Abstract

An experimental scheme, its hardware implementation, and procedure for experimental verification of tripartite quantum state sharing and perfect teleportation of the two-qubit photonic state using four different multipartite quantum channels is presented. The four multipartite channels considered are (1) a pair of Greenberger–Horne–Zeilinger triplets, (2) a six-particle cluster state, (3) a highly entangled five-particle Brown state, and (4) a highly entangled six-particle Borras state. In this experiment, optical pulses are delivered by a high repetition rate mode-locked pulsed laser and arbitrary photonic states, in the two-qubit Bloch sphere, are created by the spontaneous parametric down-conversion of optical pulses in a nonlinear crystal. The experimental implementation of the scheme is based on both single-particle and two-particle complete Bell-state measurements, and the unitary transformation required for reconstruction of the qubit is performed using single- and two-qubit operations. Two-qubit operations are implemented using the quantum controlled phase and C-NOT gates. Relative comparison among different multipartite channels along with experimental difficulties and their solutions are also discussed.

© 2013 Optical Society of America

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  29. T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  34. S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
    [CrossRef]
  35. H. Yonezawa, T. Aokl, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013

M. Luo, J. Peng, and Z. Mo, “Joint remote preparation of an arbitrary five-qubit Brown state,” Int. J. Theor. Phys. 52, 644–653 (2013).
[CrossRef]

2012

X. Chen, S. Ma, Y. Su, R. Zhang, and Y. Yang, “Controlled remote state preparation of arbitrary two and three qubit states via the Brown state,” Quant. Info. Proc. 11, 1653–1667 (2012).
[CrossRef]

2011

N. Paul, J. V. Menon, S. Karumanchi, S. Muralidharan, and P. K. Panigrahi, “Quantum tasks using six qubit cluster states,” Quant. Info. Proc. 10, 619–632 (2011).
[CrossRef]

2010

Y. Li and K. Hou, “Tripartite controlled teleportation of an arbitrary two-qubit state with multipartite cluster states,” Int. J. Quantum. Inform. 08, 969–977 (2010).
[CrossRef]

K. Hou, Y. Li, and S. Shi, “Quantum state sharing with genuinely entangled five-qubit state and Bell-state measurements,” Opt. Commun. 283, 1961–1965 (2010).
[CrossRef]

2009

S. Choudhury, S. Muralidharan, and P. K. Panigrahi, “Quantum teleportation and state sharing using a genuinely entangled six-qubit state,” J. Phys. A 42, 115303 (2009).
[CrossRef]

2008

S. Muralidharan and P. Panigrahi, “Perfect teleportation, quantum-state sharing, and superdense coding through genuinely entangled five-qubit state,” Phys. Rev. A 77, 032321 (2008).
[CrossRef]

R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008).
[CrossRef]

H. Lu, J. Zhang, X. Wang, Y. Li, and C. Wang, “Experimental high-intensity three-photon entangled source,” Phys. Rev. A 78, 033819 (2008).
[CrossRef]

2007

A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas, and A. Plastino, “Multiqubit systems: highly entangled states and entanglement distribution,” J. Phys. A 40, 13407–13421 (2007).
[CrossRef]

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

2006

T. P. Bodiya and L. M. Duan, “Scalable generation of graph-state entanglement through realistic linear optics,” Phys. Rev. Lett. 97, 143601 (2006).
[CrossRef]

2005

G. Toth and O. Guhne, “Entanglement detection in the stabilizer formalism,” Phys. Rev. A 72, 022340 (2005).
[CrossRef]

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef]

G. Rigolin, “Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement,” Phys. Rev. A 71, 032303 (2005).
[CrossRef]

D. E. Browne and T. Rudolph, “Resource-efficient linear optical quantum computation,” Phys. Rev. Lett. 95, 010501 (2005).
[CrossRef]

I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, “Searching for highly entangled multi-qubit states,” J. Phys. A 38, 1119–1131 (2005).
[CrossRef]

2004

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

M. Hein, J. Eisert, and H. J. Briegel, “Multiparty entanglement in graph states,” Phys. Rev. A 69, 062311 (2004).
[CrossRef]

