Error-detected N-photon cluster state generation based on the controlledphase gate using a quantum dot in an optical microcavity

Abstract

We propose a scheme for error-detected generation of an N-photon cluster state with a quantum dot (QD) embedded in a single-sided optical microcavity (QD-cavity system). The basic structure of this scheme is an error-detected controlled-phase (C-phase) gate on the hybrid electron–photon system. In this scheme, the fidelity of N-photon cluster state generation can be reached unity even if low-Q cavity and cavity leakage are considered. By using error detecting, the generation of an N-photon cluster state can be performed by repeating until success, which also leads to a high success probability, compared with other schemes assisted by the QD-cavity system. The error-detected generation of an N-photon cluster state in the highly controllable way may benefit on the quantum network in the future.

Keywords

controlled-phase gate / cluster state / error-detected / QD-cavity system

References

[1] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge: Cambridge University Press, 2000

[2] P. W. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, S. Goldwasser, pp 124–134, IEEE Computer Society Press, 1994

[3] L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett. 79(2), 325 (1997)

[4] G. L. Long, Grover algorithm with zero theoretical failure rate, Phys. Rev. A 64(2), 022307 (2001)

[5] Y. B. Sheng and L. Zhou, Blind quantum computation with a noise channel, Phys. Rev. A 98(5), 052343 (2018)

[6] Z. Z. Zou, X. T. Yu, and Z. C. Zhang, Quantum connectivity optimization algorithms for entanglement source deployment in a quantum multi-hop network, Front. Phys. 13(2), 130202 (2018)

[7] N. A. Gershenfeld and I. L. Chuang, Bulk spin-resonance quantum computation, Science 275(5298), 350 (1997)

[8] G. R. Feng, G. F. Xu, and G. L. Long, Experimental realization of nonadiabatic holonomic quantum computation, Phys. Rev. Lett. 110(19), 190501 (2013)

[9] Y. Long, G. R. Feng, Y. C. Tang, W. Qin, and G. L. Long, NMR realization of adiabatic quantum algorithms for the modified Simon problem, Phys. Rev. A 88(1), 012306 (2013)

[10] X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, Shortcut to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm, New J. Phys. 18(2), 023001 (2016)

[11] X. K. Song, Q. Ai, J. Qiu, and F. G. Deng, Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics, Phys. Rev. A 93(5), 052324 (2016)

[12] D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57(1), 120 (1998)

[13] A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. Di-Vincenzo, D. Loss, M. Sherwin, and A. Small, Quantum information processing using quantum dot spins and cavity QED, Phys. Rev. Lett. 83(20), 4204 (1999)

[14] T. Li and F. G. Deng, Error-rejecting quantum computing with solid-state spins assisted by low-Q optical microcavities, Phys. Rev. A 94(6), 062310 (2016)

[15] T. Li, J. C. Gao, F. G. Deng, and G. L. Long, Highfidelity quantum gates on quantum-dot-confined electron spins in low-Qoptical microcavities, Ann. Phys. 391, 150 (2018)

[16] T. van der Sar, Z. H. Wang, M. S. Blok, H. Bernien, T. H. Taminiau, D. M. Toyli, D. A. Lidar, D. D. Awschalom, R. Hanson, and V. V. Dobrovitski, Decoherence-protected quantum gates for a hybrid solid-state spin register, Nature 484(7392), 82 (2012)

[17] H. R. Wei and F. G. Deng, Compact quantum gates on electron-spin qubits assisted by diamond nitrogenvacancy centers inside cavities, Phys. Rev. A 88(4), 042323 (2013)

[18] T. Yamamoto, Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, Demonstration of conditional gate operation using superconducting charge qubits, Nature 425(6961), 941 (2003)

[19] M. Hua, M. J. Tao, A. Alsaedi, T. Hayat, and F. G. Deng, Universal distributed quantum computing on superconducting qutrits with dark photons, Ann. Phys. 530(4), 1700402 (2018)

