of the EPP scheme can be enhanced considerably, which will increase the fidelity of quantum communication processing.     

基于弱非线性实现非破坏性测量两光子Bell态及三光子Greenberger-Horne-Zeilinger态

基于弱非线性及线性光学元件提出非破坏性测量两光子Bell态及三光子 Greenberger-Horne-Zeilinger (GHZ)态方案. 方案中, 首先应用光束分束器及交叉克尔非线性介质对两光子Bell态进行对称性分析, 进而结合控制非门提出三光子分析方案实现对八个三光子GHZ态完全且非破坏性区分. 关键词： Bell态测量 Greenberger-Horne-Zeilinger态测量 弱非线性 量子非破坏性测量