Abstract

We theoretically implement some hyperparallel optical elements, including quantum single photon transistor, router, and dynamic random access memory (DRAM). The inevitable side leakage and the imperfect birefringence of the quantum dot (QD)-cavity mediates are taken into account, and unity fidelities of our optical elements can be achieved. The hyperparallel constructions are based on polarization and spatial degrees of freedom (DOFs) of the photon to increase the parallel efficiency, improve the capacity of channel, save the quantum resources, reduce the operation time, and decrease the environment noises. Moreover, the practical schemes are robust against the side leakage and the coupling strength limitation in the microcavities.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (6)

B. X. Wang, M. J. Tao, Q. Ai, T. Xin, N. Lambert, D. Ruan, Y. C. Cheng, F. Nori, D. Fu-Guo, and G. L. Long, “Efficient quantum simulation of photosynthetic light harvesting,” NPJ Quantum Information 4(1), 52 (2018).
[Crossref]

M. Y. Wang, J. Z. Xu, F. L. Yan, and T. Gao, “Entanglement concentration for polarization–spatial–time-bin hyperentangled Bell states,” EPL 123(6), 60002 (2018).
[Crossref]

B. Y. Xia, C. Cao, Y. H. Han, and R. Zhang, “Universal photonic three-qubit quantum gates with two degrees of freedom assisted by charged quantum dots inside single-sided optical microcavities,” Laser Phys. 28(9), 095201 (2018).
[Crossref]

G. Y. Wang, T. Li, Q. Ai, and F. G. Deng, “Self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom,” Opt. Express 26(18), 23333–23346 (2018).
[Crossref]

T. Li, J. C. Gao, F. G. Deng, and G. L. Long, “High-fidelity quantum gates on quantum-dot-confined electron spins in low-Q optical microcavities,” Ann. Phys. 391, 150–160 (2018).
[Crossref]

J. Frey, H. Snijders, J. Norman, A. Gossard, J. Bowers, W. Löffler, and D. Bouwmeester, “Electro-optic polarization tuning of microcavities with a single quantum dot,” Opt. Lett. 43(17), 4280–4283 (2018).
[Crossref]

2017 (5)

C. Cao, Y. W. Duan, X. Chen, R. Zhang, T. J. Wang, and C. Wang, “Implementation of single-photon quantum routing and decoupling using a nitrogen-vacancy center and a whispering-gallery-mode resonator-waveguide system,” Opt. Express 25(15), 16931–16946 (2017).
[Crossref]

C. Hu, “Photonic transistor and router using a single quantum-dot-confined spin in a single-sided optical microcavity,” Sci. Rep. 7(1), 45582 (2017).
[Crossref]

Y. He, Y. M. He, Y. J. Wei, X. Jiang, K. Chen, C. Y. Lu, J. W. Pan, C. Schneider, M. Kamp, and S. Höfling, “Quantum state transfer from a single photon to a distant quantum-dot electron spin,” Phys. Rev. Lett. 119(6), 060501 (2017).
[Crossref]

R. Keil, M. Zopf, Y. Chen, B. Höfer, J. Zhang, F. Ding, and O. G. Schmidt, “Solid-state ensemble of highly entangled photon sources at rubidium atomic transitions,” Nat. Commun. 8(1), 15501 (2017).
[Crossref]

S. K. Andersen, S. Kumar, and S. I. Bozhevolnyi, “Ultrabright linearly polarized photon generation from a nitrogen vacancy center in a nanocube dimer antenna,” Nano Lett. 17(6), 3889–3895 (2017).
[Crossref]

2016 (13)

N. Bruno, V. Pini, A. Martin, V. B. Verma, S. W. Nam, R. Mirin, A. Lita, F. Marsili, B. Korzh, and F. Bussières, “Heralded amplification of photonic qubits,” Opt. Express 24(1), 125–133 (2016).
[Crossref]

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).
[Crossref]

