Abstract

Exploiting the input-output process of low-Q cavities confining nitrogen-vacancy centers, we present an efficient entanglement concentration protocol on electron spin state in decoherence free subspace. Less entangled state can be concentrated to maximally entangled state with the assistance of single photon detection. With its robustness and scalability, the present protocol is immune to dephasing and can be further applied to quantum repeaters and distributed quantum computation.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  4. D. M. Toyli, C. D. Weis, G. D. Fuchs, T. Schenkel, D. D. Awschalom, “Chip-scale nanofabrication of single spins and spin arrays in diamond,” Nano Lett. 10(8), 3168–3172(2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  27. J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nature Photonics 4, 46–49 (2010)
    [CrossRef]
  28. Y.-S. Park, A. K. Cook, H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Letters 6, 2075–2079(2006).
    [CrossRef] [PubMed]
  29. H. Bernien, L. Childress, L. Robledo, M. Markham, D. Twitchen, R. Hanson, “Two-photon quantum interference from separate nitrogen vacancy centers in diamond,” Phys. Rev. Lett. 108, 043604 (2012).
    [CrossRef] [PubMed]
  30. D. K. Armani, T. J. Kippenberg, S. M. Spillance, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
    [CrossRef] [PubMed]
  31. J. Zhu, S. K. Ozdemir, L. He, L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Optics Express 18, 23535–23543 (2010).
    [CrossRef] [PubMed]
  32. P. E. Barclay, F. M. C. Fu, C. Santori, R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” App. Phys. Lett. 95, 191115 (2009).
    [CrossRef]
  33. A. Faraon, C. Santori, Z. Huang, V. M. Acosta, R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
    [CrossRef] [PubMed]
  34. A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, D. Budke, “Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond,” Phys. Rev. Lett. 108, 197601 (2012).
    [CrossRef] [PubMed]
  35. P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008).
    [CrossRef] [PubMed]
  36. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nature Material 8, 383–387 (2009).
    [CrossRef]

2014 (1)

A. P. Liu, L. -Y. Cheng, L. Chen, S. -L. Su, H. -F. Wang, S. Zhang, “Quantum information processing in decoherence-free subspace with nitrogen-vacancy centers coupled to a whispering-gallery mode microresonator,” Opt. Comm. 313, 180–185 (2014).
[CrossRef]

2012 (4)

H. Bernien, L. Childress, L. Robledo, M. Markham, D. Twitchen, R. Hanson, “Two-photon quantum interference from separate nitrogen vacancy centers in diamond,” Phys. Rev. Lett. 108, 043604 (2012).
[CrossRef] [PubMed]

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[CrossRef] [PubMed]

A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, D. Budke, “Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond,” Phys. Rev. Lett. 108, 197601 (2012).
[CrossRef] [PubMed]

P. C. Maurer, G. Kucsko, C. Latta, L. Jiang, N. Y. Yao, S. D. Bennett, F. Pastawski, D. Hunger, N. Chisholm, M. Markham, D. J. Twitchen, J. I. Cirac, M. D. Lukin, “Room-temperature quantum bit memory exceeding one second,” Science 336, 1283–1286(2012).
[CrossRef] [PubMed]

2011 (5)

B. J. M. Hausmann, T. M. Babinec, J. T. Choy, J. S. Hodges, S. Hong, I. Bulu, A. Yacoby, M. D. Lukin, M. Lonc̆ar, “Single-color centers implanted in diamond nanostructures,” New J. Phys. 13, 045004(2011).
[CrossRef]

L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, R. Hanson, “High-fidelity projective read-out of a solid-state spin quantum register,” Nature 477, 574–578(2011).
[CrossRef] [PubMed]

G. D. Fuchs, G. Burkard, P. V. Klimov, D. D. Awschalom, “A quantum memory intrinsic to single nitrogenC-vacancy centres in diamond,” Nature Physics 7, 789–793(2011).
[CrossRef]

Q. Chen, W. L. Yang, M. Fang, J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[CrossRef]

C. Wang, Y. Zhang, G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
[CrossRef]

2010 (8)

Y. B. Sheng, F. G. Deng, H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication.,” Quantum Inform. Comput. 10, 272–281 (2010).

