Abstract

The preparation of multipartite entangled states is the prerequisite for exploring quantum information networks and quantum computation. In this Letter, we present what we believe is the first experimental demonstration of an eight-partite spatially separated continuous variable (CV) cluster state of optical modes. Via the linearly optical transformation of eight squeezed states of light, the eight-partite cluster entangled state with amplitude and phase quadrature correlations are prepared. The generated eight entangled photonic qumodes are spatially separated, which provides valuable quantum resources for implementing CV quantum information protocols.

© 2012 Optical Society of America

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  19. Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys. Rev. A 62, 023813 (2000).
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2012

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
[CrossRef]

2011

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

R. Ukai, S. Yokoyama, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

Y. Wang, Y. Zheng, C. Xie, and K. Peng, IEEE J. Quantum Electron. 47, 1006 (2011).
[CrossRef]

P. van Loock, Laser Photon. Rev. 5, 167 (2011).
[CrossRef]

2010

Y. Wang, H. Shen, X. Jin, X. Su, C. Xie, and K. Peng, Opt. Express 18, 6149 (2010).
[CrossRef]

Y. Wang, X. Su, H. Shen, A. Tan, C. Xie, and K. Peng, Phys. Rev. A 81, 022311 (2010).
[CrossRef]

2009

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, and P. van Loock, Phys. Rev. A 79, 062318 (2009).
[CrossRef]

Y. Miwa, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. A 80, 050303(R) (2009).
[CrossRef]

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[CrossRef]

2008

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, Phys. Rev. A 78, 012301 (2008).
[CrossRef]

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

2007

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

P. van Loock, J. Opt. Soc. Am. B 24, 340 (2007).
[CrossRef]

P. van Loock, C. Weedbrook, and M. Gu, Phys. Rev. A 76, 032321 (2007).
[CrossRef]

2006

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Phys. Rev. Lett. 97, 110501 (2006).
[CrossRef]

J. Zhang and S. L. Braunstein, Phys. Rev. A 73, 032318 (2006).
[CrossRef]

2003

P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003).
[CrossRef]

2001

R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).
[CrossRef]

2000

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Armstrong, S. C.

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

Bloomer, R.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

Braunstein, S. L.

J. Zhang and S. L. Braunstein, Phys. Rev. A 73, 032318 (2006).
[CrossRef]

Briegel, H. J.

R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).
[CrossRef]

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
[CrossRef]

Furusawa, A.

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

R. Ukai, S. Yokoyama, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

Y. Miwa, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. A 80, 050303(R) (2009).
[CrossRef]

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[CrossRef]

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, Phys. Rev. A 78, 012301 (2008).
[CrossRef]

P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003).
[CrossRef]

García-Patrón, R.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
[CrossRef]

Gu, M.

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, and P. van Loock, Phys. Rev. A 79, 062318 (2009).
[CrossRef]

P. van Loock, C. Weedbrook, and M. Gu, Phys. Rev. A 76, 032321 (2007).
[CrossRef]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Phys. Rev. Lett. 97, 110501 (2006).
[CrossRef]

Iwata, N.

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

Jia, X.

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

Jin, X.

Y. Wang, H. Shen, X. Jin, X. Su, C. Xie, and K. Peng, Opt. Express 18, 6149 (2010).
[CrossRef]

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

Jing, J.

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Li, X.

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Lloyd, S.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
[CrossRef]

Menicucci, N. C.

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, and P. van Loock, Phys. Rev. A 79, 062318 (2009).
[CrossRef]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Phys. Rev. Lett. 97, 110501 (2006).
[CrossRef]

Miwa, Y.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

Y. Miwa, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. A 80, 050303(R) (2009).
[CrossRef]

Nielsen, M. A.

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Phys. Rev. Lett. 97, 110501 (2006).
[CrossRef]

O’Brien, J. L.

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[CrossRef]

Peng, K.