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef]

H. Yonezawa, T. Aokl, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[CrossRef]

2002

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[CrossRef]

H. F. Hofmann and S. Takeuchi, “Quantum phase gate for photonic qubits using only beam splitters and postselection,” Phys. Rev. A 66, 024308 (2002).
[CrossRef]

2001

Y. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell-state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

K. Banaszek, A. B. U’Ren, and I. A. Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett. 26, 1367–1369 (2001).
[CrossRef]

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef]

1999

J. G. Rarity and P. R. Tapster, “Three-particle entanglement from entangled photon pairs and a weak coherent state,” Phys. Rev. A 59, R35–R38 (1999).
[CrossRef]

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B 68, 1095–1108 (1999).
[CrossRef]

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[CrossRef]

1998

H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76, 127–137 (1998).
[CrossRef]

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

1995

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

1992

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Aokl, T.

H. Yonezawa, T. Aokl, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[CrossRef]

Banaszek, K.

Batle, J.

A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas, and A. Plastino, “Multiqubit systems: highly entangled states and entanglement distribution,” J. Phys. A 40, 13407–13421 (2007).
[CrossRef]

Bhatia, P. S.

P. S. Bhatia, “Controlled quantum dense coding using six-photon cluster state,” submitted for publication.

Blatt, R.

R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008).
[CrossRef]

Bodiya, T. P.

T. P. Bodiya and L. M. Duan, “Scalable generation of graph-state entanglement through realistic linear optics,” Phys. Rev. Lett. 97, 143601 (2006).
[CrossRef]

Borras, A.

A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas, and A. Plastino, “Multiqubit systems: highly entangled states and entanglement distribution,” J. Phys. A 40, 13407–13421 (2007).
[CrossRef]

Bourennane, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[CrossRef]

Braunstein, S. L.

I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, “Searching for highly entangled multi-qubit states,” J. Phys. A 38, 1119–1131 (2005).
[CrossRef]

Briegel, H. J.

M. Hein, J. Eisert, and H. J. Briegel, “Multiparty entanglement in graph states,” Phys. Rev. A 69, 062311 (2004).
[CrossRef]

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef]

Brown, I. D. K.

I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, “Searching for highly entangled multi-qubit states,” J. Phys. A 38, 1119–1131 (2005).
[CrossRef]

Browne, D. E.

D. E. Browne and T. Rudolph, “Resource-efficient linear optical quantum computation,” Phys. Rev. Lett. 95, 010501 (2005).
[CrossRef]

Bru, D.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Casas, M.

A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas, and A. Plastino, “Multiqubit systems: highly entangled states and entanglement distribution,” J. Phys. A 40, 13407–13421 (2007).
[CrossRef]

Chen, X.

X. Chen, S. Ma, Y. Su, R. Zhang, and Y. Yang, “Controlled remote state preparation of arbitrary two and three qubit states via the Brown state,” Quant. Info. Proc. 11, 1653–1667 (2012).
[CrossRef]

Choudhury, S.

S. Choudhury, S. Muralidharan, and P. K. Panigrahi, “Quantum teleportation and state sharing using a genuinely entangled six-qubit state,” J. Phys. A 42, 115303 (2009).
[CrossRef]

Daniell, M.

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[CrossRef]

Duan, L. M.

T. P. Bodiya and L. M. Duan, “Scalable generation of graph-state entanglement through realistic linear optics,” Phys. Rev. Lett. 97, 143601 (2006).
[CrossRef]

Eibl, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Eisert, J.

M. Hein, J. Eisert, and H. J. Briegel, “Multiparty entanglement in graph states,” Phys. Rev. A 69, 062311 (2004).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Franson, J. D.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

Furusawa, A.

H. Yonezawa, T. Aokl, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[CrossRef]

Gaertner, S.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Gao, W.

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Gasparoni, S.

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef]

Goebel, A.

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer Academic, 1989), pp. 73–76.

Guhne, O.

