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Generation and entanglement study of generalized N-mode single-photon perfect W-states

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Abstract

We propose generation and entanglement detection schemes for generalized N-mode single-photon perfect W-states. These states are suitable for perfect teleportation and superdense coding. Based on the evolution of single-photon wavefunction in scalable integrated photonic lattices, we present schemes to generate these states using both planar and ring type waveguide structures. The integrated waveguide structures can be precisely fabricated, offer low photon propagation losses and can be integrated on a chip. In addition, we derive set of generalized entanglement conditions using the sum uncertainty relations of generalized su(2) algebra operators. We show that any given genuinely entangled N-mode single-photon state is a squeezed state of a specific su(2) algebra operator and can be expressed as superposition of a pair of orthonormal generalized N-mode single-photon perfect W-states which are eigenstates of that specific su(2) algebra operator. Within the single-photon subspace, the generalized entanglement condition reduces to a simplified single-photon separability condition. Detection of entanglement of single-photon states, using this single-photon separability condition, requires finding fidelity with two pairs of orthonormal generalized N-mode single-photon perfect W-states and hence more suitable for our purpose. Finally, we propose an experimental scheme to verify the entanglement using the proposed conditions. This scheme uses a photonic circuit consisting of directional couplers and phase shifters. The same photonic circuit can also be used to generate generalized N-mode single-photon perfect W-states.

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References

  1. Borras, A., Plastino, A., Batle, J., Zander, C., Casas, M., Plastino, A.: Multiqubit systems: highly entangled states and entanglement distribution. J. Phys. A Math. Theor. 40(44), 13407 (2007)

    ADS  MathSciNet  MATH  Google Scholar 

  2. Facchi, P., Florio, G., Parisi, G., Pascazio, S.: Maximally multipartite entangled states. Phys. Rev. A 77(6), 060304 (2008)

    ADS  MathSciNet  Google Scholar 

  3. Enríquez, M., Wintrowicz, I., Życzkowski, K.: Maximally entangled multipartite states: a brief survey. J. Phys. Conf. Ser. 698, 012003 (2016)

    Google Scholar 

  4. Miyake, A.: Classification of multipartite entangled states by multidimensional determinants. Phys. Rev. A 67(1), 012108 (2003)

    ADS  MathSciNet  Google Scholar 

  5. Koashi, M., Bužek, V., Imoto, N.: Entangled webs: tight bound for symmetric sharing of entanglement. Phys. Rev. A 62(5), 050302 (2000)

    ADS  MathSciNet  Google Scholar 

  6. Kafatos, M.: Bell’s Theorem, Quantum Theory and Conceptions of the Universe Bell’s theorem, Quantum Theory and Conceptions of the Universe, vol. 37. Springer, New York (2013)

    Google Scholar 

  7. Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62(6), 062314 (2000)

    ADS  MathSciNet  Google Scholar 

  8. Dür, W., Aschauer, H., Briegel, H.J.: Multiparticle entanglement purification for graph states. Phys. Rev. Lett. 91(10), 107903 (2003)

    ADS  MathSciNet  Google Scholar 

  9. Hein, M., Eisert, J., Briegel, H.J.: Multiparty entanglement in graph states. Phys. Rev. A 69(6), 062311 (2004)

    ADS  MathSciNet  MATH  Google Scholar 

  10. Nielsen, M.A.: Cluster-state quantum computation. Rep. Math. Phys. 57(1), 147 (2006)

    ADS  MathSciNet  MATH  Google Scholar 

  11. Kempe, J.: Multiparticle entanglement and its applications to cryptography. Phys. Rev. A 60(2), 910 (1999)

    ADS  MathSciNet  Google Scholar 

  12. Yeo, Y., Chua, W.K.: Teleportation and dense coding with genuine multipartite entanglement. Phys. Rev. Lett. 96(6), 060502 (2006)

    ADS  Google Scholar 

  13. Pirandola, S., Eisert, J., Weedbrook, C., Furusawa, A., Braunstein, S.L.: Advances in quantum teleportation. Nat. Photon. 9(10), 641 (2015)

