Efficient entanglement concentration for arbitrary less-entangled NOON state assisted by single photons

We put forward two efficient entanglement concentration protocols(ECPs) for arbitrary less-entangled NOON state.Both ECPs only require one pair of less-entangled NOON state and an auxiliary photon.In the first ECP,the auxiliary photon is shared by two parties,while in the second ECP,the auxiliary photon is only possessed by one party,which can increase the practical success probability by avoiding the transmission loss and simplify the operations.Moreover,both ECPs can be used repeatedly to get a high success probability.Based on the above features,our two ECPs,especially the second one,may be useful in the quantum information processing.     

Concentrating partially entangled W-class states on nonlocal atoms using low-Q optical cavity and linear optical elements

Entanglement plays an important role in quantum information science, especially in quantum communications. Here we present an efficient entanglement concentration protocol (ECP) for nonlocal atom systems in the partially entangled W-class states, using the single-photon input-output process regarding low-Q cavity and linear optical elements. Compared with previously published ECPs for the concentration of non-maximally entangled atomic states, our protocol is much simpler and more efficient as it employs the Faraday rotation in cavity quantum electrodynamics (QED) and the parameter-splitting method. The Faraday rotation requires the cavity with low-Q factor and weak coupling to the atom, which makes the requirement for entanglement concentration much less stringent than the previous methods, and achievable with current cavity QED techniques. The parameter-splitting method resorts to linear-optical elements only. This ECP has high efficiency and fidelity in realistic experiments, and some imperfections during the experiment can be avoided efficiently with currently available techniques.     

Entanglement Concentration of Partially Entangled Multi-electron Spin W States with CNOT Gates

We propose a novel entanglement concentration protocol (ECP) for nonlocal N-electron systems in a partially entangled W state, resorting to an ancillary single electron and controlled-not gates. Compared with other ECPs for W states, our ECP has some illustrious advantages. First, each N-electron entangled system can be used to complete the entanglement concentration with only an ancillary electron. It does not require that there are two copies of N-electron entangled systems in each round of entanglement concentration. Second, only one of the users, say Charlie, needs to perform the protocol, while all parties should perform the same operations as Charlie in other ECPs for W-class states. Third, only Charlie asks other parities to retain or discard their electrons, and they do not need to check their measurement results, which greatly simplifies the complication of classical communication. Fourth, our ECP has a higher success probability than other ECPs for W-class states as its success probability equals to the limit value of an ECP for a W state in theory. These advantages maybe make our ECP more useful in practical applications.     

Entanglement Concentration for Arbitrary Four-Photon Cluster State Assisted with Single Photons

We present an entanglement concentration protocol (ECP) to concentrate arbitrary four-photon less-entangled cluster state into maximally entangled cluster state. Different from other ECPs for cluster state, we only exploit the single photon as auxiliary, which makes this protocol feasible and economic. In our ECP, the concentrated maximally entangled state can be retained for further application and the discarded state can be reused for a higher success probability. This ECP works with the help of cross-Kerr nonlinearity and conventional photon detectors. This ECP may be useful in future one-way quantum computation.     

Maximum efficiency of a linear-optical Bell-state analyzer

In a photonic realization of qubits the implementation of quantum logic is rather difficult due to the extremely weak interaction on the few photon level. On the other hand, in these systems interference is available to process the quantum states. We formalize the use of interference by the definition of a simple class of operations which include linear-optical elements, auxiliary states and conditional operations. We investigate an important subclass of these tools, namely linear-optical elements and auxiliary modes in the vacuum state. For these tools, we are able to extend a previous qualitative result, a no-go theorem for perfect Bell-state analyzer on two qubits in polarization entanglement, by a quantitative statement. We show that within this subclass it is not possible to discriminate unambiguously four equiprobable Bell states with a probability higher than 50%. Received: 18 July 2000 / Revised version: 15 September 2000 / Published online: 6 December 2000     

Hybrid entanglement concentration assisted with single coherent state

Hybrid entangled state(HES) is a new type of entanglement, which combines the advantages of an entangled polarization state and an entangled coherent state. HES is widely discussed in the applications of quantum communication and computation. In this paper, we propose three entanglement concentration protocols(ECPs) for Bell-type HES, W-type HES, and cluster-type HES, respectively. After performing these ECPs, we can obtain the maximally entangled HES with some success probability. All the ECPs exploit the single coherent state to complete the concentration. These protocols are based on the linear optics, which are feasible in future experiments.     

