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.     

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.     

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.     

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.     

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.     

基于自发参量下转换源二阶激发过程产生四光子超纠缠态

目前,多光子纠缠态的制备大多通过线性光学器件演化自发参量下转换一阶激发过程产生的纠缠光子对得到.本文考虑由自发参量下转换源二阶激发产生四个不可区分的纠缠光子制备四光子超纠缠态的情况.通过几组分束器、半波片和偏振分束器等线性光学器件设计量子线路演化四光子系统,结合四模符合探测,可得到同时具有偏振纠缠和空间纠缠的四光子超纠缠态.     

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.     

Polarization-momentum hyper-entangled two photon states

We present a parametric source which allows the engineering of polarization-momentum hyperentangled two photon states based on linear optics and a single type-I nonlinear crystal. The nonlocal character of these states has been verified by various tests, including the “All Versus Nothing” test of local realism [A. Cabello, Phys. Rev. Lett. 87, 010403 (2001)], which represents a generalization of the GHZ to the case of two entangled particles and two observers. We have also created a complete and deterministic Bell-state measurement by a novel experimental scheme which adopts polarization-momentum hyper-entanglement and requires linear optics and single photon detectors. The text was submitted by the authors in English.     

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.     

Self-error-rejecting photonic qubit transmission in polarization-spatial modes with linear optical elements

We present an original self-error-rejecting photonic qubit transmission scheme for both the polarization and spatial states of photon systems transmitted over collective noise channels. In our scheme, we use simple linear-optical elements, including half-wave plates, 50:50 beam splitters, and polarization beam splitters, to convert spatial-polarization modes into different time bins. By using postselection in different time bins, the success probability of obtaining the uncorrupted states approaches 1/4 for single-photon transmission, which is not influenced by the coefficients of noisy channels. Our self-error-rejecting transmission scheme can be generalized to hyperentangled n-photon systems and is useful in practical high-capacity quantum communications with photon systems in two degrees of freedom.     

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.     

High-Capacity Quantum Secure Direct Communication with Single Photons in Both Polarization and Spatial-Mode Degrees of Freedom

We present a high-capacity quantum secure direct communication (QSDC) protocol with single photons in both the polarization and the spatial-mode degrees of freedom. With a single photon traveling forth and back from the receiver to the sender, it can carry 2 bits of information as the sender can encode his message on both the polarization states and the spatial-mode states of single photons independently. Moreover, our QSDC protocol is feasible as the preparation and the measurement of a single-photon quantum state in both the polarization and the spatial-mode degrees of freedom is not difficult with current technology.     

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.     

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.     

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.     

All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement

We report the experimental realization and the characterization of polarization and momentum hyperentangled two-photon states, generated by a new parametric source of correlated photon pairs. By adoption of these states an "all-versus-nothing" test of quantum mechanics was performed. The two-photon hyperentangled states are expected to find at an increasing rate a widespread application in state engineering and quantum information.     

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.     

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.     

Complete Deterministic Analyzer for Multi-Electron Greenberger–Horne–Zeilinger States Assisted by Double-Side Optical Microcavities

We present a complete deterministic scheme for the multi-electron Greenberger–Horne–Zeilinger (GHZ) state analyzer, resorting to an interface between the polarization of a probe photon and the spin of an electron in a quantum dot embedded in a double-sided optical microcavity. All the multi-spin GHZ states can be completely discriminated by using single-photon detectors and linear optical elements. Our scheme has some features. First, it is a complete GHZ-state analyzer for multi-electron spin systems. Second, the initial entangled states remain after being identified and they can be used for a successive task. Third, the electron qubits are static and the photons play a role of a medium for information transfer, which has a good application in quantum repeater in which the electron qubits are used to store the information and the photon qubits are used to transfer the information between others.