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Frontiers of Physics

Logic Bell state concentration with parity check measurement

Jiu Liu, Lan Zhou, Wei Zhong, Yu‐Bo Sheng

Published Oct 23, 2018• 22 citations
Publisher

Abstract

Logic qubit plays an important role in current quantum communication. In this paper, we propose an efficient entanglement concentration protocol (ECP) for a new kind of logic Bell state, where the logic qubit is the concatenated Greenber–Horne–Zeilinger (C-GHZ) state. Our ECP relies on the nondemolition polarization parity check (PPC) gates constructed with cross-Kerr nonlinearity, and can distill one pair of maximally entangled logic Bell state from two same pairs of less-entangled logic Bell states. Benefit from the nondemolition PPC gates, the concentrated maximally entangled logic Bell state can be remained for further application. Moreover, our ECP can be repeated to further concentrate the less-entangled logic Bell state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in future long-distance quantum communication.

DOI
10.1007/s11467-018-0866-z

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Logic qubit plays an important role in current quantum communication. In this paper, we propose an efficient entanglement concentration protocol (ECP) for a new kind of logic Bell state, where the logic qubit is the concatenated Greenber–Horne–Zeilinger (C-GHZ) state. Our ECP relies on the nondemolition polarization parity check (PPC) gates constructed with cross-Kerr nonlinearity, and can distill one pair of maximally entangled logic Bell state from two same pairs of less-entangled logic Bell states. Benefit from the nondemolition PPC gates, the concentrated maximally entangled logic Bell state can be remained for further application. Moreover, our ECP can be repeated to further concentrate the less-entangled logic Bell state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in future long-distance quantum communication.
Logic W state, which replaces each physical qubit in a W state with a Greenberger–Horne–Zeilinger state is robust against photon transmission loss in long-distance quantum communication. In practical application, the environmental noise may make maximally entangled logic W state degrade to less entangled state, which largely limits its application. In this article, we propose an efficient entanglement concentration protocol (ECP) for logic W state, which can recover the less entangled logic W state into the maximally entangled logic W state. Our ECP relies on the nondemolition polarization parity check (PPC) gate constructed with cross-Kerr nonlinearity. The distilled maximally entangled logic W state can be preserved for other application. Moreover, when the ECP fails, we can repeat the ECP to further concentrate the distilled less entangled logic W state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in quantum communication field.
Concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is a new type of logic-qubit entanglement, which has attracted a lot of attentions recently. We propose a protocol for concentrating the less-entangled C-GHZ state assisted with an auxiliary single logic qubit. In this protocol, by utilizing the quantum nondemolition detection (QND) constructed by cross-Kerr nonlinearities, we demonstrate that our protocol exhibits much higher success probability compared to conventional methods in linear optics. Moreover, the protocol requires less operations and classical communications. It may be useful in the implementation of long-distance quantum communication.
The Bell state plays a significant role in the fundamental tests of quantum mechanics, such as the nonlocality of the quantum world. The Bell-state analysis is of vice importance in quantum communication. Existing Bell-state analysis protocols usually focus on the Bell-state encoding in the physical qubit directly. In this paper, we will describe an alternative approach to realize the near complete logic Bell-state analysis for the polarized concatenated Greenberger-Horne-Zeilinger (C-GHZ) state with two logic qubits. We show that the logic Bell-state can be distinguished in two steps with the help of the parity-check measurement (PCM) constructed by the cross-Kerr nonlinearity. This approach can be also used to distinguish arbitrary C-GHZ state with N logic qubits. As both the recent theoretical and experiment work showed that the C-GHZ state has its robust feature in practical noisy environment, this protocol may be useful in future long-distance quantum communication based on the logic-qubit entanglement.
We present an efficient hyperentanglement concentration protocol (hyper-ECP) for two-photon six-qubit systems in nonlocal partially hyperentangled Bell states with unknown parameters. In our scheme, we use two identical partially hyperentangled states which are simultaneously entangled in polarization and two different longitudinal momentum degrees of freedom (DOFs) to distill the maximally hyperentangled Bell state. The quantum nondemolition detectors based on the cross-Kerr nonlinearity are used to realize the parity checks of two-photon systems in three DOFs. The hyper-ECP can extract all the useful entanglement source, and the success probability can reach the theory limit with the help of iteration. All these advantages make our hyper-ECP useful in long-distance quantum communication in the future.
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 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.