J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nature Photonics 4, 46–49 (2010)
[CrossRef]

Q. Chen, M. Feng, “Quantum-information processing in decoherence-free subspace with low-Q cavities,” Phys. Rev. A 82, 052329 (2010).
[CrossRef]

J. Zhu, S. K. Ozdemir, L. He, L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Optics Express 18, 23535–23543 (2010).
[CrossRef] [PubMed]

W. L. Yang, Z. Y. Xu, M. Feng, J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys. 12, 113039 (2010).
[CrossRef]

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature 466, 730–734 (2010).
[CrossRef] [PubMed]

D. M. Toyli, C. D. Weis, G. D. Fuchs, T. Schenkel, D. D. Awschalom, “Chip-scale nanofabrication of single spins and spin arrays in diamond,” Nano Lett. 10(8), 3168–3172(2010).
[CrossRef] [PubMed]

M. Saffman, T. G. Walker, K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[CrossRef]

2009 (3)

J. H. An, M. Feng, C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79, 032303 (2009).
[CrossRef]

P. E. Barclay, F. M. C. Fu, C. Santori, R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” App. Phys. Lett. 95, 191115 (2009).
[CrossRef]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nature Material 8, 383–387 (2009).
[CrossRef]

2008 (3)

P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008).
[CrossRef] [PubMed]

Y. B. Sheng, F. G. Deng, H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[CrossRef]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef] [PubMed]

2007 (1)

M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science 316, 1312–1316(2007).
[CrossRef]

2006 (2)

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nature Physics 2, 408–413(2006).
[CrossRef]

Y.-S. Park, A. K. Cook, H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Letters 6, 2075–2079(2006).
[CrossRef] [PubMed]

2003 (4)

M. Mohseni, J. S. Lundeen, K. J. Resch, A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett. 91, 187903 (2003).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillance, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef] [PubMed]

Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, J. W. Pan, “Experimental realization of entanglement concentration and a quantum repeater,” Phys. Rev. Lett. 90, 207901(2003).
[CrossRef] [PubMed]

T. Yamamoto, M. Koashi, S. K. Ozdemir, N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346(2003).
[CrossRef] [PubMed]

2002 (1)

D. Kielpinski, C. Monroe, D.J. Wineland, “Architecture for a large-scale ion-trap quantum computer,” Nature 417, 709–711 (2002).
[CrossRef] [PubMed]

1998 (1)

D. A. Lidar, I. L. Chuang, K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594–2597 (1998).
[CrossRef]

1997 (1)

L. M. Duan, G. C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953–1956 (1997).
[CrossRef]

1996 (1)

C. H. Bennett, H. J. Bernstein, S. Popescu, B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052(1996).
[CrossRef] [PubMed]

Achard, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nature Material 8, 383–387 (2009).
[CrossRef]

Acosta, V. M.

A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, D. Budke, “Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond,” Phys. Rev. Lett. 108, 197601 (2012).
[CrossRef] [PubMed]

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[CrossRef] [PubMed]

Alkemade, P. F. A.

L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, R. Hanson, “High-fidelity projective read-out of a solid-state spin quantum register,” Nature 477, 574–578(2011).
[CrossRef] [PubMed]

An, J. H.

J. H. An, M. Feng, C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79, 032303 (2009).
[CrossRef]

Aoki, T.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef] [PubMed]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillance, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef] [PubMed]

Awschalom, D. D.

G. D. Fuchs, G. Burkard, P. V. Klimov, D. D. Awschalom, “A quantum memory intrinsic to single nitrogenC-vacancy centres in diamond,” Nature Physics 7, 789–793(2011).
[CrossRef]

D. M. Toyli, C. D. Weis, G. D. Fuchs, T. Schenkel, D. D. Awschalom, “Chip-scale nanofabrication of single spins and spin arrays in diamond,” Nano Lett. 10(8), 3168–3172(2010).
[CrossRef] [PubMed]

Babinec, T. M.

B. J. M. Hausmann, T. M. Babinec, J. T. Choy, J. S. Hodges, S. Hong, I. Bulu, A. Yacoby, M. D. Lukin, M. Lonc̆ar, “Single-color centers implanted in diamond nanostructures,” New J. Phys. 13, 045004(2011).
[CrossRef]

Balasubramanian, G.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nature Material 8, 383–387 (2009).
[CrossRef]

Barclay, P. E.