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

G. Toth and O. Guhne, “Entanglement detection in the stabilizer formalism,” Phys. Rev. A 72, 022340 (2005).
[CrossRef]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Harris, S. E.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

Hau, L. V.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

Hein, M.

M. Hein, J. Eisert, and H. J. Briegel, “Multiparty entanglement in graph states,” Phys. Rev. A 69, 062311 (2004).
[CrossRef]

Hofmann, H. F.

H. F. Hofmann and S. Takeuchi, “Quantum phase gate for photonic qubits using only beam splitters and postselection,” Phys. Rev. A 66, 024308 (2002).
[CrossRef]

Horne, M. A.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer Academic, 1989), pp. 73–76.

Hou, K.

Y. Li and K. Hou, “Tripartite controlled teleportation of an arbitrary two-qubit state with multipartite cluster states,” Int. J. Quantum. Inform. 08, 969–977 (2010).
[CrossRef]

K. Hou, Y. Li, and S. Shi, “Quantum state sharing with genuinely entangled five-qubit state and Bell-state measurements,” Opt. Commun. 283, 1961–1965 (2010).
[CrossRef]

Hyllus, P.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Jacobs, B. C.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Karlsson, A.

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

Karumanchi, S.

N. Paul, J. V. Menon, S. Karumanchi, S. Muralidharan, and P. K. Panigrahi, “Quantum tasks using six qubit cluster states,” Quant. Info. Proc. 10, 619–632 (2011).
[CrossRef]

Kiesel, N.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef]

Kim, Y.

Y. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell-state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).
[CrossRef]

Kimble, H. J.

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B 68, 1095–1108 (1999).
[CrossRef]

H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76, 127–137 (1998).
[CrossRef]

Kulik, S. P.

Y. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell-state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).
[CrossRef]

Kurtsiefer, C.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Lewenstein, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Li, Y.

Y. Li and K. Hou, “Tripartite controlled teleportation of an arbitrary two-qubit state with multipartite cluster states,” Int. J. Quantum. Inform. 08, 969–977 (2010).
[CrossRef]

K. Hou, Y. Li, and S. Shi, “Quantum state sharing with genuinely entangled five-qubit state and Bell-state measurements,” Opt. Commun. 283, 1961–1965 (2010).
[CrossRef]

H. Lu, J. Zhang, X. Wang, Y. Li, and C. Wang, “Experimental high-intensity three-photon entangled source,” Phys. Rev. A 78, 033819 (2008).
[CrossRef]

Liu, D.

D. Liu, X. Zhou, and G. L. Long, “Multiple entropy measures for multipartite quantum entanglement,” arXiv:0705.3904 (2007).

Long, G. L.

D. Liu, X. Zhou, and G. L. Long, “Multiple entropy measures for multipartite quantum entanglement,” arXiv:0705.3904 (2007).

Lu, C.

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Lu, H.

H. Lu, J. Zhang, X. Wang, Y. Li, and C. Wang, “Experimental high-intensity three-photon entangled source,” Phys. Rev. A 78, 033819 (2008).
[CrossRef]

Luo, M.

M. Luo, J. Peng, and Z. Mo, “Joint remote preparation of an arbitrary five-qubit Brown state,” Int. J. Theor. Phys. 52, 644–653 (2013).
[CrossRef]

Ma, S.

X. Chen, S. Ma, Y. Su, R. Zhang, and Y. Yang, “Controlled remote state preparation of arbitrary two and three qubit states via the Brown state,” Quant. Info. Proc. 11, 1653–1667 (2012).
[CrossRef]

Mabuchi, H.

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B 68, 1095–1108 (1999).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Menon, J. V.

N. Paul, J. V. Menon, S. Karumanchi, S. Muralidharan, and P. K. Panigrahi, “Quantum tasks using six qubit cluster states,” Quant. Info. Proc. 10, 619–632 (2011).
[CrossRef]

Mo, Z.

M. Luo, J. Peng, and Z. Mo, “Joint remote preparation of an arbitrary five-qubit Brown state,” Int. J. Theor. Phys. 52, 644–653 (2013).
[CrossRef]

Muralidharan, S.