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).
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H. R. Wei, F. G. Deng, and G. L. Long, “Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities,” Opt. Express 24(16), 18619–18630 (2016).
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H. R. Wei and P. J. Zhu, “Implementations of two-photon four-qubit Toffoli and Fredkin gates assisted by nitrogen-vacancy centers,” Sci. Rep. 6(1), 35529 (2016).
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H. J. Liu, Y. Xia, and J. Song, “Efficient hyperentanglement concentration for n-particle Greenberger–Horne–Zeilinger state assisted by weak cross-Kerr nonlinearity,” Quantum Inf. Process. 15(5), 2033–2052 (2016).
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C. Cao, X. Chen, Y. W. Duan, L. Fan, R. Zhang, T. J. Wang, and C. Wang, “Concentrating partially entangled w-class states on nonlocal atoms using low-Q optical cavity and linear optical elements,” Sci. China: Phys., Mech. Astron. 59(10), 100315 (2016).
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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 quantum-dot spins in double-sided optical microcavities,” Opt. Express 24(25), 28444–28458 (2016).
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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).
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X. H. Li and S. Ghose, “Complete hyperentangled Bell state analysis for polarization and time-bin hyperentanglement,” Opt. Express 24(16), 18388–18398 (2016).
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J. L. Zhang, S. L. Su, S. Zhang, A. D. Zhu, and H. F. Wang, “Complete and nondestructive polarization-entangled cluster state analysis assisted by a cavity input–output process,” J. Opt. Soc. Am. B 33(3), 342–350 (2016).
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2015 (9)

B. C. Ren, G. Y. Wang, and F. G. Deng, “Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime,” Phys. Rev. A 91(3), 032328 (2015).
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M. P. Bakker, A. V. Barve, T. Ruytenberg, W. Löffler, L. A. Coldren, D. Bouwmeester, and M. P. van Exter, “Polarization degenerate solid-state cavity quantum electrodynamics,” Phys. Rev. B 91(11), 115319 (2015).
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X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
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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).
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X. H. Li and S. Ghose, “Hyperentanglement concentration for time-bin and polarization hyperentangled photons,” Phys. Rev. A 91(6), 062302 (2015).
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Y. H. Kang, Y. Xia, and P. M. Lu, “Efficient spin Bell states and Greenberger–Horne–Zeilinger states analysis in the quantum dot–microcavity coupled system,” Appl. Phys. B: Lasers Opt. 119(2), 259–271 (2015).
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Y. H. Kang, Y. Xia, and P. M. Lu, “Effective scheme for preparation of a spin-qubit Greenberger–Horne–Zeilinger state and W state in a quantum-dot-microcavity system,” J. Opt. Soc. Am. B 32(7), 1323–1329 (2015).
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2014 (11)

M. Hua, M. J. Tao, and F. G. Deng, “Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics,” Phys. Rev. A 90(1), 012328 (2014).
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L. L. Fan, Y. Xia, and J. Song, “Complete hyperentanglement-assisted multi-photon Greenberger–Horne–Zeilinger states analysis with cross-Kerr nonlinearity,” Opt. Commun. 317, 102–106 (2014).
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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).
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W. H. Zhang, Q. Q. Qi, J. Zhou, and L. X. Chen, “Mimicking faraday rotation to sort the orbital angular momentum of light,” Phys. Rev. Lett. 112(15), 153601 (2014).
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T. J. Wang, Y. Zhang, and C. Wang, “Universal hybrid hyper-controlled quantum gates assisted by quantum dots in optical double-sided microcavities,” Laser Phys. Lett. 11(2), 025203 (2014).
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Y. Xia, Y. H. Kang, and P. M. Lu, “Complete polarized photons Bell-states and Greenberger–Horne–Zeilinger-states analysis assisted by atoms,” J. Opt. Soc. Am. B 31(9), 2077–2082 (2014).
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2013 (10)

