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Separability of heterogeneous quantum systems using multipartite concurrence and tangle

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Abstract

As heterogeneous quantum systems become a high-impact topic in the state of the art through hybrid entanglement, none of the many competing measures of multipartite entanglement has yet been shown to provide a complete characterization. In this paper, for the first time, we connect two of the most popular research directions on entanglement of heterogeneous systems: correlation tensors on the one hand, and concurrence and tangle on the other. We find the first ever separability criteria for heterogeneous quantum systems under any arbitrary partition in terms of multipartite concurrence and tangle, respectively, generalizing and refining previous work on m-separability of homogeneous systems, and we derive the first relations between the Frobenius norms of correlation tensors, concurrence and tangle, generalizing previous work for homogeneous systems.

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References

  1. Qin, H., Dai, Y.: Dynamic quantum secret sharing by using d-dimensional GHZ state. Quantum Inf. Process. 16(3), 64 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  2. Zhou, Y., Yu, J., Yan, Z., Jia, X., Zhang, J., Xie, C., Peng, K.: Quantum secret sharing among four players using multipartite bound entanglement of an optical field. Phys. Rev. Lett. 121(15), 150502 (2018)

    ADS  Google Scholar 

  3. Acín, A., Masanes, L.: Certified randomness in quantum physics. Nature 540(7632), 213 (2016)

    ADS  Google Scholar 

  4. Vazirani, U., Vidick, T.: Fully device independent quantum key distribution. Commun. ACM 62(4), 133 (2019)

    Google Scholar 

  5. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science. IEEE (1994)

  6. Jozsa, R., Linden, N.: On the role of entanglement in quantum-computational speed-up. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 459(2036), 2011 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

  7. Kimble, H.J.: The quantum internet. Nature 453(7198), 1023 (2008)

    ADS  Google Scholar 

  8. Wehner, S., Elkouss, D., Hanson, R.: Quantum internet: a vision for the road ahead. Science 362(6412), eaam9288 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  9. Yuan, Z.S., Bao, X.H., Lu, C.Y., Zhang, J., Peng, C.Z., Pan, J.W.: Entangled photons and quantum communication. Phys. Rep. 497(1), 1 (2010)

    ADS  MathSciNet  Google Scholar 

  10. Yu, Y., Ma, F., Luo, X.Y., Jing, B., Sun, P.F., Fang, R.Z., Yang, C.W., Liu, H., Zheng, M.Y., Xie, X.P., et al.: Entanglement of two quantum memories via fibres over dozens of kilometres. Nature 578(7794), 240 (2020)

    ADS  Google Scholar 

  11. Tomamichel, M., Fehr, S., Kaniewski, J., Wehner, S.: A monogamy-of-entanglement game with applications to device-independent quantum cryptography. New J. Phys. 15(10), 103002 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  12. Gharibian, S.: Strong NP-hardness of the quantum separability problem (2008). arXiv:0810.4507

  13. Guo, Y., Zhang, L.: Multipartite entanglement measure and complete monogamy relation. Phys. Rev. A 101(3), 032301 (2020)

    ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

  15. Horodecki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232(5), 333 (1997)

    ADS  MathSciNet  MATH  Google Scholar 

  16. Rudolph, O.: Some properties of the computable cross-norm criterion for separability. Phys. Rev. A 67, 032312 (2003)

    ADS  MathSciNet  Google Scholar 

  17. Rudolph, O.: Further results on the cross norm criterion for separability. Quantum Inf. Process. 4, 219 (2005)

    MathSciNet  MATH  Google Scholar 

  18. Chen, K., Wu, L.A.: A matrix realignment method for recognizing entanglement. Quantum Info. Comput. 3(3), 193 (2003)

    MathSciNet  MATH  Google Scholar 

  19. Liu, B.H., Hu, X.M., Chen, J.S., Zhang, C., Huang, Y.F., Li, C.F., Guo, G.C., Karpat, G., Fanchini, F.F., Piilo, J., Maniscalco, S.: Time-invariant entanglement and sudden death of nonlocality. Phys. Rev. A 94, 062107 (2016). https://doi.org/10.1103/PhysRevA.94.062107

    Article  ADS  Google Scholar 

  20. Lewenstein, M., Kraus, B., Cirac, J.I., Horodecki, P.: Optimization of entanglement witnesses. Phys. Rev. A 62, 052310 (2000)

    ADS  Google Scholar 

  21. Huber, M., de Vicente, J.I.: Structure of multidimensional entanglement in multipartite systems. Phys. Rev. Lett. 110(3), 030501 (2013)

