Efficient Entanglement Concentration Protocol Research Articles

Logic W‐state concentration with parity check

Logic W state, which replaces each physical qubit in a W state with a Greenberger–Horne–Zeilinger state is robust against photon transmission loss in long-distance quantum communication. In practical application, the environmental noise may make maximally entangled logic W state degrade to less entangled state, which largely limits its application. In this article, we propose an efficient entanglement concentration protocol (ECP) for logic W state, which can recover the less entangled logic W state into the maximally entangled logic W state. Our ECP relies on the nondemolition polarization parity check (PPC) gate constructed with cross-Kerr nonlinearity. The distilled maximally entangled logic W state can be preserved for other application. Moreover, when the ECP fails, we can repeat the ECP to further concentrate the distilled less entangled logic W state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in quantum communication 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 entanglement concentration of arbitrary unknown less-entangled three-atom W states via photonic Faraday rotation in cavity QED

We propose an efficient entanglement concentration protocol (ECP) for nonlocal three-atom systems in an arbitrary unknown less-entangled W state, resorting to the Faraday rotation of photonic polarization in cavity quantum electrodynamics and the systematic concentration method. In the first step of the present ECP, one party in quantum communication performs a parity-check measurement on her two atoms in two three-atom systems for dividing the composite six-atom systems into two groups. In the first group, the three parties will obtain some three-atom systems in a less-entangled state with two unknown coefficients. In the second group, they will obtain some less-entangled two-atom systems. In the second step of the ECP, the three parties can obtain a subset of three-atom systems in the standard maximally entangled W state by exploiting the above three-atom and two-atom systems. Moreover, the preserved systems in the failed instances can be used as the resource for the entanglement concentration in the next round. The total success probability of the ECP can therefore be largely increased by iterating the entanglement concentration process several rounds. The distinct feature of our ECP is that we can concentrate arbitrary unknown atomic entangled W states via photonic Faraday rotation, and thus it may be universal and useful for entanglement concentration in future quantum communication network.

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.

Efficient entanglement concentration for concatenated Greenberger–Horne–Zeilinger state with the cross-Kerr nonlinearity

Concatenated Greenberger---Horne---Zeilinger (C-GHZ) state, which encodes physical qubits in a logic qubit, has great application in the future quantum communication. We present an efficient entanglement concentration protocol (ECP) for recovering less-entangled C-GHZ state into the maximally entangled C-GHZ state with the help of cross-Kerr nonlinearities and photon detectors. With the help of the cross-Kerr nonlinearity, the obtained maximally entangled C-GHZ state can be remained for other applications. Moreover, the ECP can be used repeatedly, which can increase the success probability largely. Based on the advantages above, our ECP may be useful in the future long-distance quantum communication.

Efficient multipartite entanglement concentration protocol for nitrogen-vacancy center and microresonator coupled systems

Here in this study we propose an efficient entanglement concentration protocol (ECP) for separate nitrogen-vacancy (NV) centers, resorting to the single-photon input---output process of the NV center and microtoroidal resonator coupled system. In the proposed ECP, one ancillary single-photon is prepared and passed through a hybrid quantum circuit. By measuring the photon under the suitable polarization basis, maximally entangled state between the separate NV centers can be obtained with a certain success probability. The solid entanglement will be preserved during the process, which can be iterated several rounds to obtain an optimal total success probability. We also discuss the experimental feasibility of the protocol by considering current technologies, and we believe that the protocol is useful in the future applications of long-distance quantum communication and distributed quantum computation.

Entanglement distillation for quantum communication network with atomic-ensemble memories.

Atomic ensembles are effective memory nodes for quantum communication network due to the long coherence time and the collective enhancement effect for the nonlinear interaction between an ensemble and a photon. Here we investigate the possibility of achieving the entanglement distillation for nonlocal atomic ensembles by the input-output process of a single photon as a result of cavity quantum electrodynamics. We give an optimal entanglement concentration protocol (ECP) for two-atomic-ensemble systems in a partially entangled pure state with known parameters and an efficient ECP for the systems in an unknown partially entangled pure state with a nondestructive parity-check detector (PCD). For the systems in a mixed entangled state, we introduce an entanglement purification protocol with PCDs. These entanglement distillation protocols have high fidelity and efficiency with current experimental techniques, and they are useful for quantum communication network with atomic-ensemble memories.

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.