Optimal multi-photon entanglement concentration with the photonic Faraday rotation

We put forward an optimal entanglement concentration protocol(ECP) for recovering an arbitrary less-entangled multi-photon Greenberger–Horne–Zeilinger(GHZ) state into the maximally entangled GHZ state based on the photonic Faraday rotation in low-quality(Q) cavity. In the ECP, only one pair of less-entangled multi-photon GHZ state and one auxiliary photon are required, and the concentration task can be realized by local operations. Moreover, our ECP can be used repeatedly to further concentrate the discarded items of conventional ECPs, which can increase its success probability largely. Under the practical imperfect detection condition, our protocol can still work with relatively high success probability. This ECP has application potential in current and future quantum communication.     

Entanglement concentration for W-type entangled coherent states

An entangled coherent state(ECS) is one type of entanglement, which is widely discussed in the application of quantum information processing(QIP). In this paper, we propose an entanglement concentration protocol(ECP) to distill the maximally entangled W-type ECS from the partially entangled W-type ECS. In the ECP, we adopt the balanced beam splitter(BS) to make the parity check measurement. Our ECP is quite different from the conventional ECPs. After performing the ECP, not only can we obtain the maximally entangled ECS with some success probability, but also we can increase the amplitude of the coherent state. Therefore, it is especially useful in long-distance quantum communication, if the photon loss is considered.     

Optimal Entanglement Concentration of the Greenberger-Horne-Zeilinger States in Quantum-dot and Micro-cavity Coupled System

The distillation of the triplet Greenberger-Horne-Zeilinger (GHZ) state is demonstrated by using the entanglement concentrating process for the partially electron-spin-entangled systems. We designate an entanglement concentration protocol (ECP) in the quantum-dot (QD) and micro-cavity coupled systems based on the post-selection, from which the partially entangled state can be concentrated with an aid of the ancillary QD and single photon. This protocol can be repeated several rounds to get an optimal success probability. With the current technology, the maximally entangled electron spins can be achieved in the GHZ states after performing some suitable unitary operation locally for the long-distance quantum communications. The advantage is that during the whole process only the single photon needs to pass through the micro-cavity which increases the total success probability even if the cavity is imperfect in implementations.     

电子自旋辅助实现光子偏振态的量子纠缠浓缩

量子纠缠浓缩可以将非最大的纠缠态转变为最大纠缠态,提高量子通信的安全性.本文基于圆偏振光和量子点-腔系统的相互作用,用一个单光子作为连接远距离纠缠光子对的桥梁,在理想条件下实现了光子偏振纠缠态的浓缩.计算结果显示,这个纠缠浓缩方案在考虑耦合强度和腔泄漏的情况下也可以保持较高的保真度,而且不需要知道部分纠缠态的初始信息,也不必重复执行纠缠浓缩过程.这不仅提高了量子纠缠浓缩的安全性,也有助于通过消耗最少的量子资源来实现高效的量子信息处理.     

Efficient Entanglement Concentration Schemes for Separated Nitrogen-Vacancy Centers Coupled to Low-Q Microresonators

We present several efficient entanglement concentration protocols (ECPs) with the nitrogen-vacancy (N-V) centers coupled to low-Q microresonators. Based on the input-output process of ancillary coherent light pulse in low-Q microresonators, we can obtain the maximally entangled states among remote participants via local operations and classical communication. Our protocols use a conventional photon detector to discriminate the two coherent states |α〉 and |?α〉, which is more convenient than homodyne measurement. We discuss the feasibility of our protocols, and they may be beneficial for quantum repeaters and quantum information processing.     

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.     