N. Paul, J. V. Menon, S. Karumanchi, S. Muralidharan, and P. K. Panigrahi, “Quantum tasks using six qubit cluster states,” Quant. Info. Proc. 10, 619–632 (2011).
[CrossRef]

S. Choudhury, S. Muralidharan, and P. K. Panigrahi, “Quantum teleportation and state sharing using a genuinely entangled six-qubit state,” J. Phys. A 42, 115303 (2009).
[CrossRef]

S. Muralidharan and P. Panigrahi, “Perfect teleportation, quantum-state sharing, and superdense coding through genuinely entangled five-qubit state,” Phys. Rev. A 77, 032321 (2008).
[CrossRef]

Pan, J. W.

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[CrossRef]

Pan, J.-W.

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Panigrahi, P.

S. Muralidharan and P. Panigrahi, “Perfect teleportation, quantum-state sharing, and superdense coding through genuinely entangled five-qubit state,” Phys. Rev. A 77, 032321 (2008).
[CrossRef]

Panigrahi, P. K.

N. Paul, J. V. Menon, S. Karumanchi, S. Muralidharan, and P. K. Panigrahi, “Quantum tasks using six qubit cluster states,” Quant. Info. Proc. 10, 619–632 (2011).
[CrossRef]

S. Choudhury, S. Muralidharan, and P. K. Panigrahi, “Quantum teleportation and state sharing using a genuinely entangled six-qubit state,” J. Phys. A 42, 115303 (2009).
[CrossRef]

Paul, N.

N. Paul, J. V. Menon, S. Karumanchi, S. Muralidharan, and P. K. Panigrahi, “Quantum tasks using six qubit cluster states,” Quant. Info. Proc. 10, 619–632 (2011).
[CrossRef]

Peng, J.

M. Luo, J. Peng, and Z. Mo, “Joint remote preparation of an arbitrary five-qubit Brown state,” Int. J. Theor. Phys. 52, 644–653 (2013).
[CrossRef]

Pittman, T. B.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

Plastino, A.

A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas, and A. Plastino, “Multiqubit systems: highly entangled states and entanglement distribution,” J. Phys. A 40, 13407–13421 (2007).
[CrossRef]

Plastino, A. R.

A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas, and A. Plastino, “Multiqubit systems: highly entangled states and entanglement distribution,” J. Phys. A 40, 13407–13421 (2007).
[CrossRef]

Rarity, J. G.

J. G. Rarity and P. R. Tapster, “Three-particle entanglement from entangled photon pairs and a weak coherent state,” Phys. Rev. A 59, R35–R38 (1999).
[CrossRef]

Raussendorf, R.

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef]

Rigolin, G.

G. Rigolin, “Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement,” Phys. Rev. A 71, 032303 (2005).
[CrossRef]

Rudolph, T.

D. E. Browne and T. Rudolph, “Resource-efficient linear optical quantum computation,” Phys. Rev. Lett. 95, 010501 (2005).
[CrossRef]

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef]

Sanpera, A.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

Schmid, C.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Shi, S.

K. Hou, Y. Li, and S. Shi, “Quantum state sharing with genuinely entangled five-qubit state and Bell-state measurements,” Opt. Commun. 283, 1961–1965 (2010).
[CrossRef]

Shih, Y.

Y. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell-state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Stepney, S.

I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, “Searching for highly entangled multi-qubit states,” J. Phys. A 38, 1119–1131 (2005).
[CrossRef]

Su, Y.

X. Chen, S. Ma, Y. Su, R. Zhang, and Y. Yang, “Controlled remote state preparation of arbitrary two and three qubit states via the Brown state,” Quant. Info. Proc. 11, 1653–1667 (2012).
[CrossRef]

Sudbery, A.

I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, “Searching for highly entangled multi-qubit states,” J. Phys. A 38, 1119–1131 (2005).
[CrossRef]

Takeuchi, S.