K. Lemr, K. Bartkiewicz, A. Černoch, and J. Soubusta, “Resource-efficient linear-optical quantum router,” Phys. Rev. A 87(6), 062333 (2013).
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K. Lemr, K. Bartkiewicz, A. Černoch, and J. Soubusta, “Resource-efficient linear-optical quantum router,” Phys. Rev. A 87(6), 062333 (2013).
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H. R. Wei and F. G. Deng, “Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities,” Phys. Rev. A 87(2), 022305 (2013).
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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).
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J. J. Pla, K. Y. Tan, J. P. Dehollain, W. H. Lim, J. J. Morton, F. A. Zwanenburg, D. N. Jamieson, A. S. Dzurak, and A. Morello, “High-fidelity readout and control of a nuclear spin qubit in silicon,” Nature 496(7445), 334–338 (2013).
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N. B. Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4(1), 1743 (2013).
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Y. Xia, S. Y. Hao, Y. J. Dong, and J. Song, “Effective schemes for preparation of Greenberger–Horne–Zeilinger and W maximally entangled states with cross-Kerr nonlinearity and parity-check measurement,” Appl. Phys. B: Lasers Opt. 110(4), 551–561 (2013).
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2012 (3)

J. Minář, H. de Riedmatten, and N. Sangouard, “Quantum repeaters based on heralded qubit amplifiers,” Phys. Rev. A 85(3), 032313 (2012).
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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).
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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).
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2011 (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
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I. Buluta, S. Ashhab, and F. Nori, “Natural and artificial atoms for quantum computation,” Rep. Prog. Phys. 74(10), 104401 (2011).
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2010 (10)

P. Neumann, J. Beck, M. Steiner, F. Rempp, H. Fedder, P. R. Hemmer, J. Wrachtrup, and F. Jelezko, “Single-shot readout of a single nuclear spin,” Science 329(5991), 542–544 (2010).
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F. Z. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, and W. Harneit, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105(4), 040504 (2010).
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S. Straupe and S. Kulik, “Quantum optics: The quest for higher dimensionality,” Nat. Photonics 4(9), 585–586 (2010).
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T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, “Entanglement of two individual neutral atoms using Rydberg blockade,” Phys. Rev. Lett. 104(1), 010502 (2010).
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D. Press, K. D. Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4(6), 367–370 (2010).
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W. B. Gao, C. Y. Lu, X. Yao, P. Xu, O. Gühne, A. Goebel, Y. A. Chen, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state,” Nat. Phys. 6(5), 331–335 (2010).
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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).
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Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82(4), 044305 (2010).
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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).
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C. Bonato, F. Haupt, S. S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104(16), 160503 (2010).
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2009 (4)

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).
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B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
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C. Hu, W. Munro, J. O’Brien, and J. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B 80(20), 205326 (2009).
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J. H. An, M. Feng, and C. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79(3), 032303 (2009).
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2008 (4)

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456(7219), 218–221 (2008).
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J. Berezovsky, M. Mikkelsen, N. Stoltz, L. Coldren, and D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science 320(5874), 349–352 (2008).
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J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
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C. Hu, A. Young, J. O’Brien, W. Munro, and J. 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).
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2007 (4)

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAsAlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90(25), 251109 (2007).
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M. Barbieri, G. Vallone, P. Mataloni, and F. D. Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75(4), 042317 (2007).
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S. Walborn, D. Ether, R. de Matos Filho, and N. Zagury, “Quantum teleportation of the angular spectrum of a single-photon field,” Phys. Rev. A 76(3), 033801 (2007).
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Z. Deng, M. Feng, and K. Gao, “Preparation of entangled states of four remote atomic qubits in decoherence-free subspace,” Phys. Rev. A 75(2), 024302 (2007).
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2006 (2)

M. Scholz, T. Aichele, S. Ramelow, and O. Benson, “Deutsch-Jozsa algorithm using triggered single photons from a single quantum dot,” Phys. Rev. Lett. 96(18), 180501 (2006).
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C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96(19), 190501 (2006).
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2005 (1)

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).
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2004 (3)

