Abstract

A hybrid quantum device consisting of three ensembles of nitrogen-vacancy centers (NVEs) whose spins are collectively coupled to a superconducting coplanar waveguide resonator is shown to enable the generation of controllable tripartite macroscopic entangled states. The density matrix of such NVEs can be encoded to recast a three-qubit system state, which can be characterized in terms of the entanglement witnesses in relation to the Greenberger-Horne-Zeilinger (GHZ) states. We identify the parameter space within which the generated entangled states can have an arbitrarily large overlap with GHZ states, indicating an enhanced entanglement in the system.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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  24. Y. -C. Ou and H. Fan, “Monogamy inequality in terms of negativity for three-qubit states,” Phys. Rev. A 75062308 (2007).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]

2018 (2)

Y. Maleki and A. M. Zheltikov, “Generating maximally-path-entangled number states in two spin ensembles coupled to a superconducting flux qubit,” Phys. Rev. A 97, 012312 (2018).
[Crossref]

Y. Maleki and A. Maleki, “Entangled multimode spin coherent states of trapped ions,” JOSA B 35, 1211–1217 (2018).
[Crossref]

2017 (1)

T. Astner, S. Nevlacsil, N. Peterschofsky, A. Angerer, S. Rotter, S. Putz, J. Schmiedmayer, and J. Majer, “Coherent Coupling of Remote Spin Ensembles via a Cavity Bus”, Phys. Rev. Lett. 118, 140502 (2017).
[Crossref] [PubMed]

2016 (4)

Yimin Liu, Jiabin You, and Qizhe Hou, “Entanglement dynamics of Nitrogen-vacancy centers spin ensembles coupled to a superconducting resonator,” Sci. Rep. 6, 21775 (2016).
[Crossref] [PubMed]

Y. Maleki, “Generation and entanglement of multi–dimensional multi–mode coherent fields in cavity QED,” Quantum Inf. Process. 15, 4537–4562 (2016).
[Crossref]

M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
[Crossref]

T. Liu, Q. -P. Su, S. -J. Xiong, J. -M. Liu, C. -P. Yang, and F. Nori, “Generation of a macroscopic entangled coherent state using quantum memories in circuit QED,” Sci. Rep. 6, 32004 (2016).
[Crossref] [PubMed]

2015 (2)

W. Song, Z. Yin, W. Yang, X. Zhu, F. Zhou, and M. Feng, “One-step generation of multipartite entanglement among nitrogen-vacancy center ensembles,” Sci. Rep. 5, 7755 (2015).
[Crossref] [PubMed]

W. B. Gao, A. Imamoglu, H. Bernien, and R. Hanson, “Coherent manipulation, measurement and entanglement of individual solid-state spins using optical fields,” Nature Photonics 9, 363–373 (2015).
[Crossref]

2013 (7)

N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743 (2013).
[Crossref] [PubMed]

Z. -L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Physics,  85, 623–653 (2013).
[Crossref]

V. Ranjan, G. de Lange, R. Schutjens, T. Debelhoir, J. P. Groen, D. Szombati, D. J. Thoen, T. M. Klapwijk, R. Hanson, and L. DiCarlo, “Probing Dynamics of an Electron-Spin Ensemble via a Superconducting Resonator,” Phys. Rev. Lett. 110, 067004 (2013).
[Crossref] [PubMed]

Z. -L. Xiang, X. -Y. Lu, T. F. Li, J. Q. You, and F. Nori, “Hybrid quantum circuit consisting of a superconducting flux qubit coupled to a spin ensemble and a transmission-line resonator,” Phys. Rev. B 87, 144516 (2013).
[Crossref]

S. Saito, X. Zhu, R. Amsüss, Y. Matsuzaki, K. Kakuyanagi, T. Shimo-Oka, N. Mizuochi, K. Nemoto, W. J. Munro, and K. Semba, “Towards realizing a quantum memory for a superconducting qubit: Storage and retrieval of quantum states,” Phys. Rev. Lett. 111, 107008 (2013).
[Crossref]

