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  • Open Access

Transmission and transformation of entangled states with high fidelity in a non-Hermitian system

Zan Tang*, Bo Wang*, Tian Chen*,†, and Xiangdong Zhang‡

  • Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, 100081, Beijing, China

  • *These authors contributed equally to this work.
  • †chentian@bit.edu.cn
  • ‡zhangxd@bit.edu.cn
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Phys. Rev. Research 4, 043144 – Published 28 November, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.043144

Abstract

The study of non-Hermitian systems has attracted more and more attention, because physical properties in many real systems should be described by non-Hermitian Hamiltonians. Due to the existence of absorption and dissipation, transmission and transformation of entangled states with high fidelity are very difficult to realize in the non-Hermitian systems. How to realize transmission and transformation of entangled states with high fidelity in these dissipative systems becomes an open problem. Here we provide an inverse design scheme for topologically protected channels to solve such a problem. From our scheme, topologically protected channels can be designed according to the requirements for the overlap integrals among the initial states, target states, and eigenstates of the system. As a result, robust transmission and transformation of entangled states with high fidelity can be achieved in the non-Hermitian systems. Our proposed scheme has been demonstrated experimentally using the constructed non-Hermitian quantum walk platform. This work interconnects topology, quantum physics, and non-Hermitian systems, and opens up an avenue for quantum engineering in real systems.

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References (74)