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-not gate,” Phys. Rev. Lett. 93(25), 250502 (2004).
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L. Duan and H. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92(12), 127902 (2004).
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J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. Keldysh, V. Kulakovskii, T. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot–semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
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2003 (1)

S. Walborn, S. Pádua, and C. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68(4), 042313 (2003).
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2002 (1)

M. A. Nielsen and I. Chuang, “Quantum computation and quantum information,” Am. J. Phys. 70(5), 558–559 (2002).
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2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
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1998 (1)

C. Hu, W. Ossau, D. Yakovlev, G. Landwehr, T. Wojtowicz, G. Karczewski, and J. Kossut, “Optically detected magnetic resonance of excess electrons in type-I quantum wells with a low-density electron gas,” Phys. Rev. B 58(4), R1766–R1769 (1998).
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1997 (1)

R. Warburton, C. Dürr, K. Karrai, J. Kotthaus, G. Medeiros-Ribeiro, and P. Petroff, “Charged excitons in self-assembled semiconductor quantum dots,” Phys. Rev. Lett. 79(26), 5282–5285 (1997).
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1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
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Ai, Q.

B. X. Wang, M. J. Tao, Q. Ai, T. Xin, N. Lambert, D. Ruan, Y. C. Cheng, F. Nori, D. Fu-Guo, and G. L. Long, “Efficient quantum simulation of photosynthetic light harvesting,” NPJ Quantum Information 4(1), 52 (2018).
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G. Y. Wang, T. Li, Q. Ai, and F. G. Deng, “Self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom,” Opt. Express 26(18), 23333–23346 (2018).
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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 quantum-dot spins in double-sided optical microcavities,” Opt. Express 24(25), 28444–28458 (2016).
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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).
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Aichele, T.

M. Scholz, T. Aichele, S. Ramelow, and O. Benson, “Deutsch-Jozsa algorithm using triggered single photons from a single quantum dot,” Phys. Rev. Lett. 96(18), 180501 (2006).
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Almeida, M. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
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An, J. H.

J. H. An, M. Feng, and C. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79(3), 032303 (2009).
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Andersen, S. K.

S. K. Andersen, S. Kumar, and S. I. Bozhevolnyi, “Ultrabright linearly polarized photon generation from a nitrogen vacancy center in a nanocube dimer antenna,” Nano Lett. 17(6), 3889–3895 (2017).
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Ashhab, S.

I. Buluta, S. Ashhab, and F. Nori, “Natural and artificial atoms for quantum computation,” Rep. Prog. Phys. 74(10), 104401 (2011).
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Awschalom, D.

J. Berezovsky, M. Mikkelsen, N. Stoltz, L. Coldren, and D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science 320(5874), 349–352 (2008).
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Bakker, M. P.

M. P. Bakker, A. V. Barve, T. Ruytenberg, W. Löffler, L. A. Coldren, D. Bouwmeester, and M. P. van Exter, “Polarization degenerate solid-state cavity quantum electrodynamics,” Phys. Rev. B 91(11), 115319 (2015).
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Barbieri, M.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
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M. Barbieri, G. Vallone, P. Mataloni, and F. D. Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75(4), 042317 (2007).
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Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
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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).
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Bartkiewicz, K.

K. Lemr, K. Bartkiewicz, A. Černoch, and J. Soubusta, “Resource-efficient linear-optical quantum router,” Phys. Rev. A 87(6), 062333 (2013).
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K. Lemr, K. Bartkiewicz, A. Černoch, and J. Soubusta, “Resource-efficient linear-optical quantum router,” Phys. Rev. A 87(6), 062333 (2013).
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Barve, A. V.

M. P. Bakker, A. V. Barve, T. Ruytenberg, W. Löffler, L. A. Coldren, D. Bouwmeester, and M. P. van Exter, “Polarization degenerate solid-state cavity quantum electrodynamics,” Phys. Rev. B 91(11), 115319 (2015).
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Bechler, O.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345(6199), 903–906 (2014).
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Beck, J.

