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Precision protection through multi-body indirect correlations and the reconstruction of stable probe qubit system

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Abstract

The obstacle restricting us to generalize the ideal quantum metrology scheme to practice is the decay of the precision of estimation induced by the environment. When the parameter to be estimated is the phase parameter of atomic state, the loss of precision is caused by the spontaneous emission of the atom, which is the result of the interaction between the atom and the background quantum fields. Since the probe qubit constructed by the ground state and excited state of single atom is sensitive to the environment, we have provided schemes to use two proper states of n proper arrangement atoms as the new stable qubit states instead of the usual ground and excited state of single atom, to reduce the decay rate of the precision of estimation through the multi-atom indirect correlations.

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References

  1. Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976)

    MATH  Google Scholar 

  2. Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory. North-Holland, Amsterdam (1982)

    MATH  Google Scholar 

  3. Hübner, M.: Explicit computation of the Bures distance for density matrices. Phys. Lett. A 163, 239–242 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  4. Hübner, M.: Computation of Uhlmann’s parallel transport for density matrices and the Bures metric on three-dimensional Hilbert space. Phys. Lett. A 179, 226–230 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  5. Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439–3443 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Bollinger, J.J., Itano, W.M., Wineland, D.J., Heinzen, D.J.: Optimal frequency measurements with maximally correlated states. Phys. Rev. A 54, R4649–R4652 (1996)

    Article  ADS  Google Scholar 

  7. Yurke, B., McCall, S.L., Klauder, J.R.: SU(2) and SU(1,1) interferometers. Phys. Rev. A 33, 4033–4054 (1986)

    Article  ADS  Google Scholar 

  8. Dowling, J.P.: Correlated input-port, matter-wave interferometer: quantum-noise limits to the atom-laser gyroscope. Phys. Rev. A 57, 4736–4746 (1998)

    Article  ADS  Google Scholar 

  9. Kok, P., Braunstein, S.L., Dowling, J.P.: Quantum lithography, entanglement and Heisenberg-limited parameter estimation. J. Opt. B Quantum Semiclass 6, S811–S815 (2004)

    Article  ADS  Google Scholar 

  10. Giovannetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004)

    Article  ADS  Google Scholar 

  11. Giovannetti, V., Lloyd, S., Maccone, L.: Quantum metrology. Phys. Rev. Lett. 96(010401), 1–4 (2006)

    MathSciNet  Google Scholar 

  12. Boixo, S., Flammia, S.T., Caves, C.M., Geremia, J.M.: Generalized limits for single-parameter quantum estimation. Phys. Rev. Lett. 98(090401), 1–4 (2007)

    Google Scholar 

  13. Roy, S.M., Braunstein, S.L.: Exponentially enhanced quantum metrology. Phys. Rev. Lett. 100(220501), 1–4 (2008)

    Google Scholar 

  14. Boixo, S., Datta, A., Davis, M.J., Flammia, S.T., Shaji, A., Caves, C.M.: Quantum metrology: dynamics versus entanglement. Phys. Rev. Lett. 101(040403), 1–4 (2008)

    Google Scholar 

  15. Hofmann, H.F.: All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry. Phys. Rev. A 79(033822), 1–4 (2009)

    Google Scholar 

  16. Estève, J., Gross, C., Weller, A., Giovanazzi, S., Oberthaler, M.K.: Squeezing and entanglement in a Bose–Einstein condensate. Nature (London) 455, 1216–1219 (2008)

    Article  ADS  Google Scholar 

  17. Hyllus, P., Pezzé, L., Smerzi, A.: Entanglement and sensitivity in precision measurements with states of a fluctuating number of particles. Phys. Rev. Lett. 105(120501), 1–4 (2010)

    Google Scholar 

  18. Pezzé, L., Smerzi, A.: Entanglement, nonlinear dynamics, and the Heisenberg limit. Phys. Rev. Lett. 102(100401), 1–4 (2009)

