Efficient entanglement concentration for electron-spin W state with the charge detection

We propose an optimal entanglement concentration protocol (ECP) for nonlocal \(N\)-electron systems in a partially entangled Greenberger–Horne–Zeilinger (GHZ) pure state, resorting to charge detection and the projection measurement on an additional electron. For each nonlocal \(N\)-electron system in a partially entangled GHZ state, one party in quantum communication, say Alice first entangles it with an additional electron, and then, she projects the additional electron into 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, the theoretical limit of an ECP as it just equals to the entanglement of the partially entangled state, far higher than others. Moreover, this ECP for an \(N\)-electron GHZ-type state requires only one additional electron, not two or more, and it does not resort to a collective unitary evolution, far different from others, which may decrease the difficulty for its implementation in experiment. When it is used for an \(N\)-electron W-type state, \(N-1\) additional electrons are required only.

Three entanglement concentration protocols (ECPs) are proposed. The first ECP and a modified version of that are shown to be useful for the creation of maximally entangled cat and GHZ-like states from their non-maximally entangled counterparts. The last two ECPs are designed for the creation of maximally entangled $(n+1)$-qubit state $\frac{1}{\sqrt{2}}\left(|\Psi_{0}\rangle|0\rangle+|\Psi_{1}\rangle|1\rangle\right)$ from the partially entangled $(n+1)$-qubit normalized state $\alpha|\Psi_{0}\rangle|0\rangle+\beta|\Psi_{1}\rangle|1\rangle$, where $\langle\Psi_{1}|\Psi_{0}\rangle=0$ and $|\alpha|\neq\frac{1}{\sqrt{2}}$. It is also shown that W, GHZ, GHZ-like, Bell and cat states and specific states from the 9 SLOCC-nonequivalent families of 4-qubit entangled states can be expressed as $\frac{1}{\sqrt{2}}\left(|\Psi_{0}\rangle|0\rangle+|\Psi_{1}\rangle|1\rangle\right)$ and consequently the last two ECPs proposed here are applicable to all these states. Quantum circuits for implementation of the proposed ECPs are provided and it is shown that the proposed ECPs can be realized using linear optics. Efficiency of the ECPs are studied using a recently introduced quantitative measure (Phys. Rev. A $\textbf{85}$, 012307 (2012)). Limitations of the measure are also reported.

The distribution of maximal entanglement stands as a pivotal technique in long-distance practical quantum communication. Specifically, achieving high-fidelity entanglement distribution leans upon efficacious entanglement purification and entanglement concentration. In this paper, we materialize error-rejecting nonlocal entanglement purification protocol (EPP) and entanglement concentration protocol (ECP) for solid-state emitter systems assisted by the scattering property of photon-emitter in one-dimensional waveguide. The parity-check gates of both the EPP and ECP can herald the faulty events with the help of the detectors that click, so they are accomplished, in principle, with unity fidelities, which are conducive to implement two protocols. Moreover, additional emitters are unnecessary except a single photon.

We propose a single-photon-assisted entanglement concentration protocol (ECP) for nonlocal N-photon systems in a partially entangled pure W-class state with linear optical elements. Only one of the N parties in quantum communication prepares an ancillary photon and operates the entanglement concentration process for picking up the standard N-photon W state from each partially entangled pure W-class state by choosing the two-mode instances from a polarization beam splitter. Compared with other ECPs for W-class states, our protocol has some advantages. First, it requires only linear optical elements. Second, it requires an N-photon system and an ancillary photon for each round of concentration, not two systems. Third, only one party asks other parties to retain or discard their photons. All these advantages make our ECP more feasible and more convenient than others.

We demonstrate two entanglement concentration protocols (ECPs) for photon pairs in less-hyperentanglement, the simultaneous entanglement in multiple degrees of freedom. Using these ECPs, some maximally entangled states in polarization can be reconstructed deterministically from less-hyperentangled ones shared between remote participants. Both of the success probabilities are 100% in principle, and they do not require additional single photons. The former is implemented with the passive linear optics, which is achievable with current technology. The later adopts the cross-Kerr nonlinearity media to complete this task, which can increase the efficiency of the entanglement concentration process since it does not require the sophisticated single-photon detectors for measurements. The two ECPs are useful for practical long-distance quantum communication due to the fact that the entangled state in either the spatial degree of freedom or the frequency degree of freedom suffers little from channel noise in optical fiber.

We propose an optimal nonlocal entanglement concentration protocol (ECP) for\nmulti-photon systems in a partially entangled pure state, resorting to the\nprojection measurement on an additional photon. One party in quantum\ncommunication first performs a parity-check measurement on her photon in an\nN-photon system and an additional photon, and then she projects the additional\nphoton into an orthogonal Hilbert space for dividing the original $N$-photon\nsystems into two groups. In the first group, the N parties will obtain a subset\nof $N$-photon systems in a maximally entangled state. In the second group, they\nwill obtain some less-entangled N-photon systems which are the resource for the\nentanglement concentration in the next round. By iterating the entanglement\nconcentration process several times, the present ECP has the maximal success\nprobability which is just equivalent to the entanglement of the partially\nentangled state. That is, this ECP is an optimal one.\n

We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon in a certain probability, while the conventional ones require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second one is implemented with cross-Kerr nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with current experiment. With cross-Kerr nonlinearities, it does not require the sophisticated single-photon detectors and can be repeated to get a higher success probability. Moreover, the second protocol can get the higher entanglement transformation efficiency and it maybe the most economical one by far. Meanwhile, both of protocols are more suitable for multi-photon system concentration, because they need less operations and classical communications. All these advantages make two protocols be useful in current long-distance quantum communications.