P. Neumann, J. Beck, M. Steiner, F. Rempp, H. Fedder, P. R. Hemmer, J. Wrachtrup, and F. Jelezko, “Single-shot readout of a single nuclear spin,” Science 329(5991), 542–544 (2010).
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Beck, K. M.

W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341(6147), 768–770 (2013).
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Benson, O.

M. Scholz, T. Aichele, S. Ramelow, and O. Benson, “Deutsch-Jozsa algorithm using triggered single photons from a single quantum dot,” Phys. Rev. Lett. 96(18), 180501 (2006).
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Berezovsky, J.

J. Berezovsky, M. Mikkelsen, N. Stoltz, L. Coldren, and D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science 320(5874), 349–352 (2008).
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M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
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M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73(1), 58–61 (1994).
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A. F. Van Loo, A. Fedorov, K. Lalumière, B. C. Sanders, A. Blais, and A. Wallraff, “Photon-mediated interactions between distant artificial atoms,” Science 342(6165), 1494–1496 (2013).
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Bonato, C.

C. Bonato, F. Haupt, S. S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104(16), 160503 (2010).
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Bouwmeester, D.

J. Frey, H. Snijders, J. Norman, A. Gossard, J. Bowers, W. Löffler, and D. Bouwmeester, “Electro-optic polarization tuning of microcavities with a single quantum dot,” Opt. Lett. 43(17), 4280–4283 (2018).
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M. P. Bakker, A. V. Barve, T. Ruytenberg, W. Löffler, L. A. Coldren, D. Bouwmeester, and M. P. van Exter, “Polarization degenerate solid-state cavity quantum electrodynamics,” Phys. Rev. B 91(11), 115319 (2015).
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C. Bonato, F. Haupt, S. S. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104(16), 160503 (2010).
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Bowers, J.

Bozhevolnyi, S. I.

S. K. Andersen, S. Kumar, and S. I. Bozhevolnyi, “Ultrabright linearly polarized photon generation from a nitrogen vacancy center in a nanocube dimer antenna,” Nano Lett. 17(6), 3889–3895 (2017).
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Browaeys, A.

T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, “Entanglement of two individual neutral atoms using Rydberg blockade,” Phys. Rev. Lett. 104(1), 010502 (2010).
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Phys. Rev. A (23)

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Figures (5)

Fig. 1.
Fig. 1. (a) A schematic diagram of a singly charged QD confined in a double-sided microcavity. (b) Energy levels and the spin-dependent optical transition rules for a charged QD-cavity emitter. $|R^\uparrow \rangle$ ($|L^\downarrow \rangle$) represents the propagation direction of the right- (left-) circularly polarized photon is parallel (antiparallel) to the growth axis of the QD. $|\Uparrow \rangle$ and $|\Downarrow \rangle$ denote the heavy-hole spin states $|\pm 3/2\rangle$, respectively. $|\uparrow \rangle$ and $|\downarrow \rangle$ indicate the electron spin states $|\pm 1/2\rangle$, respectively.
Fig. 2.
Fig. 2. A description for implementing a p-transistor. HWP$^{22.5^\circ }_{1,\ldots ,8}$ with using half wave plates rotated at 22.5$^\circ$ represent Hadamard operations on polarization DOF. HWP$^{45^\circ }_{1,2}$ stand for half wave plate oriented at 45$^\circ$ performing bit-flip operations $\sigma _{p,x}=|R\rangle \langle L|+|L\rangle \langle R|$. PBS$_{1,\ldots ,4}$ are circularly polarizing beam splitters. BS$_{1,2}$ are nonpolarizing balanced beam splitters performing Hadamard operations on the spatial DOF, i.e., $|l^1\rangle \leftrightarrow (|l^{\tilde {1}}\rangle +|l^{\tilde {3}}\rangle )/\sqrt {2}$, $|l^3\rangle \leftrightarrow (|l^{\tilde {1}}\rangle -|l^{\tilde {3}}\rangle )/\sqrt {2}$. VBS$_{1,2}$ are adjustable beam splitters with transmission coefficient ($t-t_0$) and reflection coefficient $(\sqrt {1-(t-t_0)^2})$. $D_i$ ($i=1,\ldots , 4$) are single-photon detectors.
Fig. 3.
Fig. 3. A schematic diagram for implementing a s-transistor.
Fig. 4.
Fig. 4. Schematic diagram of hyper-router.
Fig. 5.
Fig. 5. Schematic diagram of hyper-DRAM.