H. F. Hofmann and S. Takeuchi, “Quantum phase gate for photonic qubits using only beam splitters and postselection,” Phys. Rev. A 66, 024308 (2002).
[CrossRef]

Tapster, P. R.

J. G. Rarity and P. R. Tapster, “Three-particle entanglement from entangled photon pairs and a weak coherent state,” Phys. Rev. A 59, R35–R38 (1999).
[CrossRef]

Toth, G.

G. Toth and O. Guhne, “Entanglement detection in the stabilizer formalism,” Phys. Rev. A 72, 022340 (2005).
[CrossRef]

U’Ren, A. B.

Ursin, R.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef]

Walmsley, I. A.

Walther, P.

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef]

Wang, C.

H. Lu, J. Zhang, X. Wang, Y. Li, and C. Wang, “Experimental high-intensity three-photon entangled source,” Phys. Rev. A 78, 033819 (2008).
[CrossRef]

Wang, X.

H. Lu, J. Zhang, X. Wang, Y. Li, and C. Wang, “Experimental high-intensity three-photon entangled source,” Phys. Rev. A 78, 033819 (2008).
[CrossRef]

Weber, U.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef]

Weinfurter, H.

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Wineland, D.

R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008).
[CrossRef]

Yang, T.

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Yang, Y.

X. Chen, S. Ma, Y. Su, R. Zhang, and Y. Yang, “Controlled remote state preparation of arbitrary two and three qubit states via the Brown state,” Quant. Info. Proc. 11, 1653–1667 (2012).
[CrossRef]

Ye, J.

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B 68, 1095–1108 (1999).
[CrossRef]

Yonezawa, H.

H. Yonezawa, T. Aokl, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[CrossRef]

Yuan, Z.

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Zander, C.

A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas, and A. Plastino, “Multiqubit systems: highly entangled states and entanglement distribution,” J. Phys. A 40, 13407–13421 (2007).
[CrossRef]

Zeilinger, A.

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer Academic, 1989), pp. 73–76.

Zhang, J.

H. Lu, J. Zhang, X. Wang, Y. Li, and C. Wang, “Experimental high-intensity three-photon entangled source,” Phys. Rev. A 78, 033819 (2008).
[CrossRef]

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Zhang, R.

X. Chen, S. Ma, Y. Su, R. Zhang, and Y. Yang, “Controlled remote state preparation of arbitrary two and three qubit states via the Brown state,” Quant. Info. Proc. 11, 1653–1667 (2012).
[CrossRef]

Zhou, X.

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

D. Liu, X. Zhou, and G. L. Long, “Multiple entropy measures for multipartite quantum entanglement,” arXiv:0705.3904 (2007).

Appl. Phys. B

H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B 68, 1095–1108 (1999).
[CrossRef]

IEEE J. Quantum Electron.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Int. J. Quantum. Inform.

Y. Li and K. Hou, “Tripartite controlled teleportation of an arbitrary two-qubit state with multipartite cluster states,” Int. J. Quantum. Inform. 08, 969–977 (2010).
[CrossRef]

Int. J. Theor. Phys.

M. Luo, J. Peng, and Z. Mo, “Joint remote preparation of an arbitrary five-qubit Brown state,” Int. J. Theor. Phys. 52, 644–653 (2013).
[CrossRef]

J. Phys. A

S. Choudhury, S. Muralidharan, and P. K. Panigrahi, “Quantum teleportation and state sharing using a genuinely entangled six-qubit state,” J. Phys. A 42, 115303 (2009).
[CrossRef]

I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, “Searching for highly entangled multi-qubit states,” J. Phys. A 38, 1119–1131 (2005).
[CrossRef]

A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas, and A. Plastino, “Multiqubit systems: highly entangled states and entanglement distribution,” J. Phys. A 40, 13407–13421 (2007).
[CrossRef]

Nat. Phys.

C. Lu, X. Zhou, O. Guhne, W. Gao, J. Zhang, Z. Yuan, A. Goebel, T. Yang, and J.-W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Nature

H. Yonezawa, T. Aokl, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[CrossRef]

R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008).
[CrossRef]

Opt. Commun.