  1. T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe and J. L. O'Brien, Quantum computers, Nature (London) 464, 45 (2010).
  2. J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, Multiphoton entanglement and interferometry, Rev. Mod. Phys. 84, 777 (2012).
  3. L. Lu, J. D. Joannopoulos, and M. Soljacic, Topological Photonics, Nat. Photonics 8, 821 (2014).
  4. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
  5. S. Mittal, V. V. Orre, and M. Hafezi, Topologically robust transport of entangled photons in a 2D photonic system, Opt. Express 24, 15631 (2016).
  6. M. C. Rechtsman, Y. Lumer, Y. Plotnik, A. Perez-Leija, A. Szameit, and Mordechai Segev, Topological protection of photonic path entanglement, Optica 3, 925 (2016).
  7. J. Perczel, J. Borregaard, D. E. Chang, H. Pichler, S. F. Yelin, P. Zoller, and M. D. Lukin, Topological Quantum Optics in Two-Dimensional Atomic Arrays, Phys. Rev. Lett. 119, 023603 (2017).
  8. S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, A topological quantum optics interface, Science 359, 666 (2018).
  9. S. Mittal, E. A. Goldschmidt, and M. Hafezi, A topological source of quantum light, Nature (London) 561, 502 (2018).
  10. J.-L. Tambasco, G. Corrielli, R. J. Chapman, A. Crespi, O. Zilberberg, R. Osellame, and A. Peruzzo, Quantum interference of topological states of light, Sci. Adv. 4, eaat3187 (2018).
  11. A. Blanco-Redondo, B. Bell, D. Oren, B. J. Eggleton, and M. Segev, Topological protection of biphoton states, Science 362, 568 (2018).
  12. S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vuckovic, and A. W. Rodriguez, Inverse design in nanophotonics, Nat. Photonics 12, 659 (2018).
  13. K. Yao, D. R. Unni, and Y. Zheng, Intelligent nanophotonics: Merging photonics and artificial intelligence at the nanoscale, Nanophotonics 8, 339 (2019).
  14. Y. Wang, X.-L. Pang, Y.-H. Lu, J. Gao, Y.-J. Chang, L.-F. Qiao, Z.-Q. Jiao, H. Tang, and X.-M. Jin, Topological protection of two-photon quantum correlation on a photonic chip, Optica 6, 955 (2019).
  15. T. Giordani, E. Polino, S. Emiliani, A. Suprano, L. Innocenti, H. Majury, L. Marrucci, M. Paternostro, A Ferraro, N. Spagnolo, and F. Sciarrino, Experimental Engineering of Arbitrary Qudit States with Discrete-Time Quantum Walks, Phys. Rev. Lett. 122, 020503 (2019).
  16. L. Su, D. Vercruysse, J. Skarda, N. V. Sapra, J. A.Petykiewicz, and J. Vu kovi, Nanophotonic inverse design with spins: Software architecture and practical considerations, Appl. Phys. Rev. 7, 011407 (2020).
  17. J. Perczel, J. Borregaard, D. E. Chang, S. F. Yelin, and M. D. Lukin, Topological Quantum Optics Using Atomlike Emitter Arrays Coupled to Photonic Crystals, Phys. Rev. Lett. 124, 083603 (2020).
  18. K. Tschernig, A. Jimenez-Galán, D. N. Christodoulides, M. Ivanov, K. Busch, M. A. Bandres, and A. Perez-Leija, Topological protection versus degree of entanglement of two-photon light in photonic topological insulators, Nat. Commun. 12, 1974 (2021).
  19. B. Wang, Z. Tang, T. Chen, and X. Zhang, Nearly perfect transmission and transformation of entangled states in topologically protected channels, Laser Photonics Rev. 16, 2100519 (2022).
  20. Y. Wang, Y.-H. Lu, J. Gao, Y.-J. Chang, R.-J. Ren, Z.-Q. Jiao, Z.-Y. Zhang, X.-M. Jin, Topologically protected polarization quantum entanglement on a photonic chip, Chip 1, 100003 (2022).
  21. N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, Cambridge, 2011).
  22. R. EI-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Non-Hermitian physics and PT symmetry, Nat. Phys. 14, 11 (2018).
  23. T. A. Brun, H. A. Carteret, and A. Ambainis, Quantum to Classical Transition for Random Walks, Phys. Rev. Lett. 91, 130602 (2003).
  24. D. Shapira, O. Biham, A. J. Bracken, and M. Hackett, One-dimensional quantum walk with unitary noise, Phys. Rev. A 68, 062315 (2003).
  25. C. Oliveira, R. Portugal, and R. Donangelo, Decoherence in two-dimensional quantum walks, Phys. Rev. A 74, 012312 (2006).
  26. V. Kendon, Decoherence in quantum walks—a review, Math. Struct. Comput. Sci. 17, 1169 (2007).
  27. H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, Realization of Quantum Walks with Negligible Decoherence in Waveguide Lattices, Phys. Rev. Lett. 100, 170506 (2008).
  28. A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, P. J. Mosley, E. Andersson, I. Jex, and C. Silberhorn, Photons Walking the Line: A Quantum Walk with Adjustable Coin Operations, Phys. Rev. Lett. 104, 050502 (2010).
  29. A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Decoherence and Disorder in Quantum Walks: From Ballistic Spread to Localization, Phys. Rev. Lett. 106, 180403 (2011).
  30. P. Xue and B. C. Sanders, Controlling and reversing the transition from classical diffusive to quantum ballistic transport in a quantum walk by driving the coin, Phys. Rev. A 87, 022334 (2013).
  31. T. E. Lee, Anomalous Edge State in a Non-Hermitian Lattice, Phys. Rev. Lett. 116, 133903 (2016).
  32. S. Weimann, M. Kremer, Y. Plotnik, Y. Lumer, S. Nolte, K. G. Makris, M. Segev, M. C. Rechtsman, and A. Szameit, Topologically protected bound states in photonic parity–time-symmetric crystals, Nat. Mater. 16, 433 (2017).
  33. L. Xiao, X. Zhan, Z. H. Bian, K. K. Wang, X. Zhang, X. P. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami et al., Observation of topological edge states in parity–time-symmetric quantum walks, Nat. Phys. 13, 1117 (2017).
  34. S. Yao and Z. Wang, Edge States and Topological Invariants of Non-Hermitian Systems, Phys. Rev. Lett. 121, 086803 (2018).
  35. H. Shen, B. Zhen, and L. Fu, Topological Band Theory for Non-Hermitian Hamiltonians, Phys. Rev. Lett. 120, 146402 (2018).
  36. Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Topological Phases of Non-Hermitian Systems, Phys. Rev. X 8, 031079 (2018).
  37. M.-A. Miri and A. Alù, Exceptional points in optics and photonics, Science 363, 7709 (2019).
  38. K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Symmetry and Topology in Non-Hermitian Physics, Phys. Rev. X 9, 041015 (2019).