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon schrödinger cat states,” Science 342, 607–610 (2013).
[Crossref]

N. Behzadi, B. Ahansaz, and S. Shojaei, “Genuine entanglement among coherent excitonic states of three quantum dots located individually in separated coupled QED cavities,” Eur. Phys. J. D 67, 5 (2013).
[Crossref]

2012 (1)

A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, “Temperature- and Magnetic-Field-Dependent Longitudinal Spin Relaxation in Nitrogen-Vacancy Ensembles in Diamond,” Phys. Rev. Lett. 108, 197601 (2012).
[Crossref] [PubMed]

2011 (3)

N. Ganguly, S. Adhikari, A. S. Majumdar, and J. Chatterjee, “Entanglement Witness Operator for Quantum Teleportation”, Phys. Rev. Lett. 107, 270501 (2011).
[Crossref]

R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, and J. Majer, “Cavity QED with Magnetically Coupled Collective Spin States,” Phys. Rev. Lett. 107, 060502 (2011).
[Crossref] [PubMed]

W. L. Yang, Y. Hu, Z. Q. Yin, Z. J. Deng, and M. Feng, “Entanglement of nitrogen-vacancy-center ensembles using transmission line resonators and a superconducting phase qubit,” Phys. Rev. A 83, 022302 (2011).
[Crossref]

2010 (5)

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105, 210501 (2010).
[Crossref]

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

J. R. Weber, W. F. Koehl, J. B. Varley, A. Janotti, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, “Quantum computing with defects,” PNAS 07, 8513–8518 (2010).
[Crossref]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. -F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a Spin Ensemble to a Superconducting Resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

K. Hammerer, A. S. Søensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041 (2010).
[Crossref]

2007 (1)

Y. -C. Ou and H. Fan, “Monogamy inequality in terms of negativity for three-qubit states,” Phys. Rev. A 75062308 (2007).
[Crossref]

2006 (1)

L. Childress, M. V. G. Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science 314, 281–285 (2006).
[Crossref] [PubMed]

2004 (1)

M. Bourennance, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Brus, M. Lewenstein, and A. Sanpera, “Experimental Detection of Multipartite Entanglement using Witness Operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref]

2003 (1)

M. Barbieri, F. D. Martini, G. D. Nepi, P. Mataloni, G. M. D’Ariano, and C. Macchiavello,” Detection of Entanglement with Polarized Photons: Experimental Realization of an Entanglement Witness,” Phys. Rev. Lett. 91, 227901 (2003).
[Crossref] [PubMed]

2001 (1)

A. Acin, D. Brus, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

1998 (1)

W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80, 2245 (1998).
[Crossref]

1996 (1)

M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1 (1996).
[Crossref]

1989 (1)

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H.J. Carmichael, “Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity,” Phys. Rev. Lett. 63, 240 (1989).
[Crossref] [PubMed]

Acin, A.

A. Acin, D. Brus, M. Lewenstein, and A. Sanpera, “Classification of Mixed Three-Qubit States,” Phys. Rev. Lett. 87, 040401 (2001).
[Crossref] [PubMed]

Acosta, V. M.

A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, “Temperature- and Magnetic-Field-Dependent Longitudinal Spin Relaxation in Nitrogen-Vacancy Ensembles in Diamond,” Phys. Rev. Lett. 108, 197601 (2012).
[Crossref] [PubMed]

Adhikari, S.

N. Ganguly, S. Adhikari, A. S. Majumdar, and J. Chatterjee, “Entanglement Witness Operator for Quantum Teleportation”, Phys. Rev. Lett. 107, 270501 (2011).
[Crossref]

Aguado, R.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105, 210501 (2010).
[Crossref]

Ahansaz, B.

