title: Matching relations for optimal entanglement concentration and purification.
abstract: The bilateral controlled NOT (CNOT) operation plays a key role in standard entanglement purification process, but the CNOT operation may not be the optimal joint operation in the sense that the output entanglement is maximized. In this paper, the CNOT operations in both the Schmidt-projection based entanglement concentration and the entanglement purification schemes are replaced with a general joint unitary operation, and the optimal matching relations between the entangling power of the joint unitary operation and the non-maximal entangled channel are found for optimizing the entanglement in- crement or the output entanglement. The result is somewhat counter-intuitive for entanglement concentration. The output entanglement is maximized when the entangling power of the joint unitary operation and the quantum channel satisfy certain relation. There exist a variety of joint operations with non-maximal entangling power that can induce a maximal output entanglement, which will greatly broaden the set of the potential joint operations in entanglement concentration. In addition, the entanglement increment in purification process is maximized only by the joint unitary operations (including CNOT) with maximal entangling power.
authors.affiliation: School of Physics &Material Science, Anhui University, Hefei 230601, China.|Department of Computer Science, Jining University, Qufu, Shandong 273155, China.
authors.forename: Fan-Zhen
authors.initials: FZ
authors.lastname: Kong
authors.affiliation: School of Physics &Material Science, Anhui University, Hefei 230601, China.
authors.forename: Hui-Zhi
authors.initials: HZ
authors.lastname: Xia
authors.affiliation: School of Physics &Material Science, Anhui University, Hefei 230601, China.
authors.forename: Ming
authors.initials: M
authors.lastname: Yang
authors.affiliation: School of Physics &Material Science, Anhui University, Hefei 230601, China.
authors.forename: Qing
authors.initials: Q
authors.lastname: Yang
authors.affiliation: Institute for Quantum Control and Quantum Information, School of Electronic and Information Engineering, Hefei Normal University, Hefei 230601, China.
authors.forename: Zhuo-Liang
authors.initials: ZL
authors.lastname: Cao
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D055585:Physical Phenomena; D011789:Quantum Theory