  39. N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, Topological Origin of Non-Hermitian Skin Effects, Phys. Rev. Lett. 124, 086801 (2020).
  40. D. S. Borgnia, A. J. Kruchkov, and R.-J. Slager, Non-Hermitian Boundary Modes and Topology, Phys. Rev. Lett. 124, 056802 (2020).
  41. K. Zhang, Z. Yang, and C. Fang, Correspondence between Winding Numbers and Skin Modes in Non-Hermitian Systems, Phys. Rev. Lett. 125, 126402 (2020).
  42. L. Xiao, T. Deng, K. Wang, G. Zhu, Z. Wang, W. Yi, and P. Xue, Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics, Nat. Phys. 16, 761 (2020).
  43. T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L. W. Molenkamp, C. H. Lee, A. Szameit, M. Greiter and R. Thomale, Generalized bulk-boundary correspondence in non-Hermitian topolectrical circuits, Nat. Phys. 16, 747 (2020).
  44. A. Ghatak, M. Brandenbourger, J. van Wezel, and C. Coulais, Observation of non-Hermitian topology and its bulk-edge correspondence, Proc. Natl Acad. Sci. USA 117, 29561 (2020).
  45. B. Wang, T. Chen, and X. Zhang, Observation of novel robust edge states in dissipative non-hermitian quantum walks, Laser Photonics Rev. 14, 2000092 (2020).
  46. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
  47. L. S. Palacios, S. Tchoumakov, M. Guix, I. Pagonabarraga, S. Sánchez, and A. G Grushin, Guided accumulation of active particles by topological design of a second-order skin effect, Nat. Commun. 12, 4691 (2021).
  48. L. Li, C. H. Lee, and J. Gong, Topological Switch for Non-Hermitian Skin Effect in Cold-Atom Systems with Loss, Phys. Rev. Lett. 124, 250402 (2020).
  49. D. Zou, T. Chen, W. He, J. Bao, C. H. Lee, H. Sun, and X. Zhang, Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits, Nat. Commun. 12, 7201 (2021).
  50. P. S.-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch and A. Amo, Lasing in topological edge states of a one-dimensional lattice, Nat. Photonics 11, 651 (2017).
  51. H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. ElGanainy, H. Schomerus, and L. Feng, Topological hybrid silicon microlasers, Nat. Commun. 9, 981 (2018).
  52. G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, Topological insulator laser: Theory, Science 359, 1230 (2018).
  53. M. A. Bandres, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, Topological insulator laser: Experiments, Science 359, 1231 (2018).
  54. W. Zhang, X. Xie, H. Hao, J. Dang, S. Xiao, S. Shi, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, and X. Xu, Low-threshold topological nanolasers based on the second order corner state, Light: Sci. Appl. 9, 109 (2020).
  55. K. Mochizuki, D. Kim, and H. Obuse, Explicit definition of PT symmetry for nonunitary quantum walks with gain and loss, Phys. Rev. A 93, 062116 (2016).
  56. T. Chen, B. Wang, and X. Zhang, Characterization of topological phases and selection of topological interface modes in the parity-time-symmetric quantum walk, Phys. Rev. A 97, 052117 (2018).
  57. K. Manouchehri and J. B. Wang, Physical Implementation of Quantum Walks (Springer, Berlin, 2014).
  58. R. Portugal, Quantum Walks and Search Algorithms (Springer, Cham, Switzerland, 2018).
  59. A. M. Childs, Universal Computation by Quantum Walk, Phys. Rev. Lett. 102, 180501 (2009).
  60. A. Schreiber, A. Gábris, P. P. Rohde, K. Laiho, M. Štefanák, V. Potocek, C. Hamilton, I. Jex, and C. Silberhorn, A 2D quantum walk simulation of two-particle dynamics, Science 336, 55 (2012).
  61. A. M. Childs, D. Gosset, and Z. Webb, Universal computation by multiparticle quantum walk, Science 339, 791 (2013).
  62. A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, and P. Mataloni, Anderson localization of entangled photons in an integrated quantum walk, Nat. Photonics 7, 322 (2013).
  63. F. De Nicola, L. Sansoni, A. Crespi, R. Ramponi, R. Osellame, V. Giovannetti, R. Fazio, P. Mataloni, and F. Sciarrino, Quantum simulation of bosonic-fermionic noninteracting particles in disordered systems via a quantum walk, Phys. Rev. A 89, 032322 (2014).
  64. D. A. Meyer and T. G. Wong, Connectivity is a Poor Indicator of Fast Quantum Search, Phys. Rev. Lett. 114, 110503 (2015).
  65. T. Rakovszky and J. K. Asboth, Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk, Phys. Rev. A 92, 052311 (2015).
  66. J. K. Asboth and J. M. Edge, Edge-state-enhanced transport in a two-dimensional quantum walk, Phys. Rev. A 91, 022324 (2015).
  67. S. Chakraborty, L. Novo, A. Ambainis, and Y. Omar, Spatial Search by Quantum Walk is Optimal for Almost All Graphs, Phys. Rev. Lett. 116, 100501 (2016).
  68. D. N. Biggerstaff, R. Heilmann, A. A. Zecevik, M. Gräfe, M. A. Broome, A. Fedrizzi, S. Nolte, A. Szameit, A. G. White, and I. Kassal, Enhancing coherent transport in a photonic network using controllable decoherence, Nat. Commun. 7, 11282 (2016).
  69. X. Qiang, T. Loke, A. Montanaro, K. Aungskunsiri, X. Zhou, J. L. O’Brien, J. B. Wang, and J. C. F. Matthews, Efficient quantum walk on a quantum processor, Nat. Commun. 7, 11511 (2016).
  70. L. Innocenti, H. Majury, T. Giordani, N. Spagnolo, F. Sciarrino, M. Paternostro, and A. Ferraro, Quantum state engineering using one-dimensional discrete-time quantum walks, Phys. Rev. A 96, 062326 (2017).
  71. H. Tang, C. Di Franco, Z.-Y. Shi, T.-S. He, Z. Feng, J. Gao, K. Sun, Z.-M. Li, Z.-Q. Jiao, T.-Y. Wang et al., Experimental quantum fast hitting on hexagonal graphs, Nat. Photonics 12, 754 (2018).
  72. A. Montanaro, Quantum-walk speedup of backtracking algorithms, Theor. Comput. 14, 1 (2018).
  73. T. Wu, J. A. Izaac, Z.-X. Li, K. Wang, Z.-Z. Chen, S. Zhu, J. B. Wang, and X.-S. Ma, Experimental Parity-Time Symmetric Quantum Walks for Centrality Ranking on Directed Graphs, Phys. Rev. Lett. 125, 240501 (2020).
  74. X. Qiang, Y. Wang, S. Xue, R. Ge, L. Chen, Y. Liu, A. Huang, X. Fu, P. Xu, T. Yi et al., Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor, Sci. Adv. 7, eabb8375 (2021).

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Phys. Rev. Research 4, 043144– Published 28 November, 2022
  • Received 8 May 2022
  • Accepted 28 October 2022
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