Equations (39)

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d a ^ d t = [ i ( ω c ω ) + κ + κ s 2 ] a ^ g σ ^ κ a ^ i n κ a ^ i n + H ^ , d σ ^ d t = [ i ( ω X ω ) + γ 2 ] σ ^ g σ z a ^ + G ^ , a ^ r = a ^ i n + κ a ^ , a ^ t = a ^ i n + κ a ^ .
r ( ω ) = 1 + t ( ω ) , t ( ω ) = κ [ i ( ω X ω ) + γ 2 ] [ i ( ω X ω ) + γ 2 ] [ i ( ω c ω ) + κ + κ s 2 ] + g 2 .
| R r | L + t | R , | R t 0 | R + r 0 | L , | L r | R + t | L , | L t 0 | L + r 0 | R , | L r | R + t | L , , | R t 0 | R + r 0 | L , | R r | L + t | R , | L t 0 | L + r 0 | R .
| ψ gate photon = α | R + β | L , | ψ electron = 1 2 ( | | ) ,
| R 1 2 ( | R + | L ) , | L 1 2 ( | R | L ) .
| l 1 1 2 ( | l 1 ~ + | l 3 ~ ) , | l 3 1 2 ( | l 1 ~ | l 3 ~ ) , | l 1 ~ 1 2 ( | l 1 + | l 3 ) , | l 3 ~ 1 2 ( | l 1 | l 3 ) .
| ψ p 0 = 1 2 ( α | R + β | L ) ( | | ) ,
| ψ p 1 = 1 2 [ α ( r + t 0 ) | R 1 + α ( t t 0 ) | R 4 + β ( r + t 0 ) | R 1 + β ( t t 0 ) | R 4 α ( r + t 0 ) | R 1 + α ( t t 0 ) | R 4 β ( r + t 0 ) | R 1 + β ( t t 0 ) | R 4 + α | L 2 β | L 2 α | L 2 + β | L 2 ] .
| ψ p 2 = 1 2 [ α ( t t 0 ) | R 4 + β ( t t 0 ) | R 4 + α ( t t 0 ) | R 4 + β ( t t 0 ) | R 4 + α ( t t 0 ) | L 6 β ( t t 0 ) | L 6 α ( t t 0 ) | L 6 + β ( t t 0 ) | L 6 + α ( r + t 0 ) | R 1 + β ( r + t 0 ) | R 1 α ( r + t 0 ) | R 1 β ( r + t 0 ) | R 1 + ( 1 ( t t 0 ) 2 ) ( α | L 5 β | L 5 α | L 5 + β | L 5 ) ] .
| ψ p 3 = 1 2 [ α ( t t 0 ) | R 7 + β ( t t 0 ) | R 7 + α ( t t 0 ) | R 7 + β ( t t 0 ) | R 7 + α ( t t 0 ) | L 7 β ( t t 0 ) | L 7 α ( t t 0 ) | L 7 + β ( t t 0 ) | L 7 + α ( r + t 0 ) | R 1 + β ( r + t 0 ) | R 1 α ( r + t 0 ) | R 1 β ( r + t 0 ) | R 1 + ( 1 ( t t 0 ) 2 ) ( α | L 5 β | L 5 α | L 5 + β | L 5 ) ] .
| ψ p 4 = α | + β | .
| ψ p 4 = α | + β | .
| ψ p 5 = ( t t 0 ) ( α | R 1 β | L 1 ) ( ζ 1 | c 1 + ξ 1 | d 1 ) .
| ψ p 6 = ( t t 0 ) N [ α | R 1 R 2 R N + ( 1 ) N β | L 1 L 2 L N ] ( ζ 1 | c 1 + ξ 1 | d 1 ) ( ζ 2 | c 2 + ξ 2 | d 2 ) ( ζ N | c N + ξ N | d N ) .