P. E. Barclay, F. M. C. Fu, C. Santori, R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” App. Phys. Lett. 95, 191115 (2009).
[CrossRef]

Beausoleil, R. G.

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[CrossRef] [PubMed]

P. E. Barclay, F. M. C. Fu, C. Santori, R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” App. Phys. Lett. 95, 191115 (2009).
[CrossRef]

Beck, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nature Material 8, 383–387 (2009).
[CrossRef]

Bennett, C. H.

C. H. Bennett, H. J. Bernstein, S. Popescu, B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052(1996).
[CrossRef] [PubMed]

Bennett, S. D.

P. C. Maurer, G. Kucsko, C. Latta, L. Jiang, N. Y. Yao, S. D. Bennett, F. Pastawski, D. Hunger, N. Chisholm, M. Markham, D. J. Twitchen, J. I. Cirac, M. D. Lukin, “Room-temperature quantum bit memory exceeding one second,” Science 336, 1283–1286(2012).
[CrossRef] [PubMed]

Bernien, H.

H. Bernien, L. Childress, L. Robledo, M. Markham, D. Twitchen, R. Hanson, “Two-photon quantum interference from separate nitrogen vacancy centers in diamond,” Phys. Rev. Lett. 108, 043604 (2012).
[CrossRef] [PubMed]

L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, R. Hanson, “High-fidelity projective read-out of a solid-state spin quantum register,” Nature 477, 574–578(2011).
[CrossRef] [PubMed]

Bernstein, H. J.

C. H. Bennett, H. J. Bernstein, S. Popescu, B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052(1996).
[CrossRef] [PubMed]

Budke, D.

A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, D. Budke, “Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond,” Phys. Rev. Lett. 108, 197601 (2012).
[CrossRef] [PubMed]

Bulu, I.

B. J. M. Hausmann, T. M. Babinec, J. T. Choy, J. S. Hodges, S. Hong, I. Bulu, A. Yacoby, M. D. Lukin, M. Lonc̆ar, “Single-color centers implanted in diamond nanostructures,” New J. Phys. 13, 045004(2011).
[CrossRef]

Burkard, G.

G. D. Fuchs, G. Burkard, P. V. Klimov, D. D. Awschalom, “A quantum memory intrinsic to single nitrogenC-vacancy centres in diamond,” Nature Physics 7, 789–793(2011).
[CrossRef]

Chemerisov, S.

A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, D. Budke, “Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond,” Phys. Rev. Lett. 108, 197601 (2012).
[CrossRef] [PubMed]

Chen, D. R.

J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nature Photonics 4, 46–49 (2010)
[CrossRef]

Chen, L.

A. P. Liu, L. -Y. Cheng, L. Chen, S. -L. Su, H. -F. Wang, S. Zhang, “Quantum information processing in decoherence-free subspace with nitrogen-vacancy centers coupled to a whispering-gallery mode microresonator,” Opt. Comm. 313, 180–185 (2014).
[CrossRef]

Chen, Q.

Q. Chen, W. L. Yang, M. Fang, J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[CrossRef]

Q. Chen, M. Feng, “Quantum-information processing in decoherence-free subspace with low-Q cavities,” Phys. Rev. A 82, 052329 (2010).
[CrossRef]

Chen, Y. A.

Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, J. W. Pan, “Experimental realization of entanglement concentration and a quantum repeater,” Phys. Rev. Lett. 90, 207901(2003).
[CrossRef] [PubMed]

Cheng, L. -Y.

A. P. Liu, L. -Y. Cheng, L. Chen, S. -L. Su, H. -F. Wang, S. Zhang, “Quantum information processing in decoherence-free subspace with nitrogen-vacancy centers coupled to a whispering-gallery mode microresonator,” Opt. Comm. 313, 180–185 (2014).
[CrossRef]

Childress, L.

