Controlled remote state preparation protocols via AKLT states

In this paper, we proposed two controlled remote state preparation of an arbitrary single-qubit state schemes one for deterministic controlled remote state preparation the other for probabilistic controlled-joint remote state preparation with 2/3 probability. Both of them used the Affleck–Kennedy–Lieb–Tasaki (AKLT) state which consisted of bulk spin-1’s and two spin-1$$/$$/2’s at the ends. Up to now, no RSP protocols using AKLT gapped ground states as a shared quantum resource had been presented thus far and Fan et al. showed the other AKLT property was that if we performed a Bell measurement on bulk, then a maximally entangled state would be shared by two ends. We utilized these properties to develop our controlled protocols.

[1]  William K. Wootters,et al.  Erratum: Remote State Preparation [Phys. Rev. Lett. 87, 077902 (2001)] , 2002 .

[2]  Xiao-Wei Guan,et al.  Controlled-Joint Remote Preparation of an Arbitrary Two-Qubit State via Non-maximally Entangled Channel , 2012 .

[3]  Cao Thi Bich,et al.  Deterministic joint remote state preparation , 2011 .

[4]  Liu Yimin,et al.  Controlled Remote State Preparation , 2009 .

[5]  V. Roychowdhury,et al.  Entanglement in a valence-bond solid state. , 2004, Physical review letters.

[6]  B. Zeng,et al.  Optical one-way quantum computing with a simulated valence-bond solid , 2010, 1004.3624.

[7]  Mingxing Luo,et al.  Joint remote state preparation of arbitrary two-particle states via GHZ-type states , 2013, Quantum Inf. Process..

[8]  C. H. Bennett,et al.  Remote state preparation. , 2000, Physical review letters.

[9]  Zhan You-bang,et al.  Scheme for probabilistic remotely preparing a multi-particle entangled GHZ state , 2008 .

[10]  A. Pati.  Minimum classical bit for remote preparation and measurement of a qubit , 1999, quant-ph/9907022.

[11]  You-Bang Zhan,et al.  Deterministic Remote Preparation of a Four-Qubit Cluster-Type Entangled State , 2013 .

[12]  Andrew S. Darmawan,et al.  Optical spin-1 chain and its use as a quantum-computational wire , 2010, 1004.3626.

[13]  Yan Xia,et al.  Joint remote state preparation of a W-type state via W-type states , 2010 .

[14]  Nguyen Ba An,et al.  Flexible deterministic joint remote state preparation with a passive receiver , 2013 .

[15]  Peter W. Shor,et al.  Quantum Information Theory , 1998, IEEE Trans. Inf. Theory.

[16]  Thi Bich Cao,et al.  Remote state preparation with unit success probability , 2011 .

[17]  Dong Wang,et al.  Multiparty-controlled joint remote state preparation , 2013, Quantum Inf. Process..

[18]  E. Lieb,et al.  Valence bond ground states in isotropic quantum antiferromagnets , 1988 .

[19]  Liu Ye,et al.  Joint Remote Preparation of a Class of Four-Qubit Cluster-Like States with Tripartite Entanglements and Positive Operator-Valued Measurements , 2013 .

[20]  N. An.  Joint remote state preparation via W and W-type states , 2010 .

[21]  Bei Zeng,et al.  Gapped two-body hamiltonian whose unique ground state is universal for one-way quantum computation. , 2008, Physical review letters.

[22]  Wang Yu-Zhu,et al.  Multiparticle Generalization of Remote State Preparation , 2004 .

[23]  You-Bang Zhan,et al.  Scheme for remotely preparing a four-particle entangled cluster-type state , 2010 .

[24]  Hong-Yi Dai,et al.  Classical communication cost and remote preparation of the four-particle GHZ class state , 2006 .

[25]  Kennedy,et al.  Rigorous results on valence-bond ground states in antiferromagnets. , 1987, Physical review letters.

[26]  H. Lo.  Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity , 1999, quant-ph/9912009.