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Advanced Quantum Technologies

A Two‐Step Entanglement Concentration for the Less‐Entangled Four‐Photon Cluster States

Zi‐Long Yang, Xiao‐Ming Xiu, Liu Lv, Xiao‐Cheng Mo, Si‐Tong Liu, Xin‐Ying Wang, Zi‐Lin Zhao, Zi-Qing Yuan, Si-Ge Chen, Xin‐Yi Zhang, Haikuan Dong, Yan‐Qiang Ji, Li Dong

Published Jan 7, 2024• 11 citations
Publisher

Abstract

Abstract Entanglement concentration serves as an essential tool to obtain the maximally entangled states from the less‐entangled states in quantum information processing tasks. An efficient two‐step entanglement concentration protocol (ECP) is proposed to concentrate the less‐entangled four‐photon cluster states with four unknown coefficients into the maximally entangled states in this paper. The protocol utilizes parity‐check gate and photon‐polarized controlled‐Z gate, constructed with a single semiconductor quantum dot in a single optical microcavity (quantum dot‐cavity coupled system) and several linear optical elements. The discarded quantum states can be recycled in the next round concentration to achieve a higher success probability. Under conditions of strong coupling and weak side leakage rate, the ECP can tend toward ideal fidelity and efficiency. Compared to the previously proposed ECPs that utilize various auxiliary tools such as additional entangled states and complex quantum logic gates, the ECP significantly simplifies the analysis process and enables efficient implementation. Thus, the ECP is more economical and feasible in future optical systems.

DOI
10.1002/qute.202300376

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We present an entanglement concentration protocol (ECP) for the less-entangled W-state with quantum-dot and microcavity coupled systems. The present protocol uses quantum nondemolition measurement on the spin parity to construct the hybrid parity check gate. Different from other ECPs, the less-entangled W-state with quantum-dot and microcavity coupled systems can be concentrated with the help of some single photons. The most significant advantage is that during the whole ECP, we do not destroy the W-state and only consume some local single photons. The whole protocol can be repeated to obtain a higher success probability. It may be useful in current quantum information processing.
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.
We present a systematic entanglement concentration protocol (ECP) for an arbitrary unknown less-entangled three-photon W state, resorting to the optical property of the quantum-dot spins inside one-sided optical microcavities. In our ECP, the parties obtain not only some three-photon systems in the partially entangled with two unknown parameters when one of the parties picks up the robust odd-parity instance with the parity-check gate (PCG) on his two photons, but also some entangled two-photon systems by keeping the even-parity instance in the first step. By exploiting the above three-photon and two-photon systems with the same parameters as the resource for the second step of our ECP, the parties can obtain a standard three-photon W state by keeping the robust odd-parity instance. Meanwhile, the systems in the even-parity instance can be used as the resource in the next round of our ECP. The success probability of our ECP is largely increased by iteration of the ECP process. As it does require that all the coefficients are unknown for the parties, our ECP maybe have good applications in quantum communication network in future.
We propose two efficient entanglement concentration protocols (ECPs) for arbitrary less-entangled single-photon entanglement (SPE). Different from all the previous ECPs, these protocols not only can obtain the maximally SPE, but also can protect the single qubit information encoded in the polarization degree of freedom. These protocols only require one pair of less-entangled single-photon entangled state and some auxiliary single photons, which makes them economical. The first ECP is operated with the linear optical elements, which can be realized in current experiment. The second ECP adopts the cross-Kerr nonlinearities. Moreover, the second ECP can be repeated to concentrate the discard states in some conventional ECPs, so that it can get a high success probability. Based on above properties, our ECPs may be useful in current and future quantum communication.
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.
Abstract We show how to concentrate an arbitrary four-photon polarization entangled state into a maximally entangled state based on some quantum nondemolition detectors. The entanglement concentration protocol (ECP) resorts to an ancillary single-photon resource and the conventional projection measurement on photons to assist the concentration, which makes it more economical. Our ECP involves weak cross-Kerr nonlinearities, X homodyne measurement and basic linear-optical elements, which make it feasible in the current experimental technology. Moreover, the ECP considers cyclic utilization to enhance a higher success probability. Thus, our scheme is meaningful in practical applications in quantum communication.