H. Bernien, L. Childress, L. Robledo, M. Markham, D. Twitchen, R. Hanson, “Two-photon quantum interference from separate nitrogen vacancy centers in diamond,” Phys. Rev. Lett. 108, 043604 (2012).
[CrossRef] [PubMed]

L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, R. Hanson, “High-fidelity projective read-out of a solid-state spin quantum register,” Nature 477, 574–578(2011).
[CrossRef] [PubMed]

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J. Zhu, S. K. Ozdemir, L. He, L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Optics Express 18, 23535–23543 (2010).
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J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nature Photonics 4, 46–49 (2010)
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Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, J. W. Pan, “Experimental realization of entanglement concentration and a quantum repeater,” Phys. Rev. Lett. 90, 207901(2003).
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Y. B. Sheng, F. G. Deng, H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication.,” Quantum Inform. Comput. 10, 272–281 (2010).

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D. K. Armani, T. J. Kippenberg, S. M. Spillance, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
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T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nature Physics 2, 408–413(2006).
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M. Mohseni, J. S. Lundeen, K. J. Resch, A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett. 91, 187903 (2003).
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E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature 466, 730–734 (2010).
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M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science 316, 1312–1316(2007).
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D. M. Toyli, C. D. Weis, G. D. Fuchs, T. Schenkel, D. D. Awschalom, “Chip-scale nanofabrication of single spins and spin arrays in diamond,” Nano Lett. 10(8), 3168–3172(2010).
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E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature 466, 730–734 (2010).
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T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nature Physics 2, 408–413(2006).
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H. Bernien, L. Childress, L. Robledo, M. Markham, D. Twitchen, R. Hanson, “Two-photon quantum interference from separate nitrogen vacancy centers in diamond,” Phys. Rev. Lett. 108, 043604 (2012).
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G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nature Material 8, 383–387 (2009).
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P. C. Maurer, G. Kucsko, C. Latta, L. Jiang, N. Y. Yao, S. D. Bennett, F. Pastawski, D. Hunger, N. Chisholm, M. Markham, D. J. Twitchen, J. I. Cirac, M. D. Lukin, “Room-temperature quantum bit memory exceeding one second,” Science 336, 1283–1286(2012).
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B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
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M. Saffman, T. G. Walker, K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
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C. Wang, Y. Zhang, G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
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Y.-S. Park, A. K. Cook, H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Letters 6, 2075–2079(2006).
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A. P. Liu, L. -Y. Cheng, L. Chen, S. -L. Su, H. -F. Wang, S. Zhang, “Quantum information processing in decoherence-free subspace with nitrogen-vacancy centers coupled to a whispering-gallery mode microresonator,” Opt. Comm. 313, 180–185 (2014).
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P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008).
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D. M. Toyli, C. D. Weis, G. D. Fuchs, T. Schenkel, D. D. Awschalom, “Chip-scale nanofabrication of single spins and spin arrays in diamond,” Nano Lett. 10(8), 3168–3172(2010).
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D. Kielpinski, C. Monroe, D.J. Wineland, “Architecture for a large-scale ion-trap quantum computer,” Nature 417, 709–711 (2002).
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T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nature Physics 2, 408–413(2006).
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Wrachtrup, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nature Material 8, 383–387 (2009).
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P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008).
[CrossRef] [PubMed]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nature Physics 2, 408–413(2006).
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J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nature Photonics 4, 46–49 (2010)
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W. L. Yang, Z. Y. Xu, M. Feng, J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys. 12, 113039 (2010).
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B. J. M. Hausmann, T. M. Babinec, J. T. Choy, J. S. Hodges, S. Hong, I. Bulu, A. Yacoby, M. D. Lukin, M. Lonc̆ar, “Single-color centers implanted in diamond nanostructures,” New J. Phys. 13, 045004(2011).
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T. Yamamoto, M. Koashi, S. K. Ozdemir, N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346(2003).
[CrossRef] [PubMed]

Yamasaki, S.

P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science 320, 1326–1329 (2008).
[CrossRef] [PubMed]

Yang, L.

J. Zhu, S. K. Ozdemir, L. He, L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Optics Express 18, 23535–23543 (2010).
[CrossRef] [PubMed]

J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nature Photonics 4, 46–49 (2010)
[CrossRef]

Yang, T.

Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, J. W. Pan, “Experimental realization of entanglement concentration and a quantum repeater,” Phys. Rev. Lett. 90, 207901(2003).
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Q. Chen, W. L. Yang, M. Fang, J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
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W. L. Yang, Z. Y. Xu, M. Feng, J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys. 12, 113039 (2010).
[CrossRef]

Yao, N. Y.