K. Hou, Y. Li, and S. Shi, “Quantum state sharing with genuinely entangled five-qubit state and Bell-state measurements,” Opt. Commun. 283, 1961–1965 (2010).
[CrossRef]

Opt. Lett.

Phys. Rev. A

H. F. Hofmann and S. Takeuchi, “Quantum phase gate for photonic qubits using only beam splitters and postselection,” Phys. Rev. A 66, 024308 (2002).
[CrossRef]

G. Toth and O. Guhne, “Entanglement detection in the stabilizer formalism,” Phys. Rev. A 72, 022340 (2005).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

J. G. Rarity and P. R. Tapster, “Three-particle entanglement from entangled photon pairs and a weak coherent state,” Phys. Rev. A 59, R35–R38 (1999).
[CrossRef]

H. Lu, J. Zhang, X. Wang, Y. Li, and C. Wang, “Experimental high-intensity three-photon entangled source,” Phys. Rev. A 78, 033819 (2008).
[CrossRef]

M. Hein, J. Eisert, and H. J. Briegel, “Multiparty entanglement in graph states,” Phys. Rev. A 69, 062311 (2004).
[CrossRef]

G. Rigolin, “Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement,” Phys. Rev. A 71, 032303 (2005).
[CrossRef]

S. Muralidharan and P. Panigrahi, “Perfect teleportation, quantum-state sharing, and superdense coding through genuinely entangled five-qubit state,” Phys. Rev. A 77, 032321 (2008).
[CrossRef]

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

Phys. Rev. Lett.

D. E. Browne and T. Rudolph, “Resource-efficient linear optical quantum computation,” Phys. Rev. Lett. 95, 010501 (2005).
[CrossRef]

T. P. Bodiya and L. M. Duan, “Scalable generation of graph-state entanglement through realistic linear optics,” Phys. Rev. Lett. 97, 143601 (2006).
[CrossRef]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Bru, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of nondeterministic quantum logic operations using linear optical elements,” Phys. Rev. Lett. 88, 257902 (2002).
[CrossRef]

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[CrossRef]

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef]

Y. Kim, S. P. Kulik, and Y. Shih, “Quantum teleportation of a polarization state with a complete Bell-state measurement,” Phys. Rev. Lett. 86, 1370–1373 (2001).
[CrossRef]

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef]

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

Phys. Scr.

H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76, 127–137 (1998).
[CrossRef]

Quant. Info. Proc.

N. Paul, J. V. Menon, S. Karumanchi, S. Muralidharan, and P. K. Panigrahi, “Quantum tasks using six qubit cluster states,” Quant. Info. Proc. 10, 619–632 (2011).
[CrossRef]

X. Chen, S. Ma, Y. Su, R. Zhang, and Y. Yang, “Controlled remote state preparation of arbitrary two and three qubit states via the Brown state,” Quant. Info. Proc. 11, 1653–1667 (2012).
[CrossRef]

Other

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer Academic, 1989), pp. 73–76.

P. S. Bhatia, “Controlled quantum dense coding using six-photon cluster state,” submitted for publication.

D. Liu, X. Zhou, and G. L. Long, “Multiple entropy measures for multipartite quantum entanglement,” arXiv:0705.3904 (2007).

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Figures (5)

Fig. 1.
Fig. 1.

This figure shows the tripartite schemes for QSTS and teleportation of the two-qubit state from sender Alice to receiver Charlie under the control of a third party who is Bob. Parts (A), (B), and (C) are valid for GHZ/cluster-, Brown-, and Borras-state channels, respectively. The dotted line between particles shows entanglement between them. Particles 1 and 2, which store two-qubit states, for all four channels, are located in Alice’s laboratory. The distribution of the remaining particles for each of the four channels is shown in the respective figure for that channel.

Fig. 2.
Fig. 2.