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.

We propose an entanglement concentration protocol (ECP) for spatially separated negatively charged nitrogen-vacancy (N-V) centers in a partially entangled W state, resorting to a hybrid quantum circuit and some ancillary single photons. The hybrid quantum circuit is composed of a single N-V center coupled on the periphery of a microtoroidal resonator and linear-optical elements. Exploiting currently available techniques (for example, the single-photon input–output process), the standard maximally entangled W state could be distilled from the initial partially entangled W state. Compared with other ECPs for W-class states, we discuss the advantages of the present protocol. Further, the feasibility and the experimental challenges of the protocol are discussed by considering currently available techniques.

Density downramp injection has been demonstrated to be an elegant and efficient approach for generating high-quality electron beams in laser wakefield accelerators. Recent studies have demonstrated the possibilities of generating electron beams with charges ranging from tens to hundreds of picocoulombs while maintaining good beam quality. However, the plasma and laser parameters in these studies have been limited to specific ranges or attention has been focused on separate physical processes such as beam loading, which affects the uniformity of the accelerating field and thus the energy spread of the trapped electrons, the repulsive force from the rear spike of the bubble, which reduces the transverse momentum p⊥ of the trapped electrons and results in small beam emittance, and the laser evolution when traveling in the plasma. In this work, we present a comprehensive numerical study of downramp injection in the laser wakefield, and we demonstrate that the current profile of the injected electron beam is directly correlated with the density transition parameters, which further affects the beam charge and energy evolution. By fine-tuning the plasma density parameters, electron beams with high charge (up to several hundreds of picocoulombs) and low energy spread (around 1% FWHM) can be obtained. All these results are supported by large-scale quasi-three-dimensional particle-in-cell simulations. We anticipate that the electron beams with tunable beam properties generated using this approach will be suitable for a wide range of applications.

Cluster states, whose model are a remarkably rich structure in measurement-based quantum computation, hold high degree of entanglement, while entanglement is very fragile during the process of transmission because of the inevitable interaction with the environment. We propose two entanglement concentration protocols for four-particle linear cluster states which and are susceptible to the decoherence and the imperfect communication setups. In the first protocol, POVM operators are introduced to maximize the success probability, and the second protocol is based on cross-Kerr nonlinearity which is utilized to check the parity between the original particle and the ancillary particle. Both of the protocols have their own advantages. The first one can be easily realized in experiment by linear optics, while the one with cross-Kerr nonlinearity reach more than 90% success probability by iteration. Since the wide application of cluster states, the two protocols are efficient and valuable to different fields of quantum communication.

The purpose of this paper is a proposal on entanglement concentration protocol for cluster states. The protocol uses CNOT gate operation and is assisted with a single qubit. Moreover, the local and non-local operations are performed by a single party. We also make a comparative numerical study of the residual entanglement left out after the execution of each step of the protocol.

We propose a scheme to implement fermionic quantum SWAP and Fredkin gates for spin qubits with the aid of charge detection. The scheme is deterministic without the need of qubit—qubit interaction, and the proposed setups consist of simple polarizing beam splitters, single-spin rotations, and charge detectors. Compared with linear optics quantum computation, this charge-measurement-based qubit scheme greatly enhances the success probability for implementing quantum SWAP and Fredkin gates and greatly simplifies the experimental realization of scalable quantum computers with noninteracting electrons.

We consider entanglement distillation with noisy operations in which quantum measurements that constitute a general quantum operation are particularly noisy. We present a protocol for purifying noisy measurements and show that imperfect local operations can distill entanglement. The protocol works for arbitrary noisy measurements in general and is cost-effective and resource-efficient with single additional qubit per party to resolve the distillation of entanglement. The purification protocol is feasible with currently available quantum technologies and readily applied to entanglement applications.

A new interferometry is presented for direct visualization of pure phase objects having low spatial frequency, such as electromagnetic microfields. A thin crystal of silicon prepared using argon ion milling is installed at the standard specimen position. This silicon crystal works as an electron beam splitter and forms diffraction spots in the back focal plane. Using the objective aperture, [000], [111] and [111] spots are selected as coherent electron sources to illuminate the specimen located at the area-selecting aperture position. The lattice image of silicon is formed below the area-selecting aperture position by decreasing the electric current of the objective lens. Three defocused images of the specimen are observed in the fluorescent screen by overexciting the first intermediate lens. We have successfully visualized equipotential lines around a latex particle charged by electron beam irradiation. The computer-simulated image was consistent with the experimental image.