[20] H. Fan and X. B. Zhu, superconducting qubits for quantum walks, Front. Phys. 14(6), 61201 (2019)

[21] X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, An all-optical quantum gate in a semiconductor quantum dot, Science 301(5634), 809 (2003)

[22] E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature 409(6816), 46 (2001)

[23] M. A. Nielsen, Optical quantum computation using cluster states, Phys. Rev. Lett. 93(4), 040503 (2004)

[24] H. R. Wei and F. G. Deng, Scalable photonic quantum computing assisted by quantum-dot spin in double-sided optical microcavity, Opt. Express 21(15), 17671 (2013)

[25] C. Wang, Y. Zhang, R. Z. Jiao, and G. S. Jin, Universal quantum controlled phase gate on photonic qubits based on nitrogen vacancy centers and microcavity resonators, Opt. Express 21(16), 19252 (2013)

[26] Y. H. Kang, Y. Xia, and P. M. Lu, Two-photon phase gate with linear optical elements and atom-cavity system, Quantum Inform. Process. 15(11), 4521 (2016)

[27] B. C. Ren and F. G. Deng, Hyper-parallel photonic quantum computing with coupled quantum dots, Sci. Rep. 4(1), 4623 (2015)

[28] B. C. Ren, G. Y. Wang, and F. G. Deng, Universal hyperparallel hybrid photonic quantum gates with dipoleinduced transparency in the weak-coupling regime, Phys. Rev. A 91(3), 032328 (2015)

[29] B. C. Ren, and F. G. Deng, Robust hyperparallel photonic quantum entangling gate with cavity QED, Opt. Express 25(10), 10863 (2017)

[30] T. Li and G. L. Long, Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities, Phys. Rev. A 94(2), 022343 (2016)

[31] G. Y. Wang, T. Li, Q. Ai, and F. G. Deng, Self-errorcorrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom, Opt. Express 26(18), 23333 (2018)

[32] B. C. Ren, A. H. Wang, A. Alsaedi, T. Hayat, and F. G. Deng, Three-photon polarization-spatial hyperparallel quantum Fredkin gate assisted by diamond nitrogen vacancy center in optical cavity, Ann. Phys. 530(5), 1800043 (2018)

[33] F. G. Deng, B. C. Ren, and X. H. Li, Quantum hyperentanglement and its applications in quantum information processing, Sci. Bull. 62(1), 46 (2017)

[34] D. Jaksch, H. J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett. 82(9), 1975 (1999)

[35] D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, Fast quantum gates for neutral atoms, Phys. Rev. Lett. 85(10), 2208 (2000)

[36] G. Z. Song, Q. Liu, J. Qiu, G. J. Yang, F. Alzahrani, A. Hobiny, F. G. Deng, and M. Zhang, Heralded quantum gates for atomic systems assisted by the scattering of photons off single emitters, Ann. Phys. 387, 152 (2017)

[37] J. Joo and D. L. Feder, Error-correcting one-way quantum computation with global entangling gates, Phys. Rev. A 80(3), 032312 (2009)

[38] A. K. Ekert, Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett. 67(6), 661 (1991)

[39] C. H. Bennett, G. Brassard, and N. D. Mermin, Quantum cryptography without Bell’s theorem, Phys. Rev. Lett. 68(5), 557 (1992)

[40] X. H. Li, F. G. Deng, and H. Y. Zhou, Efficient quantum key distribution over a collective noise channel, Phys. Rev. A 78(2), 022321 (2008)

[41] M. Hillery, V. Bužek, and A. Berthiaume, Quantum secret sharing, Phys. Rev. A 59(3), 1829 (1999)

[42] G. L. Long and X. S. Liu, Theoretically efficient highcapacity quantum-key-distribution scheme, Phys. Rev. A 65(3), 032302 (2002)

[43] F. G. Deng, G. L. Long, and X. S. Liu, Two-step quantum direct communication protocol using the Einstein– Podolsky–Rosen pair block, Phys. Rev. A 68(4), 042317 (2003)