N. Behzadi, B. Ahansaz, and S. Shojaei, “Genuine entanglement among coherent excitonic states of three quantum dots located individually in separated coupled QED cavities,” Eur. Phys. J. D 67, 5 (2013).
[Crossref]

Amsüss, R.

S. Saito, X. Zhu, R. Amsüss, Y. Matsuzaki, K. Kakuyanagi, T. Shimo-Oka, N. Mizuochi, K. Nemoto, W. J. Munro, and K. Semba, “Towards realizing a quantum memory for a superconducting qubit: Storage and retrieval of quantum states,” Phys. Rev. Lett. 111, 107008 (2013).
[Crossref]

R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, and J. Majer, “Cavity QED with Magnetically Coupled Collective Spin States,” Phys. Rev. Lett. 107, 060502 (2011).
[Crossref] [PubMed]

Angerer, A.

T. Astner, S. Nevlacsil, N. Peterschofsky, A. Angerer, S. Rotter, S. Putz, J. Schmiedmayer, and J. Majer, “Coherent Coupling of Remote Spin Ensembles via a Cavity Bus”, Phys. Rev. Lett. 118, 140502 (2017).
[Crossref] [PubMed]

Ashhab, S.

Z. -L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Physics,  85, 623–653 (2013).
[Crossref]

Astner, T.

T. Astner, S. Nevlacsil, N. Peterschofsky, A. Angerer, S. Rotter, S. Putz, J. Schmiedmayer, and J. Majer, “Coherent Coupling of Remote Spin Ensembles via a Cavity Bus”, Phys. Rev. Lett. 118, 140502 (2017).
[Crossref] [PubMed]

Auffeves, A.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. -F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a Spin Ensemble to a Superconducting Resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Awschalom, D. D.

J. R. Weber, W. F. Koehl, J. B. Varley, A. Janotti, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, “Quantum computing with defects,” PNAS 07, 8513–8518 (2010).
[Crossref]

Axline, C.

M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
[Crossref]

Barbieri, M.

M. Barbieri, F. D. Martini, G. D. Nepi, P. Mataloni, G. M. D’Ariano, and C. Macchiavello,” Detection of Entanglement with Polarized Photons: Experimental Realization of an Entanglement Witness,” Phys. Rev. Lett. 91, 227901 (2003).
[Crossref] [PubMed]

Bar-Gill, N.

N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743 (2013).
[Crossref] [PubMed]

Barthe, M. F.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. -F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a Spin Ensemble to a Superconducting Resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Behzadi, N.

N. Behzadi, B. Ahansaz, and S. Shojaei, “Genuine entanglement among coherent excitonic states of three quantum dots located individually in separated coupled QED cavities,” Eur. Phys. J. D 67, 5 (2013).
[Crossref]

Bergonzo, P.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. -F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a Spin Ensemble to a Superconducting Resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Bernien, H.

W. B. Gao, A. Imamoglu, H. Bernien, and R. Hanson, “Coherent manipulation, measurement and entanglement of individual solid-state spins using optical fields,” Nature Photonics 9, 363–373 (2015).
[Crossref]

Bertet, P.

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. -F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a Spin Ensemble to a Superconducting Resonator,” Phys. Rev. Lett. 105, 140502 (2010).
[Crossref]

Blumoff, J.

M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
[Crossref]

Bourennance, M.

M. Bourennance, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Brus, M. Lewenstein, and A. Sanpera, “Experimental Detection of Multipartite Entanglement using Witness Operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref]

Brecha, R. J.

M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H.J. Carmichael, “Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity,” Phys. Rev. Lett. 63, 240 (1989).
[Crossref] [PubMed]

Brus, D.