    MathSciNet  Google Scholar 

  19. Hyllus, L., Laskowski, W., Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Pezzé, L., Smerzi, A.: Fisher information and multiparticle entanglement. Phys. Rev. A 85(022321), 1–10 (2012)

    Google Scholar 

  20. Toth, G.: Multipartite entanglement and high precision metrology. Phys. Rev. A 85(022322), 1–10 (2012)

    Google Scholar 

  21. Rosenkranz, M., Jaksch, D.: Parameter estimation with cluster states. Phys. Rev. A 79(022103), 1–10 (2009)

    Google Scholar 

  22. Huelga, S.F., Macchiavello, C., Pellizzari, T., Ekert, A.K., Plenio, M.B., Cirac, J.I.: Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79, 3865–3868 (1997)

    Article  ADS  Google Scholar 

  23. Ulam-Orgikh, D., Kitagawa, M.: Spin squeezing and decoherence limit in Ramsey spectroscopy. Phys. Rev. A 64(052106), 1–6 (2001)

    Google Scholar 

  24. Sasaki, M., Ban, M., Barnett, S.M.: Optimal parameter estimation of a depolarizing channel. Phys. Rev. A 66(022308), 1–8 (2002)

    MathSciNet  Google Scholar 

  25. Shaji, A., Caves, C.M.: Qubit metrology and decoherence. Phys. Rev. A 76(032111), 1–13 (2007)

    Google Scholar 

  26. Monras, A., Paris, M.G.A.: Optimal quantum estimation of loss in Bosonic channels. Phys. Rev. Lett. 98(160401), 1–4 (2007)

    Google Scholar 

  27. Demkowicz-Dobrzański, R., Kołodyński, J., Guta, M.: The elusive Heisenberg limit in quantum enhanced metrology. Nat. Commun. 3(1063), 1–8 (2012)

    Google Scholar 

  28. Demkowicz-Dobrzański, R., Dorner, U., Smith, B.J., Lundeen, J.S., Wasilewski, W., Banaszek, K., Walmsley, I.A.: Quantum phase estimation with lossy interferometers. Phys. Rev. A 80(013825), 1–10 (2009)

    Google Scholar 

  29. Lee, T.-W., Huver, S.D., Lee, H., Kaplan, L., McCracken, S.B., Min, C., Uskov, D.B., Wildfeuer, C.F., Veronis, G., Dowling, J.P.: Optimization of quantum interferometric metrological sensors in the presence of photon loss. Phys. Rev. A 80(063803), 1–4 (2009)

    Google Scholar 

  30. Dorner, U., Demkowicz-Dobrzański, R., Smith, B.J., Lundeen, J.S., Wasilewski, W., Banaszek, K., Walmsley, I.A.: Optimal quantum phase estimation. Phys. Rev. Lett. 102(040403), 1–4 (2009)

    Google Scholar 

  31. Watanabe, Y., Sagawa, T., Ueda, M.: Optimal measurement on noisy quantum systems. Phys. Rev. Lett. 104(020401), 1–4 (2010)

    Google Scholar 

  32. Knysh, S., Smelyanskiy, V.N., Durkin, G.A.: Scaling laws for precision in quantum interferometry and the bifurcation landscape of the optimal state. Phys. Rev. A 83(021804), 1–4 (2011)

    Google Scholar 

  33. Kołdyński, J., Demkowicz-Dobrzański, R.: Phase estimation without a priori phase knowledge in the presence of loss. Phys. Rev. A 82(053804), 1–6 (2010)

    Google Scholar 

  34. Kacprowicz, M., Demkowicz-Dobrzański, R., Wasilewski, W., Banaszek, K., Walmsley, I.A.: Experimental quantum-enhanced estimation of a lossy phase shift. Nat. Photonics 4, 357–360 (2010)

    Article  ADS  Google Scholar 

  35. Genoni, M.G.A., Olivares, S., Paris, M.G.: Optical phase estimation in the presence of phase diffusion. Phys. Rev. Lett. 106(153603), 1–4 (2011)