[44] F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states, Sci. China Phys. Mech. Astron. 60(12), 120313 (2017)

[45] W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, Quantum secure direct communication with quantum memory, Phys. Rev. Lett. 118(22), 220501 (2017)

[46] F. Zhu, W. Zhang, Y. B. Sheng, and Y. D. Huang, Experimental long-distance quantum secure direct communication, Sci. Bull. 62(22), 1519 (2017)

[47] S. S. Chen, L. Zhou, W. Zhong, and Y. B. Sheng, Threestep three-party quantum secure direct communication, Sci. China Phys. Mech. Astron. 61, 090312 (2017)

[48] C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein–Podolsky– Rosen channels, Phys. Rev. Lett. 70(13), 1895 (1993)

[49] C. H. Bennett and S. J. Wiesner, Communication via oneand two-particle operators on Einstein–Podolsky–Rosen states, Phys. Rev. Lett. 69(20), 2881 (1992)

[50] X. S. Liu, G. L. Long, D. M. Tong, and F. Li, General scheme for superdense coding between multiparties, Phys. Rev. A 65(2), 022304 (2002)

[51] H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Quantum repeaters:the role of imperfect local operations in quantum communication, Phys. Rev. Lett. 81(26), 5932 (1998)

[52] L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Longdistance quantum communication with atomic ensembles and linear optics, Nature 414(6862), 413 (2001)

[53] N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, Quantum repeaters based on atomic ensembles and linear optics, Rev. Mod. Phys. 83(1), 33 (2011)

[54] T. J. Wang, S. Y. Song, and G. L. Long, Quantum repeater based on spatial entanglement of photons and quantum-dot spins in optical microcavities, Phys. Rev. A 85(6), 062311 (2012)

[55] T. Li, G. J. Yang, and F. G. Deng, Heralded quantum repeater for a quantum communication network based on quantum dots embedded in optical microcavities, Phys. Rev. A 93(1), 012302 (2016)

[56] G. Z. Song, M. Zhang, Q. Ai, G. J. Yang, A. Alsaedi, A. Hobiny, and F. G. Deng, Heralded quantum repeater based on the scattering of photons off single emitters in one-dimensional waveguides, Ann. Phys. 378, 33 (2017)

[57] P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Ultrabright source of polarizationentangled photons, Phys. Rev. A 60(2), R773 (1999)

[58] J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, Generation of hyperentangled photon pairs, Phys. Rev. Lett. 95(26), 260501 (2005)

[59] R. Ceccarelli, G. Vallone, F. De Martini, P. Mataloni, and A. Cabello, Experimental entanglement and nonlocality of a two-photon six-qubit cluster state, Phys. Rev. Lett. 103(16), 160401 (2009)

[60] D. Kalamidas, Linear optical scheme for error-free entanglement distribution and a quantum repeater, Phys. Rev. A 73(5), 054304 (2006)

[61] T. Yamamoto, J. Shimamura, S. K. Ozdemir, M. Koashi, and N. Imoto, Faithful qubit distribution assisted by one additional qubit against collective noise, Phys. Rev. Lett. 95(4), 040503 (2005)

[62] X. H. Li, F. G. Deng, and H. Y. Zhou, Faithful qubit transmission against collective noise without ancillary qubits, Appl. Phys. Lett. 91(14), 144101 (2007)

[63] C. Y. Gao, G. Y. Wang, H. Zhang, and F. G. Deng, Multiphoton self-error-correction hyperentanglement distribution over arbitrary collective-noise channels, Quantum Inform. Process. 16(1), 11 (2017)

[64] Y. X. Jiang, P. L. Guo, C. Y. Gao, H. B. Wang, F. Alzahrani, A. Hobiny, and F. G. Deng, Self-errorrejecting photonic qubit transmission in polarizationspatial modes with linear optical elements, Sci. China Phys. Mech. Astron. 60(12), 120312 (2017)

[65] C. H. Bennett, G. Brassard, S. Popescu, B. J. Schumacher, A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett. 76(5), 722 (1996)