Arbitrary Partially Entangled Three-Electron W State Concentration with Controlled-Not Gates

We describe an efficient entanglement concentration protocol (ECP) for an arbitrary partially entangled three-electron W state. We show that with the help of two ancillary single electrons, the concentration task can be well completed. This ECP has several advantages: Firstly, we only require one pair of partially entangled states. Secondly, only two single electrons are used during the whole protocol. Thirdly, we do not require all the parties to participate in the whole process, and only two parties are needed to perform the operation. Fourthly, the protocol can be repeated to obtain a high success probability. This ECP may be useful in current quantum computation and quantum communication.

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.

Concentration of entangled nitrogen-vacancy centers in decoherence free subspace

Exploiting the input-output process of low-Q cavities confining nitrogen-vacancy centers, we present an efficient entanglement concentration protocol on electron spin state in decoherence free subspace. Less entangled state can be concentrated to maximally entangled state with the assistance of single photon detection. With its robustness and scalability, the present protocol is immune to dephasing and can be further applied to quantum repeaters and distributed quantum computation.

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 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.

Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system

We describe a high efficient entanglement concentration protocol (ECP) for multi-particle less-entangled nitrogen-vacancy (N-V) center and microtoroidal resonator system. In the ECP, we only require one pair of less-entangled state, two auxiliary N-V center in microcavities and some single photons. After the photon passing through the microcavity, by measuring the polarization of the photon, a maximally entangled W state can be obtained with some success probability. This ECP does not need to destroy the solid qubit, which makes it more feasible. Moreover, by resorting to more single photons, it can be repeated to reach a high success probability. These features make this ECP useful in current long-distance quantum communications.

Entanglement concentration for multi-particle partially entangled W state using nitrogen vacancy center and microtoroidal resonator system

In this paper, we present an efficient entanglement concentration protocol (ECP) for N spatially separated nitrogen-vacancy (N-V) centers coupled to microtoroidal resonators in a partially entangled W state. The robustness of W-type entanglement contrasts strongly with the Greenberger-Horne-Zeilinger (GHZ) state which is fully separable after loss of one qubit. We construct the parity-check gate by introducing an auxiliary N-V center in microcavity and a single photon. Based on the parity-check measurement and local operations, the remote parities can distill a maximally entangled W state from a partially entangled state with a certain success probability. By iterating the concentration process several times, the present ECP can obtain an optimal yield. With its robustness and scalability, the present ECP for entangled N-V center ensembles can be widely applied to quantum repeaters and long-distance quantum communications.

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.

Efficient entanglement concentration for arbitrary single-photon multimode W state

We put forward an efficient entanglement concentration protocol (ECP) for recovering the single-photon less-entangled W state into the maximally entangled W state with only two conventional auxiliary photons. The ECP includes two local steps, both of which are based on the weak cross-Kerr nonlinearities and the variable beam splitter (VBS). Benefiting from the cross-Kerr nonlinearities and the VBS, the ECP can be used repeatedly to further concentrate the less-entangled W state. All the advantages indicate that our protocol may be feasible and convenient in current quantum communications areas.

Efficient entanglement concentration for quantum dot and optical microcavities systems

A recent paper (Chuan Wang in Phys Rev A 86:012323, 2012) discussed an entanglement concentration protocol (ECP) for partially entangled electrons using a quantum dot and microcavity coupled system. In his paper, each two-electron spin system in a partially entangled state can be concentrated with the assistance of an ancillary quantum dot and a single photon. In this paper, we will present an efficient ECP for such entangled electrons with the help of only one single photon. Compared with the protocol of Wang, the most significant advantage is that during the whole ECP, the single photon only needs to pass through one microcavity which will increase the total success probability if the cavity is imperfect. The whole protocol can be repeated to get a higher success probability. With the feasible technology, this protocol may be useful in current long-distance quantum communications.

Efficient entanglement concentration for arbitrary less-entangled NOON states

We put forward an efficient entanglement concentration protocol (ECP) for arbitrary less-entangled NOON state. In the protocol, we resort to the weak cross-Kerr nonlinearity to complete this task. Different from other ECPs, this protocol can be reused to get a high success probability. We do not need to know the exact coefficients of the initial state. Moreover, we even do not need to know the exact photon number of the initial NOON state. This protocol may be useful and convenient in the current quantum information processing.

Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system

We present an efficient entanglement concentration protocol (ECP) for electron spins based on quantum-dot and microcavity coupled systems. In our ECP, each two-electron spin system in a partially entangled state can be concentrated with the assistance of an ancillary quantum dot and a single photon, not two copies of two-electron spin systems. With current and near-future technology, the locally maximal entanglement of electron spins can be achieved, and our ECP can be used in long-distance quantum communications.