| ψ p 7 = ( t t 0 ) N ( α | R 1 R 2 R N + β | L 1 L 2 L N ) ( ζ 1 | c 1 + ξ 1 | d 1 ) ( ζ 2 | c 2 + ξ 2 | d 2 ) ( ζ N | c N + ξ N | d N ) .
| ψ s 0 = 1 2 ( α | R + β | L ) ( γ | a + δ | b ) ( | | ) .
| ψ s 1 = 1 2 ( α | R + β | L ) ( γ | a + γ | b + δ | a δ | b ) ( | | ) .
| ψ s 2 = 1 2 ( t t 0 ) ( α | R l + α | R l + β | L r + β | L r ) ( γ | a + δ | a ) + 1 2 ( t t 0 ) ( α | R + β | L ) ( | | ) ( γ | b δ | b ) + 1 2 ( r + t 0 ) ( α | R l , D 1 α | R l , D 1 + β | R r , D 2 β | R r , D 2 ) ( γ | a + δ | a ) + 1 2 1 ( t t 0 ) 2 ( α | R D 3 + β | L D 3 ) ( | | ) ( γ | b δ | b ) .
| ψ s 3 = 1 2 ( t t 0 ) ( α | R r + α | R r + β | L r + β | L r ) ( γ | a + δ | a ) + 1 2 ( t t 0 ) ( α | R + β | L ) ( | | ) ( γ | b δ | b ) + 1 2 ( r + t 0 ) ( α | R l , D 1 α | R l , D 1 + β | R r , D 2 β | R r , D 2 ) ( γ | a + δ | a ) + 1 2 1 ( t t 0 ) 2 ( α | R D 3 + β | L D 3 ) ( | | ) ( γ | b δ | b ) .
| ψ s 4 = 1 2 ( t t 0 ) [ | a ( γ | + δ | ) + | b ( γ | + δ | ) ] ( α | R + β | L ) + 1 2 ( r + t 0 ) ( α | R l , D 1 α | R l , D 1 + β | R r , D 2 β | R r , D 2 ) ( γ | a + δ | a ) + 1 2 1 ( t t 0 ) 2 ( α | R D 3 + β | L D 3 ) ( | | ) ( γ | b δ | b ) .
| ψ s 5 = ( γ | + δ | ) ( α | R + β | L ) .
| ψ s 5 = ( γ | + δ | ) ( α | R + β | L ) .
| ψ s 6 = ( t t 0 ) N [ γ | c 1 c 2 c N | + ( 1 ) N δ | d 1 d 2 d N | ) ] ( α 1 | R + β 1 | L ) ( α 2 | R + β 2 | L ) ( α N | R + β N | L ) .
| ψ s 7 = ( t t 0 ) N ( γ | c 1 c 2 c N + δ | d 1 d 2 d N ) ( α 1 | R + β 1 | L ) ( α 2 | R + β 2 | L ) ( α N | R + β N | L ) .
| φ 0 = ( α | R + β | L ) ( δ 1 | a + δ 2 | b ) ( γ | + η | ) ,
| φ 1 = 1 2 ( α ( | R r + | L r ) + β ( | R l | L l ) ) ( δ 1 | a + δ 2 | b ) ( γ | + η | ) .
| φ 2 = 1 2 ( α ( t t 0 ) | R r ( γ | η | ) + α ( t t 0 ) | L r ( γ | + η | ) + β ( t t 0 ) | R l ( γ | η | ) β ( t t 0 ) | L l ( γ | + η | ) ) ( δ 1 | a + δ 2 | b ) + 1 2 ( α ( r + t 0 ) | R r , D 2 + β ( r + t 0 ) | R l , D 1 + α 1 ( t t 0 ) 2 | L r , D 4 β 1 ( t t 0 ) 2 | L l , D 3 ) ( γ | + η | ) ( δ 1 | a + δ 2 | b ) .
