Entanglement concentration for a non-maximally entangled four-photon cluster state
Xiang Yan, Ya-Fei Yu, Zhi-Ming Zhang
Entanglement concentration for a non-maximally entangled four-photon cluster state
We present a scheme for locally concentrating a non-maximally entangled four-photon cluster state into a maximally-entangled four-photon cluster state. This scheme has a high success probability. The controlled-NOT (CNOT) gate is a crucial ingredient in this scheme, and we use a nearly deterministic CNOT gate, which is similar with that first introduced by Nemoto et al. (Phys. Rev. Lett., 2004, 93: 250502). This CNOT gate has a simple structure and does not need the strong nonlinearity.
cluster state / entanglement concentration / controlled-NOT gate
[1] |
H. Jeong and M. S. Kim, Efficient quantum computation using coherent states, Phys. Rev. A, 2002, 65(4): 042305
CrossRef
ADS
Google scholar
|
[2] |
T. C. Ralph, A. Gilchrist, G. J. Milburn, W. Munro, and S. Glancy, Quantum computation with optical coherent states, Phys. Rev. A, 2003, 68(4): 042319
CrossRef
ADS
Google scholar
|
[3] |
S. J. van Enk and O. Hirota, Entangled coherent states: Teleportation and decoherence, Phys. Rev. A, 2001, 64(2): 022313
CrossRef
ADS
Google scholar
|
[4] |
H. Jeong, M. S. Kim, and J. Lee, Quantum-information processing for a coherent superposition state via a mixedentangled coherent channel, Phys. Rev. A, 2001, 64(5): 052308
CrossRef
ADS
Google scholar
|
[5] |
D. Gottesman and J. Preskill, Secure quantum key distribution using squeezed states, Phys. Rev. A, 2001, 63(2): 022309
CrossRef
ADS
Google scholar
|
[6] |
N. J. Cerf, M. Lévy, and G. Assche, Quantum distribution of Gaussian keys using squeezed states, Phys. Rev. A, 2001, 63(5): 052311
CrossRef
ADS
Google scholar
|
[7] |
W. Dür, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A, 2000, 62(6): 062314
CrossRef
ADS
Google scholar
|
[8] |
C. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin, and W. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett., 1996, 76(5): 722
CrossRef
ADS
Google scholar
|
[9] |
Z. Zhao, J. W. Pan, and M. S. Zhan, Practical scheme for entanglement concentration, Phys. Rev. A, 2001, 64(1): 014301
CrossRef
ADS
Google scholar
|
[10] |
L. Ye and G. C. Guo, Scheme for entanglement concentration of atomic entangled states in cavity QED, Phys. Lett. A, 2004, 327(4): 284
CrossRef
ADS
Google scholar
|
[11] |
C. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin, and W. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett., 1996, 76(5): 722
CrossRef
ADS
Google scholar
|
[12] |
M. Yang and Z. L. Cao, Entanglement distillation for W class states, Physica A, 2004, 337(1-2): 141
CrossRef
ADS
Google scholar
|
[13] |
M. Yang, W. Song, and Z. L. Cao, Entanglement distillation for atomic states via cavity QED, Physica A, 2004, 341: 251
CrossRef
ADS
Google scholar
|
[14] |
J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, Entanglement purification for quantum communication, Nature, 2001, 410(6832): 1067
CrossRef
ADS
Google scholar
|
[15] |
H. F.Wang, S. Zhang, and K. H. Yeon, Linear optical scheme for entanglement concentration of two partially entangled three-photon W states, Eur. Phys. J. D, 2010, 56(2): 271
CrossRef
ADS
Google scholar
|
[16] |
L. L. Sun, H. F. Wang, S. Zhang, and K. H. Yeon, Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity, J. Opt. Soc. Am. B, 2012, 29(4): 630