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J. R. Weber, W. F. Koehl, J. B. Varley, A. Janotti, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, “Quantum computing with defects,” PNAS 07, 8513–8518 (2010).
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N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743 (2013).
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A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, “Temperature- and Magnetic-Field-Dependent Longitudinal Spin Relaxation in Nitrogen-Vacancy Ensembles in Diamond,” Phys. Rev. Lett. 108, 197601 (2012).
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L. Childress, M. V. G. Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science 314, 281–285 (2006).
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M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
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M. Barbieri, F. D. Martini, G. D. Nepi, P. Mataloni, G. M. D’Ariano, and C. Macchiavello,” Detection of Entanglement with Polarized Photons: Experimental Realization of an Entanglement Witness,” Phys. Rev. Lett. 91, 227901 (2003).
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M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
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V. Ranjan, G. de Lange, R. Schutjens, T. Debelhoir, J. P. Groen, D. Szombati, D. J. Thoen, T. M. Klapwijk, R. Hanson, and L. DiCarlo, “Probing Dynamics of an Electron-Spin Ensemble via a Superconducting Resonator,” Phys. Rev. Lett. 110, 067004 (2013).
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L. Childress, M. V. G. Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science 314, 281–285 (2006).
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M. Bourennance, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Brus, M. Lewenstein, and A. Sanpera, “Experimental Detection of Multipartite Entanglement using Witness Operators,” Phys. Rev. Lett. 92, 087902 (2004).
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M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
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M. Bourennance, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Brus, M. Lewenstein, and A. Sanpera, “Experimental Detection of Multipartite Entanglement using Witness Operators,” Phys. Rev. Lett. 92, 087902 (2004).
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V. Ranjan, G. de Lange, R. Schutjens, T. Debelhoir, J. P. Groen, D. Szombati, D. J. Thoen, T. M. Klapwijk, R. Hanson, and L. DiCarlo, “Probing Dynamics of an Electron-Spin Ensemble via a Superconducting Resonator,” Phys. Rev. Lett. 110, 067004 (2013).
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V. Ranjan, G. de Lange, R. Schutjens, T. Debelhoir, J. P. Groen, D. Szombati, D. J. Thoen, T. M. Klapwijk, R. Hanson, and L. DiCarlo, “Probing Dynamics of an Electron-Spin Ensemble via a Superconducting Resonator,” Phys. Rev. Lett. 110, 067004 (2013).
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M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
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M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
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E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature 466, 730–734 (2010).
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L. Childress, M. V. G. Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science 314, 281–285 (2006).
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M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
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Yimin Liu, Jiabin You, and Qizhe Hou, “Entanglement dynamics of Nitrogen-vacancy centers spin ensembles coupled to a superconducting resonator,” Sci. Rep. 6, 21775 (2016).
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W. L. Yang, Y. Hu, Z. Q. Yin, Z. J. Deng, and M. Feng, “Entanglement of nitrogen-vacancy-center ensembles using transmission line resonators and a superconducting phase qubit,” Phys. Rev. A 83, 022302 (2011).
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M. Bourennance, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Brus, M. Lewenstein, and A. Sanpera, “Experimental Detection of Multipartite Entanglement using Witness Operators,” Phys. Rev. Lett. 92, 087902 (2004).
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W. B. Gao, A. Imamoglu, H. Bernien, and R. Hanson, “Coherent manipulation, measurement and entanglement of individual solid-state spins using optical fields,” Nature Photonics 9, 363–373 (2015).
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Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. -F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a Spin Ensemble to a Superconducting Resonator,” Phys. Rev. Lett. 105, 140502 (2010).
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J. R. Weber, W. F. Koehl, J. B. Varley, A. Janotti, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, “Quantum computing with defects,” PNAS 07, 8513–8518 (2010).
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N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743 (2013).
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Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. -F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong Coupling of a Spin Ensemble to a Superconducting Resonator,” Phys. Rev. Lett. 105, 140502 (2010).
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L. Childress, M. V. G. Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science 314, 281–285 (2006).
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A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, “Temperature- and Magnetic-Field-Dependent Longitudinal Spin Relaxation in Nitrogen-Vacancy Ensembles in Diamond,” Phys. Rev. Lett. 108, 197601 (2012).
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M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, “Quantum memory with millisecond coherence in circuit QED,” Phys. Rev. B 94, 014506 (2016).
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E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature 466, 730–734 (2010).
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V. Ranjan, G. de Lange, R. Schutjens, T. Debelhoir, J. P. Groen, D. Szombati, D. J. Thoen, T. M. Klapwijk, R. Hanson, and L. DiCarlo, “Probing Dynamics of an Electron-Spin Ensemble via a Superconducting Resonator,” Phys. Rev. Lett. 110, 067004 (2013).
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M. Bourennance, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Brus, M. Lewenstein, and A. Sanpera, “Experimental Detection of Multipartite Entanglement using Witness Operators,” Phys. Rev. Lett. 92, 087902 (2004).
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B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon schrödinger cat states,” Science 342, 607–610 (2013).
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M. Bourennance, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Guhne, P. Hyllus, D. Brus, M. Lewenstein, and A. Sanpera, “Experimental Detection of Multipartite Entanglement using Witness Operators,” Phys. Rev. Lett. 92, 087902 (2004).
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L. Childress, M. V. G. Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science 314, 281–285 (2006).
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M. Barbieri, F. D. Martini, G. D. Nepi, P. Mataloni, G. M. D’Ariano, and C. Macchiavello,” Detection of Entanglement with Polarized Photons: Experimental Realization of an Entanglement Witness,” Phys. Rev. Lett. 91, 227901 (2003).
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N. Ganguly, S. Adhikari, A. S. Majumdar, and J. Chatterjee, “Entanglement Witness Operator for Quantum Teleportation”, Phys. Rev. Lett. 107, 270501 (2011).
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Figures (5)