    Google Scholar 

  36. Chin, A.W., Huelga, S.F., Plenio, M.B.: Quantum metrology in non-Markovian environments. Phys. Rev. Lett. 109(233601), 1–5 (2012)

    Google Scholar 

  37. Escher, B.M., de MatosFilho, R.L., Davidovich, L.: General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology. Nat. Phys. 7, 406–411 (2011)

    Article  Google Scholar 

  38. Ma, J., Huang, Y., Wang, X., Sun, C.: Quantum Fisher information of the Greenberger–Horne–Zeilinger state in decoherence channels. Phys. Rev. A 84(022302), 1–7 (2011)

    Google Scholar 

  39. Zhong, W., Sun, Z., Ma, J., Wang, X., Nori, F.: Fisher information under decoherence in Bloch representation. Phys. Rev. A 87(022337), 1–14 (2013)

    Google Scholar 

  40. Chaves, R., Brask, J.B., Markiewicz, M., Kołodyński, J., Acín, A.: Noisy metrology beyond the standard quantum limit. Phys. Rev. Lett. 111(120401), 1–5 (2013)

    Google Scholar 

  41. Tsang, M.: Quantum metrology with open dynamical systems. New J. Phys. 15(073005), 1–21 (2013)

    ADS  MathSciNet  Google Scholar 

  42. Alipour, S., Mehboudi, M., Rezakhani, A.T.: Quantum metrology in open systems: dissipative Cramr–Rao bound. Phys. Rev. Lett. 112(120405), 1–5 (2014)

    Google Scholar 

  43. Benatti, F., Alipour, S., Rezakhani, A.T.: Dissipative quantum metrology in manybody systems of identical particles. New J. Phys. 16(015023), 1–13 (2014)

    Google Scholar 

  44. Ozaydin, F.: Phase damping destroys quantum Fisher information of W states. Phys. Lett. A 378, 3161–3164 (2014)

    Article  ADS  MATH  Google Scholar 

  45. Wang, J., Tian, Z., Jing, J., Fan, H.: Quantum metrology and estimation of Unruh effect. Sci. Rep. 4(7195), 1–6 (2014)

    Google Scholar 

  46. Yao, Y., Xiao, X., Ge, L., Wang, X., Sun, C.: Quantum Fisher information in noninertial frames. Phys. Rev. A 89(042336), 1–7 (2014)

    Google Scholar 

  47. Ozaydin, F., Altintas, A.: Quantum metrology: surpassing the shot-noise limit with Dzyaloshinskii–Moriya interaction. Sci. Rep. 5(16360), 1–6 (2015)

    Google Scholar 

  48. Jin, Y., Yu, H.: Electromagnetic shielding in quantum metrology. Phys. Rev. A 91(022120), 1–7 (2015)

    Google Scholar 

  49. Jin, Y.: Precision protection through indirect correlations. Ann. Phys. (NY) 367, 212–218 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. Audretsch, J., Müller, R.: Spontaneous excitation of an accelerated atom: the contributions of vacuum fluctuations and radiation reaction. Phys. Rev. A 50, 1755–1763 (1994)

    Article  ADS  Google Scholar 

  51. Jin, Y.: The effects of symmetrical arrangement on quantum metrology. Sci. Rep. 7(405), 1–7 (2017)

    Google Scholar 

  52. Zhu, Z., Yu, H., Wang, B.: Temperature-dependent Casimir–Polder forces on polarizable molecules. Phys. Rev. A 86(052508), 1–10 (2012)

    Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants No. 11605030, The science and technology top talent support program of Guizhou educational department under Grant No. QJHKY[2017]084 and the Scientific Research Foundation of Guiyang university under Grant No. 20160375115.

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  1. School of Electronic and Communication Engineering, Guiyang University, Guiyang, 550005, Guizhou, China

    Yao Jin

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Correspondence to Yao Jin.

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Jin, Y. Precision protection through multi-body indirect correlations and the reconstruction of stable probe qubit system. Quantum Inf Process 17, 242 (2018). https://doi.org/10.1007/s11128-018-2015-6

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