Y. Wang, Y. Zheng, C. Xie, and K. Peng, IEEE J. Quantum Electron. 47, 1006 (2011).
[CrossRef]

Y. Wang, H. Shen, X. Jin, X. Su, C. Xie, and K. Peng, Opt. Express 18, 6149 (2010).
[CrossRef]

Y. Wang, X. Su, H. Shen, A. Tan, C. Xie, and K. Peng, Phys. Rev. A 81, 022311 (2010).
[CrossRef]

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Pfister, O.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

Pirandola, S.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
[CrossRef]

Politi, A.

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

Pysher, M.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

Ralph, T. C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
[CrossRef]

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, and P. van Loock, Phys. Rev. A 79, 062318 (2009).
[CrossRef]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Phys. Rev. Lett. 97, 110501 (2006).
[CrossRef]

Raussendorf, R.

R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).
[CrossRef]

Shahrokhshahi, R.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
[CrossRef]

Shen, H.

Y. Wang, X. Su, H. Shen, A. Tan, C. Xie, and K. Peng, Phys. Rev. A 81, 022311 (2010).
[CrossRef]

Y. Wang, H. Shen, X. Jin, X. Su, C. Xie, and K. Peng, Opt. Express 18, 6149 (2010).
[CrossRef]

Shimokawa, Y.

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

Su, X.

Y. Wang, X. Su, H. Shen, A. Tan, C. Xie, and K. Peng, Phys. Rev. A 81, 022311 (2010).
[CrossRef]

Y. Wang, H. Shen, X. Jin, X. Su, C. Xie, and K. Peng, Opt. Express 18, 6149 (2010).
[CrossRef]

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

Tan, A.

Y. Wang, X. Su, H. Shen, A. Tan, C. Xie, and K. Peng, Phys. Rev. A 81, 022311 (2010).
[CrossRef]

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

Ukai, R.

R. Ukai, S. Yokoyama, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, Phys. Rev. A 78, 012301 (2008).
[CrossRef]

van Loock, P.

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

R. Ukai, S. Yokoyama, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

P. van Loock, Laser Photon. Rev. 5, 167 (2011).
[CrossRef]

Y. Miwa, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. A 80, 050303(R) (2009).
[CrossRef]

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, and P. van Loock, Phys. Rev. A 79, 062318 (2009).
[CrossRef]

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, Phys. Rev. A 78, 012301 (2008).
[CrossRef]

P. van Loock, C. Weedbrook, and M. Gu, Phys. Rev. A 76, 032321 (2007).
[CrossRef]

P. van Loock, J. Opt. Soc. Am. B 24, 340 (2007).
[CrossRef]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Phys. Rev. Lett. 97, 110501 (2006).
[CrossRef]

P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003).
[CrossRef]

Vuckovic, J.

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[CrossRef]

Wang, H.

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Wang, Y.

Y. Wang, Y. Zheng, C. Xie, and K. Peng, IEEE J. Quantum Electron. 47, 1006 (2011).
[CrossRef]

Y. Wang, H. Shen, X. Jin, X. Su, C. Xie, and K. Peng, Opt. Express 18, 6149 (2010).
[CrossRef]

Y. Wang, X. Su, H. Shen, A. Tan, C. Xie, and K. Peng, Phys. Rev. A 81, 022311 (2010).
[CrossRef]

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

Weedbrook, C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
[CrossRef]

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, and P. van Loock, Phys. Rev. A 79, 062318 (2009).
[CrossRef]

P. van Loock, C. Weedbrook, and M. Gu, Phys. Rev. A 76, 032321 (2007).
[CrossRef]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Phys. Rev. Lett. 97, 110501 (2006).
[CrossRef]

Xie, C.

Y. Wang, Y. Zheng, C. Xie, and K. Peng, IEEE J. Quantum Electron. 47, 1006 (2011).
[CrossRef]

Y. Wang, H. Shen, X. Jin, X. Su, C. Xie, and K. Peng, Opt. Express 18, 6149 (2010).
[CrossRef]

Y. Wang, X. Su, H. Shen, A. Tan, C. Xie, and K. Peng, Phys. Rev. A 81, 022311 (2010).
[CrossRef]

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Yokoyama, S.

R. Ukai, S. Yokoyama, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

Yoshikawa, J.

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

Yoshikawa, J. I.