[66] C. Simon and J. W. Pan, Polarization entanglement purification using spatial entanglement, Phys. Rev. Lett. 89(25), 257901 (2002)

[67] Y. B. Sheng and F. G. Deng, Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement, Phys. Rev. A 81(3), 032307 (2010)

[68] Y. B. Sheng and F. G. Deng, One-step deterministic polarization-entanglement purification using spatial entanglement, Phys. Rev. A 82(4), 044305 (2010)

[69] X. H. Li, Deterministic polarization-entanglement purification using spatial entanglement, Phys. Rev. A 82(4), 044304 (2010)

[70] F. G. Deng, One-step error correction for multipartite polarization entanglement, Phys. Rev. A 83(6), 062316 (2011)

[71] Y. B. Sheng and L. Zhou, Deterministic polarization entanglement purification using time-bin entanglement, Laser Phys. Lett. 11(8), 085203 (2014)

[72] B. C. Ren, F. F. Du, and F. G. Deng, Two-step hyperentanglement purification with the quantum-state-joining method, Phys. Rev. A 90(5), 052309 (2014)

[73] G. Y. Wang, Q. Liu, and F. G. Deng, Hyperentanglement purification for two-photon six-qubit quantum systems, Phys. Rev. A 94(3), 032319 (2016)

[74] G. Y. Wang, T. Li, Q. Ai, A. Alsaedi, T. Hayat, and F. G. Deng, Heralded entanglement purification for highcapacity quantum communication with two-photon fourqubit systems, arXiv: 1802.00111 (2018)

[75] L. Zhou and Y. B. Sheng, Polarization entanglement purification for concatenated Greenberger–Horne–Zeilinger state, Ann. Phys. 385, 10 (2017)

[76] L. Zhou and Y. B. Sheng, Purification of Logic-Qubit Entanglement, Sci. Rep. 6(1), 28813 (2016)

[77] C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Concentrating partial entanglement by local operations, Phys. Rev. A 53(4), 2046 (1996)

[78] Z. Zhao, J. W. Pan, and M. S. Zhan, Practical scheme for entanglement concentration, Phys. Rev. A 64(1), 014301 (2001)

[79] T. Yamamoto, M. Koashi, and N. Imoto, Concentration and purification scheme for two partially entangled photon pairs, Phys. Rev. A 64(1), 012304 (2001)

[80] 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 77(6), 062325 (2008)

[81] B. C. Ren, F. F. Du, and F. G. Deng, Hyperentanglement concentration for two-photon four-qubit systems with linear optics, Phys. Rev. A 88(1), 012302 (2013)

[82] B. C. Ren and G. L. Long, General hyperentanglement concentration for photon systems assisted by quantumdot spins inside optical microcavities, Opt. Express 22(6), 6547 (2014)

[83] X. H. Li and S. Ghose, Hyperentanglement concentration for time-bin and polarization hyperentangled photons, Phys. Rev. A 91(6), 062302 (2015)

[84] C. Cao, T. J. Wang, S. C. Mi, R. Zhang, and C. Wang, Nonlocal hyperconcentration on entangled photons using photonic module system, Ann. Phys. 369, 128 (2016)

[85] J. Liu, L. Zhou, W. Zhong, and Y. B. Sheng, Logic Bell state concentration with parity check measurement, Front. Phys. 14(2), 21601 (2019)

[86] P. G. Kwiat and H. Weinfurter, Embedded Bell-state analysis, Phys. Rev. A 58(4), R2623 (1998)

[87] N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, Bell measurements for teleportation, Phys. Rev. A 59(5), 3295 (1999)

[88] C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, Complete deterministic linear optics Bell state analysis, Phys. Rev. Lett. 96(19), 190501 (2006)

[89] T. C. Wei, J. T. Barreiro, and P. G. Kwiat, Hyperentangled Bell state analysis, Phys. Rev. A 75(6), 060305 (2007)