    ADS  Google Scholar 

  22. Hassan, A.S.M., Joag, P.S.: Experimentally accessible geometric measure for entanglement in N-qubit pure states. Phys. Rev. A 77(6), 062334 (2008)

    ADS  Google Scholar 

  23. Hassan, A.S.M., Joag, P.S.: Geometric measure for entanglement in N-qudit pure states. Phys. Rev. A 80(4), 042302 (2009)

    ADS  MathSciNet  Google Scholar 

  24. Wang, J., Li, M., Li, H., Fei, S.M., Li-Jost, X.: Bounds on multipartite concurrence and tangle. Quantum Inf. Process. 15(10), 4211 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  25. Tănăsescu, A., Popescu, P.G.: Bloch vector norms of separable multi-partite quantum systems. EPL (Europhys. Lett.) 126(6), 60003 (2019)

    Google Scholar 

  26. Santos, M.F., Carvalho, A.R.R.: Observing different quantum trajectories in cavity QED. EPL 94(6), 64003 (2011)

    ADS  Google Scholar 

  27. Ho, C.L., Deguchi, T.: Multi-qudit states generated by unitary braid quantum gates based on Temperley–Lieb algebra. EPL 118(4), 40001 (2017)

    ADS  Google Scholar 

  28. Shang, Y., Wang, Y., Li, M., Lu, R.: Quantum communication protocols by quantum walks with two coins. EPL 124(6), 60009 (2019)

    Google Scholar 

  29. Imany, P., Jaramillo-Villegas, J.A., Alshaykh, M.S., Lukens, J.M., Odele, O.D., Moore, A.J., Leaird, D.E., Qi, M., Weiner, A.M.: High-dimensional optical quantum logic in large operational spaces. NPJ Quantum Inf. 5(1), 1 (2019)

    Google Scholar 

  30. Huber, F., Eltschka, C., Siewert, J., Gühne, O.: Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity. J. Phys. A: Math. Theor. 51(17), 175301 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  31. Qi, L., Zhang, G., Ni, G.: How entangled can a multi-party system possibly be? Phys. Lett. A 382(22), 1465 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  32. Goyeneche, D., Bielawski, J., Życzkowski, K.: Multipartite entanglement in heterogeneous systems. Phys. Rev. A 94(1), 012346 (2016)

    ADS  Google Scholar 

  33. Wang, J., Yue, R.X., Pang, S.Q.: Construction of asymmetric orthogonal arrays of high strength by juxtaposition. Commun. Stat. Theory Methods 1–11 (2019)

  34. Pang, S.Q., Zhang, X., Lin, X., Zhang, Q.J.: Two and three-uniform states from irredundant orthogonal arrays. npj Quantum Inf. 5(1), 1 (2019)

    Google Scholar 

  35. Tănăsescu, A., Popescu, P.G.: Separability of heterogeneous multipartite quantum systems using Bloch Vectors. Quantum Inf. Process. 19(6), 176 (2020). https://doi.org/10.1007/s11128-020-02668-8

    Article  ADS  MathSciNet  Google Scholar 

  36. Zhao, H., Zhang, M.M., Jing, N., Wang, Z.X.: Separability criteria based on Bloch representation of density matrices. Quantum Inf. Process. 19(1), 14 (2020)

    ADS  MathSciNet  Google Scholar 

  37. Xu, W., Zhu, C.J., Zheng, Z.J., Fei, S.M.: Necessary conditions for classifying m-separability of multipartite entanglements. Quantum Inf. Process. 19, 200 (2020)

    ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

  40. Barreiro, J.T., Wei, T.C., Kwiat, P.G.: Beating the channel capacity limit for linear photonic superdense coding. Nat. Phys. 4(4), 282 (2008)

    Google Scholar 

  41. Graham, T.M., Bernstein, H.J., Wei, T.C., Junge, M., Kwiat, P.G.: Superdense teleportation using hyperentangled photons. Nat. Commun. 6, 7185 (2015)

    ADS  Google Scholar 

  42. Fickler, R., Lapkiewicz, R., Ramelow, S., Zeilinger, A.: Quantum entanglement of complex photon polarization patterns in vector beams. Phys. Rev. A 89(6), 060301 (2014)

    ADS  Google Scholar 

  43. Fickler, R., Krenn, M., Lapkiewicz, R., Ramelow, S., Zeilinger, A.: Real-time imaging of quantum entanglement. Sci. Rep. 3, 1914 (2013)