    ADS  Google Scholar 

  14. Muralidharan, S., Panigrahi, P.K.: Perfect teleportation, quantum-state sharing, and superdense coding through a genuinely entangled five-qubit state. Phys. Rev. A 77(3), 032321 (2008)

    ADS  Google Scholar 

  15. Choudhury, S., Muralidharan, S., Panigrahi, P.K.: Quantum teleportation and state sharing using a genuinely entangled six-qubit state. J. Phys. A Math. Theor. 42(11), 115303 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  16. Saha, D., Panigrahi, P.K.: N-qubit quantum teleportation, information splitting and superdense coding through the composite GHZ-Bell channel. Quant. Inf. Process. 11(2), 615 (2012)

    MathSciNet  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

  18. Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58(6), 4394 (1998)

    ADS  MathSciNet  Google Scholar 

  19. Kumar, A., Haddadi, S., Pourkarimi, M.R., Behera, B.K., Panigrahi, P.K.: Experimental realization of controlled quantum teleportation of arbitrary qubit states via cluster states. Sci. Rep. 10(1), 1 (2020)

    Google Scholar 

  20. Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74(6), 062320 (2006)

    ADS  Google Scholar 

  21. Rao, D.B., Ghosh, S., Panigrahi, P.K.: Generation of entangled channels for perfect teleportation using multielectron quantum dots. Phys. Rev. A 78(4), 042328 (2008)

    ADS  Google Scholar 

  22. Dong, L., Wang, J.X., Li, Q.Y., Shen, H.Z., Dong, H.K., Xiu, X.M., Gao, Y.J., Oh, C.H.: Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities. Phys. Rev. A 93(1), 012308 (2016)

    ADS  Google Scholar 

  23. Xiu, X.M., Cui, C., Lin, Y.F., Dong, L., Dong, H.K., Gao, Y.J.: Splitting and acquiring quantum information with perfect states based on weak cross-Kerr nonlinearities. Progress of Theoretical and Experimental Physics 1, 013A03 (2018)

    MATH  Google Scholar 

  24. Li, X.K., Zhou, Y., Wang, G.H., Lv, D.Y., Badshah, F., Huang, H.M.: Generation of microwave photon perfect W states of three coupled superconducting resonators. Chin. Phys. B 32(4), 040306 (2022)

    Google Scholar 

  25. Li, L., Qiu, D.: The states of W-class as shared resources for perfect teleportation and superdense coding. J. Phys. A Math. Theor. 40(35), 10871 (2007)

    ADS  MathSciNet  MATH  Google Scholar 

  26. Li, K., Kong, F.Z., Yang, M., Ozaydin, F., Yang, Q., Cao, Z.L.: Generating multi-photon W-like states for perfect quantum teleportation and superdense coding. Quantum Inf. Process. 15(8), 3137 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  27. Zhao-Hui, P., Chun-Xia, J., Jun-Gang, L.: Scheme for implementing perfect quantum teleportation with non-maximally entangled W-class state in cavity QED. Commun. Theor. Phys. 50(2), 375 (2008)

    ADS  MATH  Google Scholar 

  28. Swain, M., Devrari, V., Rai, A., Behera, B.K., Panigrahi, P.K.: Generation of perfect W-state and demonstration of its application to quantum information splitting. arXiv preprint arXiv:2006.01742 (2020)

  29. Van Enk, S.: Single-particle entanglement. Phys. Rev. A 72(6), 064306 (2005)

    ADS  Google Scholar 

  30. Morin, O., Bancal, J.D., Ho, M., Sekatski, P., D’Auria, V., Gisin, N., Laurat, J., Sangouard, N.: Witnessing trustworthy single-photon entanglement with local homodyne measurements. Phys. Rev. Lett. 110(13), 130401 (2013)

    ADS  Google Scholar 

  31. Shi, J., Xu, P., Zhong, M., Gong, Y., Bai, Y., Yu, W., Li, Q., Jin, H., Zhu, S.: Heralded generation of multipartite entanglement for one photon by using a single two-dimensional nonlinear photonic crystal. Opt. Express 21(7), 7875 (2013)

