Entanglement concentration and hidden entanglement

Paul Cummins

Dan Liu, Cong Yan, Wei Ma

We propose an entanglement concentration protocol (ECP) for nonlocal N -electron systems in a partially entangled W state, resorting to ancillary single electrons and charge detection. Compared with other ECPs for W states, our ECP has some advantages. Firstly, only an entangled N -electron system is required in each round of entanglement concentration, not two copies. Secondly, only one of the users, say Charlie, needs to perform the protocol, while all parties should perform the same operations as Charlie in other ECPs for W -class states. Thirdly, only Charlie asks other parties to retain or discard their electrons, and they do not need to check their measurement results, which greatly simplifies the complication of classical communication. Fourthly, our ECP has a higher success probability than other ECPs for W -class states as the parties can recycle their concentration when they obtain a system in another W -class state with less entanglement. These advantages make our ECP more feasible for practical applications.

Zhou, Lan, Jiong Liu, Sheng-Yang Zhao

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.

Lan Zhou, Yu‐Bo Sheng

We propose two optimal entanglement concentration protocols (ECPs) for arbitrary single-photon multi-mode W state and multi-photon polarization W state, respectively. In both ECPs, we only require one pair of partially entangled W state, and do not consume any auxiliary photon. Both ECPs are based on the linear optics which can be easily realized. On the other hand, the concentrated maximally entangled states can be remained, which are quite different from the previous ECPs. Moreover, for the concentration of the arbitrary single-photon N-mode W state or N-mode polarization W state, the total success probability is equal to Nth the modulus square of the Schmidt coefficient of the smallest magnitude. It makes both ECPs optimal than all the previous ECPs. Our ECPs may be useful in current quantum communication fields.

Fuli Li, Muhammad Suhail Zubairy