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Frontiers of Physics

Entanglement concentration for a non-maximally entangled four-photon cluster state

Xiang Yan, Ya‐Fei Yu, Zhi‐Ming Zhang

Published Aug 4, 2014• 8 citations
Publisher

Abstract

We present a scheme for locally concentrating a non-maximally entangled four-photon cluster state into a maximally-entangled four-photon cluster state. This scheme has a high success probability. The controlled-NOT (CNOT) gate is a crucial ingredient in this scheme, and we use a nearly deterministic CNOT gate, which is similar with that first introduced by Nemoto et al. ( Phys. Rev. Lett. , 2004, 93: 250502). This CNOT gate has a simple structure and does not need the strong nonlinearity.

DOI
10.1007/s11467-014-0435-z

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We present a scheme for locally concentrating a non-maximally entangled four-photon cluster state into a maximally-entangled four-photon cluster state. This scheme has a high success probability. The controlled-NOT (CNOT) gate is a crucial ingredient in this scheme, and we use a nearly deterministic CNOT gate, which is similar with that first introduced by Nemoto et al. ( Phys. Rev. Lett. , 2004, 93: 250502). This CNOT gate has a simple structure and does not need the strong nonlinearity.
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 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.
We present a protocol for concentrating an arbitrary four-photon entangled state into a maximally entangled state assisted with singled photons. The concentration protocol uses the linear optics and the cross-Kerr nonlinearity based on the post selection principle. Four parties called Alice, Bob, Charlie and Dan in different distant locations can obtain the cluster state from an arbitrary entangled four-photon state with a certain probability. Quantum non-demolition (QND) measurements are available in this protocol. Moreover, this scheme can be steady with a higher success possibility.
We experimentally demonstrate an optical controlled-NOT (CNOT) gate with arbitrary single inputs based on a 4-photon 6-qubit cluster state entangled both in polarization and spatial modes. We first generate the 6-qubit state, and then, by performing single-qubit measurements, the CNOT gate is applied to arbitrary single input qubits. To characterize the performance of the gate, we estimate its quantum process fidelity and prove its entangling capability. In addition, our results show that the gate cannot be reproduced by local operations and classical communication. Our experiment shows that such hyper-entangled cluster states are promising candidates for efficient optical quantum computation.
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.