    ADS  Google Scholar 

  32. Gräfe, M., Heilmann, R., Perez-Leija, A., Keil, R., Dreisow, F., Heinrich, M., Moya-Cessa, H., Nolte, S., Christodoulides, D.N., Szameit, A.: On-chip generation of high-order single-photon W-states. Nat. Photon. 8(10), 791 (2014)

    ADS  Google Scholar 

  33. Monteiro, F., Vivoli, V.C., Guerreiro, T., Martin, A., Bancal, J.D., Zbinden, H., Thew, R.T., Sangouard, N.: Revealing genuine optical-path entanglement. Phys. Rev. Lett. 114(17), 170504 (2015)

    ADS  Google Scholar 

  34. Caspar, P., Verbanis, E., Oudot, E., Maring, N., Samara, F., Caloz, M., Perrenoud, M., Sekatski, P., Martin, A., Sangouard, N., et al.: Heralded distribution of single-photon path entanglement. Phys. Rev. Lett. 125(11), 110506 (2020)

    ADS  Google Scholar 

  35. Perez-Leija, A., Hernandez-Herrejon, J., Moya-Cessa, H., Szameit, A., Christodoulides, D.N.: Generating photon-encoded W states in multiport waveguide-array systems. Phys. Rev. A 87(1), 013842 (2013)

    ADS  Google Scholar 

  36. Hessmo, B., Usachev, P., Heydari, H., Björk, G.: Experimental demonstration of single photon nonlocality. Phys. Rev. Lett. 92(18), 180401 (2004)

    ADS  Google Scholar 

  37. White, S.J., Klauck, F., Tran, T.T., Schmitt, N., Kianinia, M., Steinfurth, A., Heinrich, M., Toth, M., Szameit, A., Aharonovich, I., et al.: Quantum random number generation using a hexagonal boron nitride single photon emitter. J. Opt. 23(1), 01LT01 (2020)

    Google Scholar 

  38. Chen, X., Greiner, J.N., Wrachtrup, J., Gerhardt, I.: Single photon randomness based on a defect center in diamond. Sci. Rep. 9(1), 1 (2019)

    Google Scholar 

  39. Luo, Q., Cheng, Z., Fan, J., Tan, L., Song, H., Deng, G., Wang, Y., Zhou, Q.: Quantum random number generator based on single-photon emitter in gallium nitride. Opt. Lett. 45(15), 4224 (2020)

    ADS  Google Scholar 

  40. Gottesman, D., Jennewein, T., Croke, S.: Longer-baseline telescopes using quantum repeaters. Phys. Rev. Lett. 109(7), 070503 (2012)

    ADS  Google Scholar 

  41. Rai, A., Agarwal, G.: Possibility of coherent phenomena such as Bloch oscillations with single photons via W states. Phys. Rev. A 79(5), 053849 (2009)

    ADS  Google Scholar 

  42. Szameit, A., Nolte, S.: Discrete optics in femtosecond-laser-written photonic structures Journal of Physics B: Atomic. Mol. Opt. Phys. 43(16), 163001 (2010)

    ADS  Google Scholar 

  43. Meany, T., Gräfe, M., Heilmann, R., Perez-Leija, A., Gross, S., Steel, M.J., Withford, M.J., Szameit, A.: Laser written circuits for quantum photonics. Laser Photon. Rev. 9(4), 363 (2015)

    ADS  Google Scholar 

  44. Keil, R., Noh, C., Rai, A., Stützer, S., Nolte, S., Angelakis, D.G., Szameit, A.: Optical simulation of charge conservation violation and Majorana dynamics. Optica 2(5), 454 (2015)

    ADS  Google Scholar 

  45. Rai, A., Lee, C., Noh, C., Angelakis, D.G.: Photonic lattice simulation of dissipation-induced correlations in bosonic systems. Sci. Rep. 5(1), 1 (2015)

    Google Scholar 

  46. Heilmann, R., Gräfe, M., Nolte, S., Szameit, A.: A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization. Sci. Bull. 60(1), 96 (2015)

