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International Journal of Modern Physics B

Entanglement concentration for six-particle cluster states

Meiqi Li, Xiaoqing Tan, Tingting Song

Published Apr 20, 2021• 2 citations
Publisher

Abstract

Multi-particle cluster states play a significant role in quantum information processing. However, due to the inevitable interaction with the environment in the transmission process, the fidelity of entanglement decreases. To distill the perfect cluster states, we present two schemes for arbitrary six-particle cluster states. POVM local unitary operators that are obtained by solving the equation according to the properties of cluster states are used in the first protocol. The second protocol is based on cross-Kerr nonlinearity which is exploited to check parity between original qubit with ancillary single qubit and it can achieve a higher probability of success through iteration. Furthermore, we can generalize the first method to concentrate entanglement on even number of particles. Our protocol will be useful in practical applications.

DOI
10.1142/s0217979221501496

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Multi-particle cluster states play a significant role in quantum information processing. However, due to the inevitable interaction with the environment in the transmission process, the fidelity of entanglement decreases. To distill the perfect cluster states, we present two schemes for arbitrary six-particle cluster states. POVM local unitary operators that are obtained by solving the equation according to the properties of cluster states are used in the first protocol. The second protocol is based on cross-Kerr nonlinearity which is exploited to check parity between original qubit with ancillary single qubit and it can achieve a higher probability of success through iteration. Furthermore, we can generalize the first method to concentrate entanglement on even number of particles. Our protocol will be useful in practical applications.
Cluster states, whose model are a remarkably rich structure in measurement-based quantum computation, hold high degree of entanglement, while entanglement is very fragile during the process of transmission because of the inevitable interaction with the environment. We propose two entanglement concentration protocols for four-particle linear cluster states which and are susceptible to the decoherence and the imperfect communication setups. In the first protocol, POVM operators are introduced to maximize the success probability, and the second protocol is based on cross-Kerr nonlinearity which is utilized to check the parity between the original particle and the ancillary particle. Both of the protocols have their own advantages. The first one can be easily realized in experiment by linear optics, while the one with cross-Kerr nonlinearity reach more than 90% success probability by iteration. Since the wide application of cluster states, the two protocols are efficient and valuable to different fields of 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.
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 put forward two efficient entanglement concentration protocols (ECPs) for distilling the maximally entangled NOON state from arbitrary less-entangled NOON state with only an auxiliary single photon. With the help of the weak cross-Kerr nonlinearities, both the two ECPs can be used repeatedly to get a high success probability. In the first ECP, the auxiliary single photon should be shared by the two parties say Alice and Bob. In the second ECP, the auxiliary single photon is only possessed by Bob, which can greatly increase the practical success probability by avoiding the transmission loss. Moreover, Bob can operate the whole protocol alone, which makes the protocol more simple. Therefore, our two ECPs, especially the second ECP may be more useful and convenient in the current quantum information processing.
We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon with a certain probability, while the conventional ECPs require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second protocol is implemented with cross-Kerr-nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with current experiments. With cross-Kerr-nonlinearities, it does not require sophisticated single-photon detectors and can be repeated to get a higher success probability. Moreover, the second protocol can get the higher entanglement transformation efficiency and it may be the most economical protocol by far. Meanwhile, both protocols are more suitable for multiphoton system concentration because they need less operations and classical communications. All these advantages make the two protocols useful in current long-distance quantum communications.
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.