    ADS  Google Scholar 

  44. Erhard, M., Qassim, H., Mand, H., Karimi, E., Boyd, R.W.: Real-time imaging of spin-to-orbital angular momentum hybrid remote state preparation. Phys. Rev. A 92(2), 022321 (2015)

    ADS  Google Scholar 

  45. Sheng, Y.B., Guo, R., Pan, J., Zhou, L., Wang, X.F.: Two-step measurement of the concurrence for hyperentangled state. Quantum Inf. Process. 14(3), 963 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  46. Zhu, S., Liu, Y.C., Zhao, B.K., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement of the concurrence of arbitrary two-photon six-qubit hyperentangled state. EPL (Europhys. Lett.) 129(5), 50004 (2020)

    ADS  Google Scholar 

  47. Zhang, M., Zhou, L., Zhong, W., Sheng, Y.B.: Direct measurement of the concurrence of hybrid entangled state based on parity check measurements. Chin. Phys. B 28(1), 010301 (2019)

    ADS  Google Scholar 

  48. Li, M., Fei, S.M., Wang, Z.X.: Bounds for multipartite concurrence. Rep. Math. Phys. 65(2), 289 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  49. Chen, W., Zhu, X.N., Fei, S.M., Zheng, Z.J.: Lower bound of multipartite concurrence based on sub-partite quantum systems. Quantum Inf. Process. 16(12), 288 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  50. Zhu, X.N., Li, M., Fei, S.M.: A lower bound of concurrence for multipartite quantum systems. Quantum Inf. Process. 17(2), 30 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  51. Li, M., Wang, Z., Wang, J., Shen, S., Fei, S.M.: Improved lower bounds of concurrence and convex-roof extended negativity based on Bloch representations. Quantum Inf. Process. 19(4), 1 (2020)

    ADS  MathSciNet  Google Scholar 

  52. Cornelio, M.F.: Multipartite monogamy of the concurrence. Phys. Rev. A 87(3), 032330 (2013)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  54. Chen, W., Fei, S.M., Zheng, Z.J.: Lower bound on concurrence for arbitrary-dimensional tripartite quantum states. Quantum Inf. Process. 15(9), 3761 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  55. Zhao, H., Zhang, M., Fei, S.M., Jing, N.: Projection based lower bounds of concurrence for multipartite quantum systems. Int. J. Theor. Phys. (2020)

  56. Rungta, P., Caves, C.M.: Concurrence-based entanglement measures for isotropic states. Phys. Rev. A 67(1), 012307 (2003)

    ADS  Google Scholar 

  57. Li, M., Fei, S.M., Li-Jost, X., Fan, H.: Genuine multipartite entanglement detection and lower bound of multipartite concurrence. Phys. Rev. A 92(6), 062338 (2015)

    ADS  Google Scholar 

  58. Shen, S.Q., Yu, J., Li, M., Fei, S.M.: Improved separability criteria based on Bloch representation of density matrices. Sci. Rep. 6, 28850 (2016)

    ADS  Google Scholar 

  59. de Vicente, J.I.: Lower bounds on concurrence and separability conditions. Phys. Rev. A 75(5), 052320 (2007)

    ADS  MathSciNet  Google Scholar 

  60. Carvalho, A.R., Mintert, F., Buchleitner, A.: Decoherence and multipartite entanglement. Phys. Rev. Lett. 93(23), 230501 (2004)

    ADS  Google Scholar 

  61. de Vicente, J.I.: Further results on entanglement detection and quantification from the correlation matrix criterion. J. Phys. A Math. Theor. 41(6), 065309 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  62. Hioe, F.T., Eberly, J.H.: N-level coherence vector and higher conservation laws in quantum optics and quantum mechanics. Phys. Rev. Lett. 47(12), 838 (1981)

    ADS  MathSciNet  Google Scholar 

  63. Aolita, L., Mintert, F.: Measuring multipartite concurrence with a single factorizable observable. Phys. Rev. Lett. 97(5), 050501 (2006)

    ADS  Google Scholar 

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  1. Computer Science and Engineering Department, University POLITEHNICA of Bucharest, Splaiul Independeţei 313, (6), Bucharest, Romania

    Andrei Tănăsescu & Pantelimon George Popescu

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  1. Andrei Tănăsescu
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  2. Pantelimon George Popescu
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Correspondence to Pantelimon George Popescu.

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Tănăsescu, A., Popescu, P.G. Separability of heterogeneous quantum systems using multipartite concurrence and tangle. Quantum Inf Process 20, 50 (2021). https://doi.org/10.1007/s11128-021-02989-2

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