Perfect entanglement concentration of an arbitrary four-photon polarization entangled state via quantum nondemolition detectors

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.

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

“…In most cases, the maximally entangled state is the optimal choice into the maximally entangled cluster states. [31][32][33][34][35][36][37] In 2013, Zhao et al proposed an ECP for a four-electron cluster state using two auxiliary two-electron entangled states assisted by charge detectors. [31] In 2014, Yan et al presented an ECP for a fourphoton cluster state using two auxiliary photon pairs based on the C-NOT gates.…”

“…In 2016, Wang et al developed an ECP based on Si et al's work, which involves concentrating an arbitrary four-photon entangled cluster state into a maximally entangled cluster state using conventional projection measurement. [34] In 2017, Du et al investigated QDcavity coupled systems to concentrate a partially entangled system of four-electron spins with two unknown parameters. [35] In 2021, Li et al proposed an ECP for the less-entangled six-photon cluster states, and in 2022, Song et al proposed an efficient ECP for the less-entangled five-photon cluster states.…”

“…[60] In this paper, a complete and economical ECP for the lessentangled four-photon cluster states with four unknown coefficients is proposed assisted by PCG and C-Z gate. Compared to the previously proposed ECPs, [28,29,[31][32][33][34][35][36][37] our ECP offers the ability to concentrate the less-entangled four-photon cluster states with four unknown coefficients while possessing several distinctive features: i) The PCG and C-Z gate are both constructed with only a QD-cavity coupled system and some linear optical elements, which simplifies quantum circuit and reduces the impact of interaction between photons and spins. ii) All coefficients of the initial less-entangled cluster states are unknown, which eliminates the need for the preparation of the additional ancillary states.…”

Generation and concentration of two-photon partially entangled Knill–Laflamme–Milburn state

“…Since the pioneering work of concentrating partial entanglement by local operations [18], entanglement concentration techniques have shown significant progress. In order to solve decoherence due to the interaction of entangled quantum systems, various kinds of entanglement concentration protocols have been proposed [19][20][21][22][23][24].…”

Optimal multi-photon entanglement concentration with the photonic Faraday rotation

“…Only a few entanglement concentration protocols can deal with the decoherence problem in the multi-photon system. [50][51][52][53][54][55][56][57][58][59][60] The cavity is a highly-efficient platform for performing the quantum information tasks, because the interaction between atoms and photons in the cavity can be well controlled. [64][65][66][67][68][69][70][71][72][73][74][75][76][77][78] In the quantum information tasks, we can adopt the spatially separated cavities to be quantum nodes by making the atoms strongly interact with the local cavities.…”