Optimal entanglement concentration for three-photon W states with parity check measurement

We present an efficient entanglement concentration protocol(ECP) for the less-entangled W state with some identical conventional polarized single photons.In the protocol,two of the parties say Alice and Charlie should perform the parity check measurements and they can ultimately obtain the maximally entangled W state with a certain success probability.Otherwise,they can obtain another less-entangled W state,which can be reconcentrated into the maximally entangled W state.By iterating this ECP,a high success probability can be achieved.This ECP may be an optimal one and it is useful in current 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 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.     

Multipartite entanglement concentration of electron-spin states with CNOT gates

We propose a different entanglement concentration protocol (ECP) for nonlocal N-electron systems in a partially entangled Bell-type pure state using the CNOT gates and the projection measurements on an additional electron. For each nonlocal N-electron system, Alice first entangles it with the additional electron, and then she projects the additional electron onto an orthogonal basis for dividing the N-electron systems into two groups. In the first group, the N parties obtain a subset of N-electron systems in a maximally entangled state directly. In the second group, they obtain some less-entangled N-electron systems, which are the resource for the entanglement concentration in the next round. By iterating the entanglement concentration process several times, the present ECP has the maximal success probability, which is the theoretical limit of an ECP, equal to the entanglement of the partially entangled state, and higher than the others. This ECP may be useful in quantum computers based on electron-spin systems in the future.     

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.     

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.     

Consequent entanglement concentration of a less-entangled electronic cluster state with controlled-not gates

We present a highly efficient entanglement concentration protocol （ECP） for a four-electron system in a less-entangled cluster state. In this ECP, we only require one pair of less-entangled electron cluster states and one ancillary electron to complete the task. With the help of the controlled-not （CNOT） gate, the concentrated maximally entangled state can be retained for further application with some success probability. On the other hand, the discarded items can be reused to obtain a high success probability. All the features make this ECP useful in the current quantum information field.     

Entanglement concentration for an arbitrary hybrid less-entangled state and W state using quantum dots and a microcavity coupled system

We propose a practical entanglement concentration protocol(ECP) for a hybrid entangled state using quantum dots and a microcavity coupled system.A hybrid less-entangled state can be concentrated to a most-entangled state with a certain probability using only one ancillary single photon.Moreover,using this protocol,we can also concentrate an arbitrary three-particle less-entangled W state using two ancillary photons and classical communication.The proposed protocols provide us with a useful method to concentrate less-entangled states,which can be implemented with current technology.     

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.     

Linear-Optics-Based Entanglement Concentration of Four-Photon χ-type States for Quantum Communication Network

We present an efficient entanglement concentration protocol (ECP) for partially entangled four-photon χ-type states in the first time with only linear optical elements and single-photon detectors. Without any ancillary particles, the parties in quantum communication network can obtain a subset of four-photon systems in the standard |χ ⁰⁰〉 state from a set of four-photon systems in a partially entangled χ-type state with the parameter-splitting method developed by Ren et al. (Phys. Rev. A 88:012302, 2013). The present ECP has the optimal success probability which is determined by the component with the minimal probability amplitude in the initial state. Moreover, it is easy to implement this ECP in experiment.     

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.     

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.     

Linear optical scheme for entanglement concentration of two partially entangled three-photon ${\sf W}$ states

We propose a practical scheme for concentrating entanglement in a pair of unknown partially entangled three-photon W states with only linear optics and photon detectors. In the scheme, Alice, Bob, and Charlie at three distant parties can obtain one maximally entangled three-photon W state with a certain success probability from two identical partially entangled three-photon W states by local operations and classical communication. The proposed setup is very simple, which greatly simplifies the experimental realization of the scheme.     

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.     

Deterministic Frequency-Based Polarization Entanglement Concentration with the Multipartite Less-Hyperentangled State

A deterministic entanglement concentration protocol (ECP) is demonstrated in a multipartite less-hyperentangled system, containing the simultaneous entanglements in polarization and frequency degrees of freedom. The motivation is that the entangled system in frequency degree of freedom suffers little from the effects of the channel noise in optical fibers. Consequently, a maximally entangled system can be generated in polarization degree of freedom from the multipartite less-hyperentangled system with cross-Kerr nonlinearity. Compared with the conventional ECPs that have success probabilities less than one while iterating their recursive entanglement concentration processes several times to achieve a maximally entangled system in polarization degree of freedom, the present ECP can generate a maximally entangled system in polarization degree of freedom in two steps with a certainty. It may be useful for enhancing the efficiency of communications in long-distance quantum computation networks.     

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.     

Electronic cluster state entanglement concentration based on charge detection

We propose an efficient entanglement concentration protocol （ECP） based on electron-spin cluster states assisted with single electrons. In the ECP, we adopt the electron polarization beam splitter （PBS） and the charge detector to construct the quantum nondemolition measurement. According to the result of the measurement of the charge detection, we can ultimately obtain the maximally entangled cluster states. Moreover, the discarded items can be reused in the next round to reach a high success probability. This ECP may be useful in current solid quantum computation.     

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.     

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.     

Efficient Entanglement Concentration for Arbitrary Less-Entangled N-Atom GHZ State

In this paper, we put forward an effective ECP for arbitrary less-entangled N-atom GHZ state with the help of the photonic Faraday rotation. In our protocol, we only require one pair of less-entangled atom state, one auxiliary atom and one auxiliary photon, and can complete the concentration task with relatively high success probability. Moreover, our ECP can be used repeatedly to further increase the success probability. Especially, if consider the practical operation and imperfect detection, our protocol is more efficient. This ECP may be useful in current quantum information processing.