    Google Scholar 

  47. Rai, A., Das, S., Agarwal, G.: Quantum entanglement in coupled lossy waveguides. Opt. Express 18(6), 6241 (2010)

    ADS  Google Scholar 

  48. Swain, M., Rai, A., Selvan, M.K., Panigrahi, P.K.: Single photon generation and non-locality of perfect W-state. J. Opt. 22(7), 075202 (2020)

    ADS  Google Scholar 

  49. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80(10), 2245 (1998)

    ADS  MATH  Google Scholar 

  50. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  51. Ma, Z.H., Chen, Z.H., Chen, J.L., Spengler, C., Gabriel, A., Huber, M.: Measure of genuine multipartite entanglement with computable lower bounds. Phys. Rev. A 83(6), 062325 (2011)

    ADS  Google Scholar 

  52. Rafsanjani, S.H., Huber, M., Broadbent, C.J., Eberly, J.H.: Genuinely multipartite concurrence of N-qubit X matrices. Phys. Rev. A 86(6), 062303 (2012)

    ADS  Google Scholar 

  53. Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61(5), 052306 (2000)

    ADS  Google Scholar 

  54. Koashi, M., Winter, A.: Monogamy of quantum entanglement and other correlations. Phys. Rev. A 69(2), 022309 (2004)

    ADS  MathSciNet  Google Scholar 

  55. Zhu, X.N., Fei, S.M.: Generalized monogamy relations of concurrence for N-qubit systems. Phys. Rev. A 92(6), 062345 (2015)

    ADS  Google Scholar 

  56. Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77(8), 1413 (1996)

    ADS  MathSciNet  MATH  Google Scholar 

  57. Horodecki, M., Horodecki, P., Horodecki, R.: On the necessary and sufficient conditions for separability of mixed quantum states. Phys. Lett. A 223(1) (1996)

  58. Terhal, B.M.: Detecting quantum entanglement. Theor. Comput. Sci. 287(1), 313 (2002)

    MathSciNet  MATH  Google Scholar 

  59. Bourennane, M., Eibl, M., Kurtsiefer, C., Gaertner, S., Weinfurter, H., Gühne, O., Hyllus, P., Bruß, D., Lewenstein, M., Sanpera, A.: Experimental detection of multipartite entanglement using witness operators. Phys. Rev. Lett. 92(8), 087902 (2004)

    ADS  Google Scholar 

  60. Gühne, O., Tóth, G.: Entanglement detection. Phys. Rep. 474(1–6), 1 (2009)

    ADS  MathSciNet  Google Scholar 

  61. Agarwal, G.S., Biswas, A.: Inseparability inequalities for higher order moments for bipartite systems. New J. Phys. 7(1), 211 (2005)

    ADS  Google Scholar 

  62. Hillery, M., Zubairy, M.S.: Entanglement conditions for two-mode states. Phys. Rev. Lett. 96(5), 050503 (2006)

    ADS  MathSciNet  Google Scholar 

  63. Hillery, M., Zubairy, M.S.: Entanglement conditions for two-mode states: applications. Phys. Rev. A 74(3), 032333 (2006)

    ADS  Google Scholar 

  64. Nha, H., Kim, J.: Entanglement criteria via the uncertainty relations in su (2) and su (1, 1) algebras: detection of non-Gaussian entangled states. Phys. Rev. A 74(1), 012317 (2006)

    ADS  Google Scholar 

  65. Nha, H.: Linear optical scheme to demonstrate genuine multipartite entanglement for single-particle W states. Phys. Rev. A 77(6), 062328 (2008)

    ADS  MathSciNet  Google Scholar 

  66. Selvan, K., Panigrahi, P.K.: Entanglement condition for W type multimode states and schemes for experimental realization. Eur. Phys. J. D 73(6), 1 (2019)

    Google Scholar 

  67. Matthews, J.C., Politi, A., Stefanov, A., O’brien, J.L.: Manipulation of multiphoton entanglement in waveguide quantum circuits. Nat. Photon. 3(6), 346 (2009)