Practical Entanglement Concentration for Entangled Coherent States

Entangled coherent state (ECS) is quite important in current quantum communication and quantum computation. In this paper, we discuss two practical entanglement concentration protocols (ECPs) to recover the maximally ECSs from the partially ECSs. In the first ECP, the parties do not need to know the initial coefficients of the partially ECSs. In the second ECP, they should know the initial coefficients. Both protocols are based on the linear optics which make them feasible in current experiment. Especially, in the second ECP, they only require one pair of initial partially ECSs, which makes this ECP optimal. Both ECPs may be useful in current quantum information processing.     

Efficient nonlocal two-step entanglement concentration protocol for three-level atoms in an arbitrary less-entangledW state using cavity input-output process

We present an efficient two-step entanglement concentration protocol (ECP) for three-level atoms trapped in one-sided optical micro-cavities in an arbitrary three-particle less-entangled W state, using the coherent state input-output process in low-Q cavity quantum electrodynamics system. In each step of the new proposed protocol, one of the three remote users prepares the auxiliary coherent optical pulses to perform cavity input-output process and then utilizes the standard homodyne measurement to discriminate the final outgoing coherent states. When both of the two steps are successful, remote parties can deterministically concentrate the less-entangled W state atoms to a standard maximally entangled W state. Compared with previous ECPs for W state, this protocol has some advantages and can be widely used in current quantum repeater and some quantum information processing tasks.     

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.     

On Extension of Optimal Entanglement Concentration of GHZ States in Quantum-Dot and Micro-Cavity Coupled System

We extend an optimal entanglement distillation of the triplet Greenberger-Horne-Zeilinger （GHZ） state via entanglement concentrating in the three-partite partially electron-spin-entangled systems. Two entanglement concen- tration protocols are similarly designed in detail with the post-selection in quantum-dot （QD） and micro-cavity coupled systems. The proposed protocol can be repeated several rounds to achieve an optimal success probability with an as- sistance of the ancillary QD, where only the single photon needs to pass through the micro-cavity for each round. It increases the total success probability of the distillation even if the implemented cavity is imperfect in practice during the whole process.     

Practical scheme for non-postselection entanglement concentration using linear optical elements

We report a practical non-postselection entanglement concentration scheme in which a maximally entangled Bell-state photon pair is produced from two pairs of partially (or non-maximally) entangled photons. Since this scheme is built only upon linear optical elements and does not require photon-number resolving detectors, it has immediate applications in experimental implementations of various quantum information protocols which require two-photon Bell-states.     

单光子纠缠态并发度的直接测量

通过分析光学分束器对单光子态的作用关系,提出了一个利用分束器和光子数探测器的单光子纠缠的直接测量方案.方案中用到单光子与空间模纠缠及其两个备份,并让它们通过一个50:50的分束器.选用并发度为纠缠度量,其可由单光子探测器的探测概率直接获得.此方案不需复杂的量子态层析方法,同时只用到在量子信息处理中常用的光学器件,增强了方案在实验上实现的可行性.     

Efficient electronic entanglement concentration assisted by single mobile electrons

We present an efficient entanglement concentration protocol （ECP） for mobile electrons with charge detection. This protocol is quite different from other ECPs for one can obtain a maximally entangled pair from a pair of less-entangled state and a single mobile electron with a certain probability. With the help of charge detection, it can be repeated to reach a higher success probability. It also does not need to know the coefficient of the original less-entangled states. All these advantages may make this protocol useful in current distributed quantum information processing.     

纠缠压缩真空态的纠缠转移

通过分析光学分束器对压缩真空态光场的作用,发现如果分束器的输入光是两束具有同样振幅和相位的单模压缩真空态光场,则输出光为双模压缩真空态光场;若分束器的输入光是两束具有同样振幅但有π相位差的单模压缩真空态光场,则输出光仍为两束单模压缩真空态光场.对于双模压缩真空态光场,每个模中容纳的光子数可以是基数或偶数.而对于单模压缩真空态光场,每个模中只能包含偶数个光子.根据这些结果,提出了一个纠缠转移的方案.在这个方案中,两个纠缠压缩真空态光场被用作量子信道,通过利用光学分束器作用和光子数探测的方法,并在经典通讯的帮助下,实现了三个通讯伙伴之间的纠缠转移.