CrossRef
ADS
Google scholar
|
[17] |
Y. B. Sheng, L. Zhou, and S. M. Zhao, Efficient two-step entanglement concentration for arbitrary W states, Phys. Rev. A, 2012, 85(4): 042302
CrossRef
ADS
Google scholar
|
[18] |
C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Concentrating partial entanglement by local operations, Phys. Rev. A, 1996, 53(4): 2046
CrossRef
ADS
Google scholar
|
[19] |
Z. Zhao, J. W. Pan, and M. S. Zhan, Practical scheme for entanglement concentration, Phys. Rev. A, 2001, 64(1): 014301
CrossRef
ADS
Google scholar
|
[20] |
Y. B. Sheng, F. G. Deng, and H. Y. Zhou, Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics, Phys. Rev. A, 2008, 77(6): 062325
CrossRef
ADS
Google scholar
|
[21] |
Z. L. Cao and M. Yang, Entanglement distillation for threeparticle W class states, J. Phys. B, 2003, 36(21): 4245
CrossRef
ADS
Google scholar
|
[22] |
L. H. Zhang, M. Yang, and Z. L. Cao, Entanglement concentration for unknown Wclass states, Physica A, 2007, 374(2): 611
CrossRef
ADS
Google scholar
|
[23] |
H. F. Wang, S. Zhang, and K. H. Yeon, Linear optical scheme for entanglement concentration of two partially entangled three-photon W states, Eur. Phys. J. D, 2010, 56(2): 271
CrossRef
ADS
Google scholar
|
[24] |
Y. B. Sheng, L. Zhou, and S. M. Zhao, Efficient two-step entanglement concentration for arbitrary W states, Phys. Rev. A, 2012, 85(4): 042302
CrossRef
ADS
Google scholar
|
[25] |
W. Dür and H. J. Briegel, Stability of macroscopic entanglement under decoherence, Phys. Rev. Lett., 2004, 92(18): 180403
CrossRef
ADS
Google scholar
|
[26] |
B. Si, S. L. Su, L. L. Sun, L. Y. Cheng, H. F. Wang, and S. Zhang, Efficient three-step entanglement concentration for an arbitrary four-photon cluster state, Chin. Phys. B, 2013, 22(3): 030305
CrossRef
ADS
Google scholar
|
[27] |
S. Y. Zhao, J. Liu, L. Zhou, and Y. B. Sheng, Two-step entanglement concentration for arbitrary electronic cluster state, Quantum Inf. Process., 2013, 12(12): 3633
CrossRef
ADS
Google scholar
|
[28] |
B. S. Choudhury and A. Dhara, An entanglement concentration protocol for cluster states, Quantum Inf. Process., 2013, 12(7): 2577
CrossRef
ADS
Google scholar
|
[29] |
Q. Lin and J. Li, Quantum control gates with weak cross-Kerr nonlinearity, Phys. Rev. A, 2009, 79(2): 022301
CrossRef
ADS
Google scholar
|
[30] |
K. Nemoto and W. J. Munro, Nearly deterministic linear optical controlled-NOT<?Pub Caret?> gate, Phys. Rev. Lett., 2004, 93(25): 250502
CrossRef
ADS
Google scholar
|
[31] |
P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys., 2007, 79(1): 135
CrossRef
ADS
Google scholar
|
[32] |
B. Yurke, Wideband photon counting and homodyne detection, Phys. Rev. A, 1985, 32(1): 311
CrossRef
ADS
Google scholar
|
[33] |
J. H. Shapiro, Single-photon Kerr nonlinearities do not help quantum computation, Phys. Rev. A, 2006, 73: 062305
CrossRef
ADS
Google scholar
|
[34] |
J. H. Shapiro and M. Razavi, Continuous-time cross-phase modulation and quantum computation, New. J. Phys., 2007, 9: 16
CrossRef
ADS
Google scholar
|
[35] |
W. J. Munro, Kae Nemoto, T. P. Spiller, S. D. Barrett, Pieter Kok, and R. G. Beausoleil, Efficient optical quantum information processing, J. Opt. B, 2005, 7(7): S135
CrossRef
ADS
Google scholar
|
/
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