Abstract
We propose a spin squeezing criterion for arbitrary multi-qubit states that is invariant under local unitary operations. We find that, for arbitrary pure two-qubit states, spin squeezing is equivalent to entanglement, and multi-qubit states are entangled if this new spin squeezing parameter is less than unity.
PACS: 03.67.-a; 03.65.Ud
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REFERENCES
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation (Springer-Verlag, Berlin, 2000).
C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895(1993).
A. Ekert, Phys. Rev. Lett. 67, 661(1991).
I. Cirac and N. Gisin, Phys. Lett. A 229, 1(1997).
C. A. Fuchs, N. Gisin, R. B. Griffiths, C.-S. Niu, and A. Peres, Phys. Rev. A 56, 1163(1997).
S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, Phys. Rev. Lett. 83, 1054(1999).
A. Ekert and R. Jozsa, Philos. Trans. R. Soc., London Ser. A 356, 1769(1998).
C. H. Bennett and S. Wiesner, Phys. Rev. Lett. 69, 2881(1992).
J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Phys. Rev. A 62, 052317(2000).
J. I. Cirac, A. Ekert, S. F. Huelga, and C. Macchiavello, Phys. Rev. A 59, 4249(1999).
A. Thapliyal, Phys. Rev. A 59, 3336(1999).
J. Kempe, Phys. Rev. A 60, 910(1999).
C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. 83, 3081(1999).
W. Dur, J. I. Cirac, and R. Tarrach, Phys. Rev. Lett. 83, 3562(1999).
D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Comm. Math. Phys. 238, 379(2003).
J. A. Smolin, Phys. Rev. A 63, 032306(2001).
W. Dur and J. I. Cirac, Phys. Rev. A 62, 022302(2000).
P. W. Shor, J. A. Smolin and A. V. Thapliyal, Phys. Rev. Lett. 90, 107901(2003).
A. Wong and N. Christensen, Phys. Rev. A 63, 044301(2001).
D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen, Phys. Rev. A 46 R6797(1992)
A. Kuzmich, K. Mølmer and E. S. Polzik, Phys. Rev. Lett. 79, 4782(1997).
A. Kuzmich, N. P. Bigelow, and L. Mandel, Europhys. Lett. 42, 481(1998).
E. S. Polzik, Phys. Rev. A 59, 4202(1999).
J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, Phys. Rev. Lett. 83, 1319(1999).
A. Kuzmich, L. Mandel, and N. P. Bigelow, Phys. Rev. Lett. 85, 1594(2000).
L.-M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, Phys. Rev. Lett. 85, 5643(2000).
A. Kozhenkin, K. Mølmer, and E. S. Polzik, Phys. Rev. A 62, 033809(2000).
A. Sørensen, L.-M. Duan, J. I. Cirac, and P. Zoller, Nature (London), 409, 63(2001).
M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138(1993).
M. D. Lukin, S. F. Yelin, and M. Fleischhauer, Phys. Rev. Lett. 84, 4232(2000); A. Andre and M. D. Lukin, Phys. Rev. A 65, 053819(2002).
L. Vernac, M. Pinard, and E. Giacobino, Phys. Rev. A 62, 063812(2000).
K. Helmerson and L. You, Phys. Rev. Lett. 87, 170402(2001); Ö. E. Mustecapliolu, M. Zhang, and L. You, Phys. Rev. A 66, 033611(2002); S. Yi, O. E. Mustecapliolu, C. P. Sun, and L. You, Phys. Rev. A 66, 011601(2002); Ö. E. Mustecapliolu, M. Zhang, and L. You, Phys. Rev. A 66, 033611(2002).
C. Orzel, A. K. Tuchman, M. L. Fenselau, M. Yasuda, and M. A. Kasevich, Science 291, 2386(2001).
U. Poulsen and K. Mølmer, Phys. Rev. A 64, 013616(2001)
D. W. Berry and B. C. Sanders, New J. Phys. 4, 8(2002).
L. K. Thomsen, S. Mancini, and H. M. Wiseman, Phys. Rev. A 65, 061801(2002); D. W. Berry and B. C. Sanders, Phys. Rev. A 66, 012313(2002).
A. R. Usha Devi, K. S. Mallesh, M. A. A. Sbaih, K. B. Nalini, and G. Ramachandran, J. Phys. A: Math. Gen. 36, 5333(2003).
T. Gasenzer, D. C. Roberts, and K. Burnett, Phys. Rev. A 65, 021605(2002).
J. K. Stockton, J. M. Geremia, A. C. Doherty, and H. Mabuchi, Phys. Rev. A 67, 022112(2003).
Z. Ficek and R. Tanas, Phys. Rep. 372, 369(2002).
L. Zhou, H. S. Song and C. Li, J. Opt. B: Quantum Semiclass. Opt. 4, 425(2002).
X. Wang, A. Sørensen, and K. Mølmer, Phys. Rev. A 64, 053815(2001); X. Wang, J. Opt. B: Quantum Semiclassical Opt. 3, 93(2001); X. Wang, Opt. Commun. 200, 277(2001).
A. Sørensen, K. Mølmer, Phys. Rev. Lett. 86, 4431(2001).
K. Wodkiewicz and J. H. Eberly, J. Opt. Soc. Am. B 2, 458(1985).
G. S. Agarwal and R. R. Puri, Phys. Rev. A 41, 3782(1990); G. S. Agarwal and R. R. Puri, Phys. Rev. A 41, 4968(1994).
D. J. Wineland, J. J. Bollinger, W. M. Itano and D. J. Heinzen, Phys. Rev. A 50, 67(1994).
B. Yurke, Phys. Rev. Lett. 56, 1515(1986); M. Kitagawa and M. Ueda, Phys. Rev. Lett. 67, 1852(1991).
R. Horodecki and M. Horodecki, Phys. Rev. A 54, 1838(1996).
L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics (Addison-Wesley Publishing Company, 1981).
D. Ulam-Orgikh and M. Kitagawa, Phys. Rev. A 64, 052106(2001).
D. W. Berry and B. C. Sanders, New J. Phys. 4, 8(2002).
M. G. Raymer, A. C. Funk, B. C. Sanders, and H. de Guise, Phys. Rev. A 67, 052104(2003).
X. Wang and B. C. Sanders, Phys. Rev. A 68, 03382(2003); X. Wang and K. Mølmer, Eur. Phys. J. D 18, 385(2002).
S. Hill and, W. K. Wootters, Phys. Rev. Lett. 78, 5022(1997); W. K. Wootters, Phys. Rev. Lett. 80, 2245(1998).
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Usha Devi, A., Wang, X. & Sanders, B. Spin Squeezing Criterion with Local Unitary Invariance. Quantum Information Processing 2, 207–220 (2003). https://doi.org/10.1023/B:QINP.0000004125.12489.f4
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DOI: https://doi.org/10.1023/B:QINP.0000004125.12489.f4