P. C. Maurer, G. Kucsko, C. Latta, L. Jiang, N. Y. Yao, S. D. Bennett, F. Pastawski, D. Hunger, N. Chisholm, M. Markham, D. J. Twitchen, J. I. Cirac, M. D. Lukin, “Room-temperature quantum bit memory exceeding one second,” Science 336, 1283–1286(2012).
[CrossRef] [PubMed]

Zhang, A. N.

Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, J. W. Pan, “Experimental realization of entanglement concentration and a quantum repeater,” Phys. Rev. Lett. 90, 207901(2003).
[CrossRef] [PubMed]

Zhang, S.

A. P. Liu, L. -Y. Cheng, L. Chen, S. -L. Su, H. -F. Wang, S. Zhang, “Quantum information processing in decoherence-free subspace with nitrogen-vacancy centers coupled to a whispering-gallery mode microresonator,” Opt. Comm. 313, 180–185 (2014).
[CrossRef]

Zhang, Y.

C. Wang, Y. Zhang, G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
[CrossRef]

Zhao, Z.

Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, J. W. Pan, “Experimental realization of entanglement concentration and a quantum repeater,” Phys. Rev. Lett. 90, 207901(2003).
[CrossRef] [PubMed]

Zhou, H. Y.

Y. B. Sheng, F. G. Deng, H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication.,” Quantum Inform. Comput. 10, 272–281 (2010).

Y. B. Sheng, F. G. Deng, H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[CrossRef]

Zhu, J.

J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nature Photonics 4, 46–49 (2010)
[CrossRef]

J. Zhu, S. K. Ozdemir, L. He, L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Optics Express 18, 23535–23543 (2010).
[CrossRef] [PubMed]

Zibrov, A. S.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature 466, 730–734 (2010).
[CrossRef] [PubMed]

M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science 316, 1312–1316(2007).
[CrossRef]

App. Phys. Lett. (1)

P. E. Barclay, F. M. C. Fu, C. Santori, R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” App. Phys. Lett. 95, 191115 (2009).
[CrossRef]

Nano Lett. (1)

D. M. Toyli, C. D. Weis, G. D. Fuchs, T. Schenkel, D. D. Awschalom, “Chip-scale nanofabrication of single spins and spin arrays in diamond,” Nano Lett. 10(8), 3168–3172(2010).
[CrossRef] [PubMed]

Nano Letters (1)

Y.-S. Park, A. K. Cook, H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Letters 6, 2075–2079(2006).
[CrossRef] [PubMed]

Nature (5)

D. K. Armani, T. J. Kippenberg, S. M. Spillance, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef] [PubMed]

D. Kielpinski, C. Monroe, D.J. Wineland, “Architecture for a large-scale ion-trap quantum computer,” Nature 417, 709–711 (2002).
[CrossRef] [PubMed]

L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, R. Hanson, “High-fidelity projective read-out of a solid-state spin quantum register,” Nature 477, 574–578(2011).
[CrossRef] [PubMed]

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature 466, 730–734 (2010).
[CrossRef] [PubMed]

T. Yamamoto, M. Koashi, S. K. Ozdemir, N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346(2003).
[CrossRef] [PubMed]

Nature Material (1)

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nature Material 8, 383–387 (2009).
[CrossRef]

Nature Photonics (1)

J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nature Photonics 4, 46–49 (2010)
[CrossRef]

Nature Physics (2)

G. D. Fuchs, G. Burkard, P. V. Klimov, D. D. Awschalom, “A quantum memory intrinsic to single nitrogenC-vacancy centres in diamond,” Nature Physics 7, 789–793(2011).
[CrossRef]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nature Physics 2, 408–413(2006).
[CrossRef]

New J. Phys. (2)

W. L. Yang, Z. Y. Xu, M. Feng, J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys. 12, 113039 (2010).
[CrossRef]

B. J. M. Hausmann, T. M. Babinec, J. T. Choy, J. S. Hodges, S. Hong, I. Bulu, A. Yacoby, M. D. Lukin, M. Lonc̆ar, “Single-color centers implanted in diamond nanostructures,” New J. Phys. 13, 045004(2011).
[CrossRef]