[90] Y. B. Sheng, F. G. Deng, and G. L. Long, Complete hyperentangled-Bell-state analysis for quantum communication, Phys. Rev. A 82(3), 032318 (2010)

[91] B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities, Opt. Express 20(22), 24664 (2012)

[92] T. J. Wang, Y. Lu, and G. L. Long, Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities, Phys. Rev. A 86(4), 042337 (2012)

[93] Q. Liu and M. Zhang, Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators, Phys. Rev. A 91(6), 062321 (2015)

[94] G. Y. Wang, Q. Ai, B. C. Ren, T. Li, and F. G. Deng, Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantumdot spins in double-sided optical microcavities, Opt. Express 24(25), 28444 (2016)

[95] X. H. Li and S. Ghose, Hyperentangled Bell-state analysis and hyperdense coding assisted by auxiliary entanglement, Phys. Rev. A 96, 020303(R) (2017)

[96] H. J. Briegel and R. Raussendorf, Persistent entanglement in arrays of interacting particles, Phys. Rev. Lett. 86(5), 910 (2001)

[97] R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86(22), 5188 (2001)

[98] H. F. Wang, C. P. Yang, and F. Nori, Robust and scalable optical one-way quantum computation, Phys. Rev. A 81(5), 052332 (2010)

[99] M. Varnava, D. E. Browne, and T. Rudolph, Loss tolerance in one-way quantum computation via counterfactual error correction, Phys. Rev. Lett. 97(12), 120501 (2006)

[100] G. Vallone, E. Pomarico, F. De Martini, and P. Mataloni, One-way quantum computation with two-photon multiqubit cluster states, Phys. Rev. A 78(4), 042335 (2008)

[101] M. Borhani and D. Loss, Cluster states from Heisenberg interactions, Phys. Rev. A 71(3), 034308 (2005)

[102] Y. Tokunaga, S. Kuwashiro, T. Yamamoto, M. Koashi, and N. Imoto, Generation of high-fidelity four-photon cluster state and quantum-domain demonstration of oneway quantum computing, Phys. Rev. Lett. 100(21), 210501 (2008)

[103] M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, Experimental generation of four-mode continuous-variable cluster states, Phys. Rev. A 78(1), 012301 (2008)

[104] T. Yu, A. D. Zhu, S. Zhang, K. H. Yeon, and S. C. Yu, Deterministic controlled-phase gate and preparation of cluster states via singly charged quantum dots in cavity quantum electrodynamics, Phys. Scr. 84(2), 025001 (2011)

[105] C. Zhang, Y. F. Huang, B. H. Liu, C. F. Li, and G. C. Guo, Experimental generation of a high-fidelity fourphoton linear cluster state, Phys. Rev. A 93(6), 062329 (2016)

[106] D. Loss and D. P. Di Vincenzo, Quantum computation with quantum dots, Phys. Rev. A 57(1), 120 (1998)

[107] C. Piermarocchi, P. Chen, L. J. Sham, and D. G. Steel, Optical RKKY interaction between charged semiconductor quantum dots, Phys. Rev. Lett. 89(16), 167402 (2002)

[108] T. Calarco, A. Datta, P. Fedichev, E. Pazy, and P. Zoller, Spin-based all-optical quantum computation with quantum dots: Understanding and suppressing decoherence, Phys. Rev. A 68(1), 012310 (2003)

[109] S. M. Clark, K. C. Fu, T. D. Ladd, and Y. Yamamoto, Quantum computers based on electron spins controlled by ultrafast off-resonant single optical pulses, Phys. Rev. Lett. 99(4), 040501 (2007)

[110] W. Yao, R. B. Liu, and L. J. Sham, Theory of control of the spin-photon interface for quantum networks, Phys. Rev. Lett. 95(3), 030504 (2005)

[111] A. Imamogłu, D. D. Awschalom, G. Burkard, D. P. Di-Vincenzo, D. Loss, M. Sherwin, and A. Small, Quantum information processing using quantum dot spins and cavity QED, Phys. Rev. Lett. 83(20), 4204 (1999)