R. Ukai, S. Yokoyama, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

Y. Miwa, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. A 80, 050303(R) (2009).
[CrossRef]

Yukawa, M.

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, Phys. Rev. A 78, 012301 (2008).
[CrossRef]

Zhang, J.

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

J. Zhang and S. L. Braunstein, Phys. Rev. A 73, 032318 (2006).
[CrossRef]

Zhang, Y.

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Zheng, Y.

Y. Wang, Y. Zheng, C. Xie, and K. Peng, IEEE J. Quantum Electron. 47, 1006 (2011).
[CrossRef]

IEEE J. Quantum Electron.

Y. Wang, Y. Zheng, C. Xie, and K. Peng, IEEE J. Quantum Electron. 47, 1006 (2011).
[CrossRef]

J. Opt. Soc. Am. B

Laser Photon. Rev.

P. van Loock, Laser Photon. Rev. 5, 167 (2011).
[CrossRef]

Nat. Photonics

J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009).
[CrossRef]

Opt. Express

Phys. Rev. A

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys. Rev. A 62, 023813 (2000).
[CrossRef]

P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003).
[CrossRef]

J. Zhang and S. L. Braunstein, Phys. Rev. A 73, 032318 (2006).
[CrossRef]

P. van Loock, C. Weedbrook, and M. Gu, Phys. Rev. A 76, 032321 (2007).
[CrossRef]

M. Gu, C. Weedbrook, N. C. Menicucci, T. C. Ralph, and P. van Loock, Phys. Rev. A 79, 062318 (2009).
[CrossRef]

Y. Miwa, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. A 80, 050303(R) (2009).
[CrossRef]

Y. Wang, X. Su, H. Shen, A. Tan, C. Xie, and K. Peng, Phys. Rev. A 81, 022311 (2010).
[CrossRef]

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, Phys. Rev. A 78, 012301 (2008).
[CrossRef]

A. Tan, Y. Wang, X. Jin, X. Su, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. A 78, 013828 (2008).
[CrossRef]

Phys. Rev. Lett.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).
[CrossRef]

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Phys. Rev. Lett. 97, 110501 (2006).
[CrossRef]

R. Ukai, N. Iwata, Y. Shimokawa, S. C. Armstrong, A. Politi, J. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 106, 240504 (2011).
[CrossRef]

R. Ukai, S. Yokoyama, J. I. Yoshikawa, P. van Loock, and A. Furusawa, Phys. Rev. Lett. 107, 250501 (2011).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

Rev. Mod. Phys.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

(a) Graph representation of the eight-partite linear cluster state. (b) Schematic of experimental setup for preparing a CV eight-partite cluster state. T: transmission efficient of beam splitter, Boxes including i are Fourier transforms, i is a 90° rotation, and 1 is a 180° rotation. BHD, balanced homodyne detector; and LO, local oscillator.

Fig. 2.
Fig. 2.

Measured noise powers of an eight-partite linear cluster state. The upper and lower curves in all graphs are the normalized quantum noise level and correlation variances of nullifiers, respectively. (a–h) are noise powers of V(p^1x^2), V(p^2x^1x^3), V(p^3x^2x^4), V(p^4x^3x^5), V(p^5x^4x^6), V(p^6x^5x^7), V(p^7x^6x^8), and V(p^8x^7), respectively. The measurement frequency is 2 MHz, the resolution bandwidth is 30 kHz, and the video bandwidth is 100 Hz.

Equations (8)

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(i2i3i10317051020001213110i3170i51020000i3i25685105100000253i3170i1534000000153433170i2500000i1051i6852513000051023170i10i3i2000i5102i31701101312).
V(p^1x^2)+V(p^2x^1x^3)<1,
V(p^2x^1x^3)+V(p^3x^2x^4)<1,
V(p^3x^2x^4)+V(p^4x^3x^5)<1,
V(p^4x^3x^5)+V(p^5x^4x^6)<1,
V(p^5x^4x^6)+V(p^6x^5x^7)<1,
V(p^6x^5x^7)+V(p^7x^6x^8)<1,
V(p^7x^6x^8)+V(p^8x^7)<1,

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