Fig. 1
Fig. 1 Time evolution of EW for an NVE with an even-cat input state for (a) g1 = g2 = g3 and (b) g2 = 0.5g1 and g3 = 1.5g1.
Fig. 2
Fig. 2 Time evolution of EW for an NVE with an odd-cat input state for (a) g1 = g2 = g3 and (b) g2 = 0.5g1 and g3 = 1.5g1.
Fig. 3
Fig. 3 Time dependence of the fidelity (a) F+ and (b) F with g1 = g2 = g3.
Fig. 4
Fig. 4 Time evolution of EW for an NVE with decoherence for (a, b) g1 = g2 = g3 and (c, d) g1 = 1, g2 = 0.5g3 = 1.5: (a, c) even-cat input state and (b, d) odd-cat input state.
Fig. 5
Fig. 5 Effect of decoherence on the time evolution of the fidelity (a) F+ and (b) F with g1 = g2 = g3.

Equations (17)

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H = ω c a a + j = 1 3 ω NV b j b j + j = 1 3 g j ( b j a + a b j ) ,
| ψ ± ( 0 ) = 1 2 ± 2 e | α | 2 / 2 ( | α c ± | α c ) | 0 | 0 | 0 .
| ψ ± ( t ) = | α ( t ) c | β 1 ( t ) | β 2 ( t ) | β 3 ( t ) ± | α ( t ) c | β 1 ( t ) | β 2 ( t ) | β 3 ( t ) ,
ρ NV ± ( t ) = N ± 2 [ | β 1 ( t ) β 1 ( t ) | | β 2 ( t ) β 2 ( t ) | | β 3 ( t ) β 3 ( t ) | + | β 1 ( t ) β 1 ( t ) | | β 2 ( t ) β 2 ( t ) | | β 3 ( t ) β 3 ( t ) | ± q ( t ) | | β 1 ( t ) β 1 ( t ) | | β 2 ( t ) β 2 ( t ) | | β 3 ( t ) β 3 ( t ) | ± q ( t ) | β 1 ( t ) β 1 ( t ) | | β 2 ( t ) β 2 ( t ) | | β 3 ( t ) β 3 ( t ) | ] ,
EW = Tr ( W ^ GHZ ρ NV + ( t ) ) = 1 4 + 4 e 2 | α | 2 [ p 1 2 ( t ) + p 2 2 ( t ) + p 3 2 ( t ) p 1 2 ( t ) p 2 2 ( t ) p 1 2 ( t ) p 3 2 ( t ) p 2 2 ( t ) p 3 2 ( t ) 2 [ q ( t ) + p 1 ( t ) p 2 ( t ) p 3 ( t ) ] 1 p 1 2 ( t ) 1 p 2 2 ( t ) 1 p 3 2 ( t ) ] .