[112] J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Coherent manipulation of coupled electron spins in semiconductor quantum dots, Science 309(5744), 2180 (2005)

[113] A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, Mode locking of electron spin coherences in singly charged quantum dots, Science 313(5785), 341 (2006)

[114] K. D. Greve, D. Press, P. L. McMahon, and Y. Yamamoto, Ultrafast optical control of individual quantum dot spin qubits, Rep. Prog. Phys. 76(9), 092501 (2013)

[115] J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, Picosecond coherent optical manipulation of a single electron spin in a quantum dot, Science 320(5874), 349 (2008)

[116] K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit, Nat. Phys. 7(11), 872 (2011)

[117] M. Atature, J. Dreiser, A. Badolato, A. Högele, K. Karrai, and A. Imamoglu, Quantum-dot spin-state preparation with near-unity fidelity, Science 312(5773), 551 (2006)

[118] J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, Picosecond coherent optical manip-ulation of a single electron spin in a quantum dot, Science 320(5874), 349 (2008)

[119] D. Press, T. D. Ladd, B. Y. Zhang, and Y. Yamamoto, Complete quantum control of a single quantum dot spin using ultrafast optical pulses, Nature 456(7219), 218 (2008)

[120] C. Y. Hu, A. Young, J. L. ÓBrien, W. J. Munro, and J. G. Rarity, Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon, Phys. Rev. B 78(8), 085307 (2008)

[121] C. Y. Hu, W. J. Munro, and J. G. Rarity, Deterministic photon entangler using a charged quantum dot inside a micro-cavity, Phys. Rev. B 78(12), 125318 (2008)

[122] P. Lodahl, S. Mahmoodian, and S. Stobbe, Interfacing single photons and single quantum dots with photonic nanos-tructures, Rev. Mod. Phys. 87(2), 347 (2015)

[123] M. J. Kastoryano, F. Reiter, and A. S. Sørensen, Dissipative preparation of entanglement in optical cavities, Phys. Rev. Lett. 106(9), 090502 (2011)

[124] Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, Robust-fidelity atom-photon entangling gates in the weak-coupling regime, Phys. Rev. Lett. 109(16), 160504 (2012)

[125] R. J. Warburton, Single spins in self-assembled quantum dots, Nat. Mater. 12(6), 483 (2013)

[126] R. J. Warburton, C. S. Dürr, K. Karrai, J. P. Kotthaus, G. Medeiros-Ribeiro, and P. M. Petroff, Charged excitons in self-assembled semiconductor quantum dots, Phys. Rev. Lett. 79(26), 5282 (1997)

[127] D. F. Walls and G. J. Milburn, Quantum Optics, Springer-Verlag, 1994

[128] A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, Quantum-dotinduced phase shift in a pillar microcavity, Phys. Rev. A 84(1), 011803 (2011)

[129] H. R. Wei and F. G. Deng, Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities, Opt. Express 22(1), 593 (2014)

[130] X. B. Zou and W. Mathis, Generating a four-photon polarization-entangled cluster state, Phys. Rev. A 71(3), 032308 (2005)

[131] Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Measurement of conditional phase shifts for quantum logic, Phys. Rev. Lett. 75(25), 4710 (1995)

[132] J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Strong coupling in a single quantum dot-semiconductor microcavity system, Nature 432(7014), 197 (2004)

[133] S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauss, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, AlAs/GaAs micropillar cavities with quality factors exceeding 150.000, Appl. Phys. Lett. 90(25), 251109 (2007)

[134] J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Coherent manipulation of coupled electron spins in semiconductor quantum dots, Science 309(5744), 2180 (2005)

[135] A. B. Young, C. Y. Hu, and J. G. Rarity, Generating entanglement with low-Q-factor microcavities, Phys. Rev. A 87(1), 012332 (2013)

[136] N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, Demonstration of a simple entangling optical gate and its use in Bell-state analysis, Phys. Rev. Lett. 95(21), 210504 (2005)]

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