    ADS  Google Scholar 

  68. Meher, N., Sivakumar, S., Panigrahi, P.K.: Duality and quantum state engineering in cavity arrays. Sci. Rep. 7(1), 1 (2017)

    Google Scholar 

  69. Pellizzari, T.: Quantum networking with optical fibres. Phys. Rev. Lett. 79(26), 5242 (1997)

    ADS  Google Scholar 

  70. Van Enk, S., Kimble, H., Cirac, J., Zoller, P.: Quantum communication with dark photons. Phys. Rev. A 59(4), 2659 (1999)

    ADS  Google Scholar 

  71. Lu, D.M., Chen, L.H.: Geometrical quantum discord in the coupled cavities system with tetrahedral structure. Int. J. Theor. Phys. 58(2), 605 (2019)

    MATH  Google Scholar 

  72. Kyoseva, E., Beige, A., Kwek, L.C.: Coherent cavity networks with complete connectivity. New J. Phys. 14(2), 023023 (2012)

    ADS  Google Scholar 

  73. Cho, J., Angelakis, D.G., Bose, S.: Heralded generation of entanglement with coupled cavities. Phys. Rev. A 78(2), 022323 (2008)

    ADS  Google Scholar 

  74. Bergou, J.A.: Entangled fields in multiple cavities as a testing ground for quantum mechanics. Found. Phys. 29(4), 503 (1999)

    MathSciNet  Google Scholar 

  75. Guo, G.C., Zhang, Y.S.: Scheme for preparation of the W state via cavity quantum electrodynamics. Phys. Rev. A 65(5), 054302 (2002)

    ADS  Google Scholar 

  76. Yang, M., Yi, Y.M., Cao, Z.L.: Scheme for preparation of W state via cavity QED. Int. J. Quant. Inf. 2(02), 231 (2004)

    MATH  Google Scholar 

  77. Hillery, M., Mlodinow, L.: Interferometers and minimum-uncertainty states. Phys. Rev. A 48(2), 1548 (1993)

    ADS  Google Scholar 

  78. Lougovski, P., van Enk, S.J., Choi, K.S., Papp, S.B., Deng, H., Kimble, H.: Verifying multipartite mode entanglement of W states. New J. Phys. 11(6), 063029 (2009)

    ADS  Google Scholar 

  79. Chen, Z., Zhou, Y., Shen, J.T.: Exact dissipation model for arbitrary photonic Fock state transport in waveguide QED systems. Opt. Lett. 42(4), 887 (2017)

    ADS  Google Scholar 

  80. Chen, Z., Zhou, Y., Shen, J.T.: Entanglement-preserving approach for reservoir-induced photonic dissipation in waveguide QED systems. Phys. Rev. A 98(5), 053830 (2018)

    ADS  Google Scholar 

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Acknowledgements

A.R gratefully acknowledges a research grant from Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India (Grant No.: CRG/2019/005749), during this work. P. K. P acknowledges a research grant from SERB, DST project (Grant No.: DST/ICPS/QuST/Theme-1/2019/2020-21/01).

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Authors and Affiliations

  1. Department of Physics and Astronomy, National Institute of Technology, Rourkela, Odisha, 769008, India

    Manoranjan Swain

  2. Department of Physics, Thiagarajar College, Madurai, Tamil Nadu, 625009, India

    M. Karthick Selvan

  3. School of Physical Sciences, Jawaharlal Nehru University, New Delhi, 110067, India

    Amit Rai

  4. Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, West Bengal, 741246, India

    Prasanta K. Panigrahi

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  1. Manoranjan Swain
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Contributions

MS derived the results given in Sect. 2. MKS derived the results of Sects. 5 and 6. MKS and MS derived the results presented in Sects. 3 and 4 and prepared the manuscript. A.R and P.K.P verified the results and reviewed the manuscript.

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Correspondence to Manoranjan Swain.

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Swain, M., Selvan, M.K., Rai, A. et al. Generation and entanglement study of generalized N-mode single-photon perfect W-states. Quantum Inf Process 22, 302 (2023). https://doi.org/10.1007/s11128-023-04057-3

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