EW ( p ( t ) ) = [ 1 p 2 ( t ) ] 4 + 4 e 2 | α | 2 [ 3 p 2 ( t ) 2 [ q ( t ) + p 3 ( t ) ] 1 p 2 ( t ) ] .
W ^ GHZ = 1 2 I I I ( σ z I I ) | GHZ GHZ | ( σ z I I )
EW = Tr ( W ^ GHZ ρ NV ( t ) ) = 1 4 4 e 2 | α | 2 [ p 1 2 ( t ) + p 2 2 ( t ) + p 3 2 ( t ) p 1 2 ( t ) p 2 2 ( t ) p 1 2 ( t ) p 3 2 ( t ) p 2 2 ( t ) p 3 2 ( t ) 2 [ q ( t ) p 1 ( t ) p 2 ( t ) p 3 ( t ) ] 1 p 1 2 ( t ) 1 p 2 2 ( t ) 1 p 3 2 ( t ) ] .
EW ( p ( t ) ) = [ 1 p 2 ( t ) ] 4 4 e 2 | α | 2 [ 3 p 2 ( t ) 2 [ q ( t ) p 3 ( t ) ] 1 p 2 ( t ) ] .
F ± = 1 4 ± 4 q ( t ) p 1 ( t ) p 2 ( t ) p 3 ( t ) [ 1 + p 1 2 ( t ) p 2 2 ( t ) p 3 2 ( t ) ± 2 q ( t ) p 1 ( t ) p 2 ( t ) p 3 ( t ) + ( 1 p 1 2 ( t ) ) ( 1 p 2 2 ( t ) ) × ( 1 p 3 2 ( t ) ) + 2 [ q ( t ) ± p 1 ( t ) p 2 ( t ) p 3 ( t ) ] 1 p 1 2 ( t ) 1 p 2 2 ( t ) 1 p 3 2 ( t ) ] ,
F ± = 1 4 ± 4 q ( t ) p 1 ( t ) p 2 ( t ) p 3 ( t ) [ 1 + p 6 ( t ) ± 2 q ( t ) p 3 ( t ) + 2 ( q ( t ) ± p 3 ( t ) ) ( 1 p 2 ( t ) ) 3 / 2 + ( 1 p 2 ( t ) ) 3 ] .
H T = H i κ 2 a a ,
a ( t ) = e i ( ω i κ / 4 ) t [ cos ( G 2 ( κ / 4 ) 2 t ) a ( 0 ) + i κ / 4 G 2 ( κ / 4 ) 2 sin ( G 2 ( κ / 4 ) 2 t ) a ( 0 ) i 1 G 2 ( κ / 4 ) 2 × sin ( G 2 ( κ / 4 ) 2 t ) ( g 1 b 1 ( 0 ) + g 2 b 2 ( 0 ) + g 3 b 3 ( 0 ) ) ] ,
| ψ ± ( t ) = | α ( t ) c | β 1 ( t ) | β 2 ( t ) | β 3 ( t )
± | α ( t ) c | β 1 ( t ) | β 2 ( t ) | β 3 ( t ) .
α ( t ) = e i ( ω i κ / 4 ) t α [ cos ( G ζ t ) + i ( λ / ζ ) sin ( G ζ t ) ] ,
β i ( t ) = i e i ( ω i κ / 4 ) t α g i G ζ sin ( G ζ t )

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