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Chinese Physics B

Optimal entanglement concentration for three-photon W states with parity check measurement

Lan Zhou, Yu‐Bo Sheng, Shengmei Zhao

Published Feb 1, 2013• 20 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/22/2/020307

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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.
We present an optimal entanglement concentration ECP for an arbitrary less-entangled W state. By two of the parties say Alice and Charlie performing one parity check measurements, they can obtain the maximally entangled W state with a certain probability. Otherwise, they can obtain another lesser-entangled W state with another probability, which can be used to reconcentrated into a maximally entangled W state. By iterating this ECP several times, it has the maximal success probability. This ECP maybe an optimal one and is useful in current quantum information processing.
We present two entanglement concentration protocols (ECPs) for arbitrary three-electron W state based on their charges and spins. Different from other ECPs, in both two ECPs, with the help of the electronic polarization beam splitter (PBS) and charge detection, the less-entangled W state can be concentrated into a maximally entangled state only with some single charge qubits. The second ECP is more optimal than the first one, for by constructing the complete parity check gate, the second ECP can be used repeatedly to further concentrate the less-entangled state and obtain a higher success probability. Therefore, both the ECPs, especially the second one may be useful in current quantum information processing.
We propose an optimal nonlocal entanglement concentration protocol (ECP) for multiphoton systems in a partially entangled pure state, resorting to the projection measurement on an additional photon. One party in quantum communication first performs a parity-check measurement on her photon in an NNN-photon system and an additional photon, and then she projects the additional photon into an orthogonal Hilbert space for dividing the original NNN-photon systems into two groups. In the first group, the NNN parties will obtain a subset of NNN-photon systems in a maximally entangled state. In the second group, they will obtain some less-entangled NNN-photon 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 just equivalent to the entanglement of the partially entangled state. That is, this ECP is an optimal one.
We present two two-step practical entanglement concentration protocols for concentrating an arbitrary three-particle less-entangled WWW state into a maximally entangled WWW state assisted with single photons. The first protocol uses the linear optics and the second protocol adopts the cross--Kerr nonlinearity to perform the protocol. In the first protocol, based on the postselection principle, three parties say Alice, Bob, and Charlie in different distant locations can obtain the maximally entangled WWW state from the arbitrary less-entangled WWW state with a certain success probability. In the second protocol, the parties are not required to possess the sophisticated single-photon detectors and the concentrated photon pair can be retained after performing this protocol successfully. Moreover, the second protocol can be repeated to get a higher success probability. Both protocols may be useful in practical quantum-information applications.
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 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.