| φ 3 = ( α ( t t 0 ) ( γ | R r | η | L r | ) + β ( t t 0 ) ( γ | L l | η | R l | ) ) ( δ 1 | a + δ 2 | b ) + 1 2 ( α ( r + t 0 ) | R r , D 2 + β ( r + t 0 ) | R l , D 1 + α 1 ( t t 0 ) 2 | L r , D 4 β 1 ( t t 0 ) 2 | L l , D 3 ) ( γ | + η | ) ( δ 1 | a + δ 2 | b ) .
| φ 4 = ( α ( t t 0 ) ( γ | R l | η | L r | ) + β ( t t 0 ) ( γ | L l | η | R r | ) ) ( δ 1 | a + δ 2 | b ) + 1 2 ( α ( r + t 0 ) | R r , D 2 + β ( r + t 0 ) | R l , D 1 + α 1 ( t t 0 ) 2 | L r , D 4 β 1 ( t t 0 ) 2 | L l , D 3 ) ( γ | + η | ) ( δ 1 | a + δ 2 | b ) .
| φ 5 = ( α ( t t 0 ) ( γ | R l | η | R r | ) + β ( t t 0 ) ( γ | L l | η | L r | ) ) ( δ 1 | a + δ 2 | b ) + 1 2 ( α ( r + t 0 ) | R r , D 2 + β ( r + t 0 ) | R l , D 1 + α 1 ( t t 0 ) 2 | L r , D 4 β 1 ( t t 0 ) 2 | L l , D 3 ) ( γ | + η | ) ( δ 1 | a + δ 2 | b ) .
| φ 6 = γ ( t t 0 ) ( α | R l + β | L l ) ( δ 1 | a l + δ 2 | b l ) | η ( t t 0 ) ( α | R r + β | L r ) ( δ 1 | a r + δ 2 | b r ) | .
| ϕ 0 = ( α | R + β | L ) ( δ 1 | a + δ 2 | b ) ( γ 1 | 1 + γ 2 | 1 ) ( η 1 | 2 + η 2 | 2 ) .
| ϕ 1 = ( α | L l , 1 + β | L r , 1 ) ( δ 1 | a + δ 2 | b ) ( γ 1 | 1 + γ 2 | 1 ) ( η 1 | 2 + η 2 | 2 ) .
| ϕ 2 = ( α | L l , 1 + β | L r , 1 ) ( δ 1 | a + δ 2 | b ) ( γ 1 | 1 + γ 2 | 1 ) ( η 1 | 2 + η 2 | 2 ) .
| L 1 1 2 ( | L 3 + | L 4 ) , | L 2 1 2 ( | L 3 | L 4 ) , | L 3 1 2 ( | L 1 + | L 2 ) , | L 4 1 2 ( | L 1 | L 2 ) .
| ϕ 3 = ( 1 ) N ( α | L l , 1 + β | L r , 1 ) ( δ 1 | a + δ 2 | b ) ( γ 1 | 1 + γ 2 | 1 ) ( η 1 | 2 + η 2 | 2 ) .
| L 1 1 2 ( | L 3 + | L 4 ) , | L 2 1 2 ( | L 3 + | L 4 ) , | L 3 1 2 ( | L 1 + | L 2 ) , | L 4 1 2 ( | L 1 + | L 2 ) .
| ϕ 4 = ( 1 ) N + 1 ( α | L l , 2 + β | L r , 2 ) ( δ 1 | a + δ 2 | b ) ( γ 1 | 1 + γ 2 | 1 ) ( η 1 | 2 + η 2 | 2 ) .
| ϕ 5 = ( 1 ) N + 1 ( α | R l , 2 + β | L r , 2 ) ( δ 1 | a + δ 2 | b ) ( γ 1 | 1 + γ 2 | 1 ) ( η 1 | 2 + η 2 | 2 ) .

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