Deterministic single-qubit operation sharing with five-qubit cluster state
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Deterministic single-qubit operation sharing with five-qubit cluster state Shengfang Wang · Yimin Liu · Jianlan Chen · Xiansong Liu · Zhanjun Zhang
Received: 12 November 2012 / Accepted: 28 January 2013 © Springer Science+Business Media New York 2013
Abstract Perfect sharing of arbitrary single-qubit operation (PSASQO) with shared entanglements and LOCC is focused. A symmetric three-party PSASQO scheme is put forward by utilizing the five-qubit cluster state proposed by Briegel and Raussendorf (Phys Rev Lett 86:910, 2001). Some concrete discussions on the scheme are made, including its important features, the essential role of the quantum channel, its direct generalization to more-party cases, the problem of entanglement structure and its application perspective in some peculiar quantum scenario as well as its security analysis. Particularly, the experimental feasibilities of the scheme and its generalizations are demonstrated, i.e., showing the employed unitary operations are local and accessible single-qubit Pauli and two-qubit control NOT operations according to nowaday experimental techniques. Keywords Single-qubit operation sharing · One-dimensional five-qubit cluster state · Single-qubit Pauli operation · Two-qubit control NOT operation · Experimental feasibility 1 Introduction Quantum entanglement is a charming quantum nonlocal property of some bipartite or multipartite systems. It has attracted much attention and been intensively studied since 1935 [1,2]. Recent decades it has been widely exploited for treating various nonlocal quantum tasks in different scenarios [3–13], including quantum
S. Wang · J. Chen · X. Liu · Z. Zhang (B) School of Physics and Material Science, Anhui University, Hefei 230039, Anhui, China e-mail: [email protected] Y. Liu Department of Physics, Shaoguan University, Shaoguan 512005, China
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state sharing [7]. Quantum state sharing is actually the generalization of classical secret sharing in quantum scenario. It is a procedure for splitting a quantum state into several parts so that no subsets but all parts are sufficient to read the information. After Hillery et al’s pioneering work [7], many other schemes are proposed with different shared entanglements [14–19]. In particular, multi-qubit cluster states as shared entanglements are concerned recently. Using four- and five-partite cluster states, i.e., |C4 = 21 (|0000 + |0110 + |1001 + |1111) and |C5 = 21 (|00000 + |00111 + |11101 + |11010), Muralidharan and Panigrahi [14] provided various schemes for splitting arbitrary single-qubit or two-qubit quantum information into two parts. Paul et al. [15] showed that six-photon cluster states can be used as shared entanglements for splitting arbitrary two-qubit states between two parties. Moreover, Muralidharan et al. [16] further provided a number of quantum state sharing schemes for splitting any two-qubit state among k parties using a N -qubit linear cluster state as a quantum channel. In 2001 with local operation and classical communication (LOCC) as
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