This figure shows the switching of entanglement among eight quantum particles in a given teleportation trial. Particles connected with dotted lines are entangled. GHZ, Greenberger–Horne–Zeilinger state; EPR, Einstein–Podolsky–Rosen state. Parts (A) and (B) are valid for GHZ- and cluster-state channels, respectively. (A1), (B1) The state of the particles before the first Bell-state measurement. (A2), (B2) The state of the particles after the first Bell-state measurement. (A3), (B3) The state of the particles after the second Bell-state measurement. (A4), (B4) The state of the particles after projecting particles 4 and 7 into a definite quantum state.

Fig. 3.
Fig. 3.

This figure shows a block diagram of the experimental apparatus required to verify QSTS and quantum teleportation of the two-qubit photonic state from sender Alice to receiver Charlie under the control of Bob. This figure is valid for GHZ- and cluster-state channels. BBO, beta barium borate crystal; M, turning mirror; P1, P2, P4, and P7, linear polarizer; BSA-1 and BSA-2, Bell-state analyzer; PR3 and PR6, time delay prism; UV, ultraviolet 100 fs light pulse; PM5 and PM8, phase modulator; HWP5 and HWP8, half-wave plate; QWP5 and QWP8, quarter-wave plate; PBS5 and PBS8, polarizing beam splitter cube; D4, D7, D5H, D5V, D8H, and D8V, single photon detector; F, narrowband filter; BS, beam splitter; PDBS, polarization-dependent beam splitter cube; PDBS-1 and PDBS-2, polarization-dependent beam splitter.

Fig. 4.
Fig. 4.

Description of this figure is very similar to that of Fig. 3 except this figure is valid for the Brown-state channel. Most of the optical components in this figure are same as that in Fig. 3 except for PR1, PR2, and PR4, time delay prism; PM6, phase modulator; HWP6 and λ/2, half-wave plate; QWP6, quarter-wave plate; PBS6, PBS-1, and PBS-2, polarizing beam splitter cube; D6H, D6V, D1, D2, D3, and D4, single photon detector.

Fig. 5.
Fig. 5.

Description of this figure is very similar to that of Figs. 3 and 4 except this figure is valid for the Borras-state channel. Most of the optical components in this figure are same as that in Figs. 3 and 4 except for BSA-3, Bell-state analyzer; PR5, time delay prism; PM7, phase modulator; HWP7, half-wave plate; QWP7, quarter-wave plate; PBS7, polarizing beam splitter cube; D7H and D7V, single photon detector; DM, DM1, and DM2, dichroic mirror; U, V, W, and X, sum frequency generation (SFG) crystals; CM-1 and CM-2, compensator; G1 and G2, 45° projector; D1, D2, D3, and D4, detectors.

Equations (4)

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|ψ345GHZ=12{|03|04|05+|13|14|15}and|ψ678GHZ=12{|06|07|08+|16|17|18},
|C6=12{+|03|04|05|06|07|08+|03|04|05|16|17|18+|13|14|15|06|07|08|13|14|15|16|17|18},
|ψ5=12{+|03|04|15|ψ67()+|03|14|05|ϕ67()+|13|04|05|ψ67(+)+|13|14|15|ϕ67(+)},
|ψ6=132{+|03|04|05|06|07|08+|13|14|15|16|17|18+|03|04|05|06|17|18+|13|14|15|16|07|08+|03|04|05|16|07|18+|13|14|15|06|17|08+|03|04|05|16|17|08+|13|14|15|06|07|18+|03|04|15|06|07|18+|13|14|05|16|17|08+|03|04|15|16|17|18+|13|14|05|06|07|08+|03|14|05|06|07|18+|13|04|15|16|17|08+|03|14|05|06|17|08+|13|04|15|16|07|18+|03|14|15|06|07|08+|13|04|05|16|17|18+|03|14|15|16|07|18+|13|04|05|06|17|08|03|04|15|06|17|08|13|14|05|16|07|18|03|04|15|16|07|08|13|14|05|06|17|18|03|14|05|16|07|08|13|04|15|06|17|18|03|14|05|16|17|18|13|04|15|06|07|08|03|14|15|06|17|18|13|04|05|16|07|08|03|14|15|16|17|08|13|04|05|06|07|18}.

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