Opt. Comm. (1)

A. P. Liu, L. -Y. Cheng, L. Chen, S. -L. Su, H. -F. Wang, S. Zhang, “Quantum information processing in decoherence-free subspace with nitrogen-vacancy centers coupled to a whispering-gallery mode microresonator,” Opt. Comm. 313, 180–185 (2014).
[CrossRef]

Optics Express (1)

J. Zhu, S. K. Ozdemir, L. He, L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Optics Express 18, 23535–23543 (2010).
[CrossRef] [PubMed]

Phys. Rev. A (6)

Q. Chen, M. Feng, “Quantum-information processing in decoherence-free subspace with low-Q cavities,” Phys. Rev. A 82, 052329 (2010).
[CrossRef]

J. H. An, M. Feng, C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79, 032303 (2009).
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Figures (4)

Fig. 1
Fig. 1

The energy level structure of the N-V center coupled to microcavity, where the lower levels are Zeeman sublevels of the ground state and the upper level is the excited one. Quantum information is encoded in the spin state |0〉 and |1〉. The energy level transition between |0〉 and |e〉 is resonated by the left(L) circularly polarized mode. And the energy level transition between |1〉 and |e〉 is resonated by the right(R) circularly polarized mode.

Fig. 2
Fig. 2

The schematic diagram shown the principle of nonlocally entanglement concentration by using single photon input-output process.

Fig. 3
Fig. 3

The yield of the ECP after different iteration times in ideal cases without considering the system decoherence. Here we simulated the yield of the protocol by one time concentration (dotted line), two times (dashed line) and three times iteration (solid line).

Fig. 4
Fig. 4

The yield of the ECP versus the coupling strength. Here we simulated the yield of the protocol by three times iteration, where γ/κ = 0.01.

Equations (10)

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H ^ = j = 1 , 2 [ ω 0 j σ ^ z j 2 + i g j ( a ^ σ ^ + j a ^ σ ^ j ) ] + ω c a ^ a ^ ,
d a ^ d t = [ i ( ω c ω ) + κ 2 + κ s 2 ] a ^ j g j σ j κ a ^ in ,
d σ j d t = [ i ( ω 0 ω ) + γ j 2 ] σ j g j a ^ σ i ,
r ( ω ) = i ( ω c ω ) κ 2 + 2 g 2 / [ i ( ω 0 ω ) + γ / 2 ] i ( ω c ω ) + κ 2 + 2 g 2 / [ i ( ω 0 ω ) + γ / 2 ] ,
r ( ω ) = 2 g 2 / γ κ / 2 2 g 2 / γ + κ / 2 .
| 0 | 0 : | L e i ϕ 2 | L , | R e i ϕ 0 | R ; | 1 | 1 : | L e i ϕ 0 | L , | R e i ϕ 2 | R .
| 0 ˜ | 0 ˜ | | 0 ˜ | 0 ˜ | ; | 1 ˜ | 1 ˜ | e i π | 1 ˜ | 1 ˜ | ; | 0 ˜ | 1 ˜ | | 0 ˜ | 1 ˜ | ; | 1 ˜ | 0 ˜ | | 1 ˜ | 0 ˜ | .
( α | 0 ˜ A | 0 ˜ B + β | 1 ˜ A | 1 ˜ B ) ( α | 0 ˜ a + β | 1 ˜ a ) ( | L + | R ) 2 α β ( | 0 ˜ | 0 ˜ | 1 ˜ + | 1 ˜ | 1 ˜ | 0 ˜ ) e 2 i ϕ 2 | L + e 2 i ϕ 0 | R 2 + ( α 2 | 0 ˜ | 0 ˜ | 0 ˜ + β 2 | 1 ˜ | 1 ˜ | 1 ˜ ) e i ( ϕ 2 + ϕ 0 ) ( | L + | R ) 2 .
| ϕ 2 = 1 | α | 2 + | β | 2 ( α 2 | 0 ˜ | 0 ˜ ± β 2 | 1 ˜ | 1 ˜ ) .
Y = n 2 | α 2 n β 2 n | | α | 2 n + | β | 2 n ,

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