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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Electronic Entanglement Concentration for the Concatenated Greenberger-Horne-Zeilinger State

Concatenated Greenberger-Horne-Zeilinger (C-GHZ) state, which encodes many physical qubits in a logic qubit will have important applications in both quantum communication and computation. In this paper, we will describe an entanglement concentration protocol (ECP) for electronic C-GHZ state, by exploiting the electronic polarization beam splitters (PBSs) and charge detection. This protocol has several advantages. First, the parties do not need to know the exact coefficients of the initial less-entangled C-GHZ state, which makes this protocol feasible. Second, with the help of charge detection, the distilled maximally entangled C-GHZ state can be remained for future application. Third, this protocol can be repeated to obtain a higher success probability. We hope that this protocol can be useful in future quantum computation based on electrons.     

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.     

Efficient three-step entanglement concentration for an arbitrary four-photon cluster state

We propose an entanglement concentration protocol to concentrate an arbitrary partially-entangled four-photon cluster state.As a pioneering three-step entanglement concentration scheme,our protocol only needs a single-photon resource to assist the concentration in each step,which makes this protocol more economical.With the help of the linear optical elements and weak cross-Kerr nonlinearity,one can obtain a maximally-entangled cluster state via local operations and classical communication.Moreover,the protocol can be iterated to obtain a higher success probability and is feasible under current experimental conditions.     

Unknown State Transmission Using GHZ States via Collective Noise Channel

Two protocols for transmitting an unknown single-photon state and anunknown non-maximally entangled EPR state are presented by using thequantum channel of three-phonton GHZ (Greenberger-Horne-Zeilinger)state, which can be realized with unitary success probability whencollective noise is taken into account. The protocols can also begeneralized to transmit multi-photon state or to realize quantumcommunication in collective noise channel.     

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.     

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.     

An Efficient Scheme for Entanglement Concentration of Arbitrary Four-Photon States

The maximally entanglement will become less-entangled state because of the effects of decoherence. However, maximally entangled states are usually important for most of the quantum information processing protocols. So we propose a practical entanglement concentration protocol of an arbitrary four-photon less-entangled state assisted with single photons, which greatly reduces the difficulty of the experimental realization. In our scheme, we only employ three steps, a four-photon cluster state can be acquired with a certain probability by three affiliated photons. The protocol adopts the linear optical elements and weak cross-Kerr media, which make the scheme more simple and feasible in the experiment.     

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.     

Multiple teleportation via partially entangled GHZ state

Quantum teleportation is important for quantum communication. We propose a protocol that uses a partially entangled Greenberger–Horne–Zeilinger (GHZ) state for single hop teleportation. Quantum teleportation will succeed if the sender makes a Bell state measurement, and the receiver performs the Hadamard gate operation, applies appropriate Pauli operators, introduces an auxiliary particle, and applies the corresponding unitary matrix to recover the transmitted state.We also present a protocol to realize multiple teleportation of partially entangled GHZ state without an auxiliary particle. We show that the success probability of the teleportation is always 0 when the number of teleportations is odd. In order to improve the success probability of a multihop, we introduce the method used in our single hop teleportation, thus proposing a multiple teleportation protocol using auxiliary particles and a unitary matrix. The final success probability is shown to be improved significantly for the method without auxiliary particles for both an odd or even number of teleportations.     

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.     

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.