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Title: Genuine multiqubit entanglement and controlled teleportation

Abstract

We construct a genuine (2N+1)-qubit entangled state to perform controlled teleportation of an arbitrary N-qubit state. The constructed state is a complementarity to the genuine 2N-qubit entangled state constructed by Yeo and Chua for N=2 [Phys. Rev. Lett. 96, 060502 (2006)] and by Chen, Zhu, and Guo for any N [Phys. Rev. A 74, 032324 (2006)]. We also quantify the entanglement of the state and classify it with the well-known GHZ and W states by means of the recently proposed generalized global entanglement and the associated auxiliary measures [Phys. Rev. A 74, 022314 (2006)]. Our study is of general importance with respect to exploring and exploiting the genuine multiqubit entanglement.

Authors:
;  [1];  [2];  [3]
  1. College of Physics and Engineering, Qufu Normal University, Qufu 273165 (China)
  2. Institute of Physics and Electronics, 10 Dao Tan, Thu Le, Ba Dinh, Hanoi (Viet Nam)
  3. (Korea, Republic of)
Publication Date:
OSTI Identifier:
20982475
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.052306; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; INFORMATION THEORY; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUANTUM TELEPORTATION; QUBITS; SIMULATION

Citation Formats

Man, Zhong-Xiao, Xia, Yun-Jie, An, Nguyen Ba, and Korea Institute for Advanced Study, 207-43 Cheongryangni 2-dong, Dongdaemun-gu, Seoul 130-722. Genuine multiqubit entanglement and controlled teleportation. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.052306.
Man, Zhong-Xiao, Xia, Yun-Jie, An, Nguyen Ba, & Korea Institute for Advanced Study, 207-43 Cheongryangni 2-dong, Dongdaemun-gu, Seoul 130-722. Genuine multiqubit entanglement and controlled teleportation. United States. doi:10.1103/PHYSREVA.75.052306.
Man, Zhong-Xiao, Xia, Yun-Jie, An, Nguyen Ba, and Korea Institute for Advanced Study, 207-43 Cheongryangni 2-dong, Dongdaemun-gu, Seoul 130-722. Tue . "Genuine multiqubit entanglement and controlled teleportation". United States. doi:10.1103/PHYSREVA.75.052306.
@article{osti_20982475,
title = {Genuine multiqubit entanglement and controlled teleportation},
author = {Man, Zhong-Xiao and Xia, Yun-Jie and An, Nguyen Ba and Korea Institute for Advanced Study, 207-43 Cheongryangni 2-dong, Dongdaemun-gu, Seoul 130-722},
abstractNote = {We construct a genuine (2N+1)-qubit entangled state to perform controlled teleportation of an arbitrary N-qubit state. The constructed state is a complementarity to the genuine 2N-qubit entangled state constructed by Yeo and Chua for N=2 [Phys. Rev. Lett. 96, 060502 (2006)] and by Chen, Zhu, and Guo for any N [Phys. Rev. A 74, 032324 (2006)]. We also quantify the entanglement of the state and classify it with the well-known GHZ and W states by means of the recently proposed generalized global entanglement and the associated auxiliary measures [Phys. Rev. A 74, 022314 (2006)]. Our study is of general importance with respect to exploring and exploiting the genuine multiqubit entanglement.},
doi = {10.1103/PHYSREVA.75.052306},
journal = {Physical Review. A},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • We present a way to teleport multiqubit quantum information from a sender to a distant receiver via the control of many agents in a network. We show that the original state of each qubit can be restored by the receiver as long as all the agents collaborate. However, even if one agent does not cooperate, the receiver cannot fully recover the original state of each qubit. The method operates essentially through entangling quantum information during teleportation, in such a way that the required auxiliary qubit resources, local operation, and classical communication are considerably reduced for the present purpose.
  • We consider pure quantum states of N qubits and study the genuine N-qubit entanglement that is shared among all the N qubits. We introduce an information-theoretic measure of genuine N-qubit entanglement based on bipartite partitions. When N is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When N is an odd number, the measure can also be obtained in principle.
  • We present a development of a geometric approach to entanglement indicators. The method is applied to detect genuine multiqubit entanglement. The criteria are given in the form of nonlinear conditions imposed on correlation tensors. Thus they involve directly observable quantities, and in some cases require only few specific measurements to find multiqubit entanglement. The nonlinearity of each of the criteria allows detection of entanglement in wide classes of states. In contrast to entanglement witnesses, which in the space of Hermitian operators define a hyperplane, these conditions define a geometric figure encapsulating the nonfully entangled states within it.
  • Recently Yeo and Chua [Phys. Rev. Lett. 96, 060502 (2006)] presented an explicit protocol for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entanglement channel. Here we generalize completely their results to teleporting an arbitrary N-qubit state via genuine N-qubit entanglement channels. And we present the general form of the genuine multipartite entanglement channels, namely, the sufficient and necessary condition the genuine N-qubit entanglement channels must satisfy to teleport an arbitrary N-qubit state.
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