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Multi-parameter quantum magnetometry with spin states in coarsened measurement reference

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Abstract

We investigate the simultaneous estimation of the intensity and the orientation of a magnetic field by the multi-parameter quantum Fisher information matrix. A general expression is achieved for the simultaneous estimation precision of the intensity and the orientation, which is better than the independent estimation precision for the given number of spin states. Moreover, we consider an imperfect measurement device, coarsened measurement reference. For the case of the measurement reference rotating around the y-axis randomly, the simultaneous estimation always performs better than the independent estimation. For all other cases, the simultaneous estimation precision will not perform better than the independent estimation when the coarsened degree is larger than a certain value.

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  • 30 July 2019

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References

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

    Article  ADS  MathSciNet  Google Scholar 

  2. Giovanetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330 (2004)

    Article  ADS  Google Scholar 

  3. Xie, D., Wang, A.: Quantum metrology in correlated environments. Phys. Lett. A 378, 2079 (2014)

    Article  ADS  Google Scholar 

  4. Paris, M.G.A.: Quantum estimation for quantum technology. Int. J. Quant. Inf. 7, 125 (2009)

    Article  Google Scholar 

  5. Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photonics 5, 222 (2011)

    Article  ADS  Google Scholar 

  6. Bongs, K., Launay, R., Kasevich, M.A.: High-order inertial phase shifts for time-domain atom interferometers. Appl. Phys. B 84, 599 (2006)

    Article  ADS  Google Scholar 

  7. Carlton, P.M., Boulanger, J., Kervrann, C., Sibarita, J.-B., Salamero, J., Gordon-Messer, S., Bressan, D., Haber, J.E., Haase, S., Shao, L., et al.: Fast live simultaneous multiwavelength four-dimensional optical microscopy. Proc. Natl. Acad. Sci. 107, 16016 (2010)

    Article  ADS  Google Scholar 

  8. Taylor, M.A., Janousek, J., Daria, V., Knittel, J., Hage, B., Bachor, H.-A., Bowen, W.P.: Biological measurement beyond the quantum limit. Nat. Photonics 7, 229 (2013)

    Article  ADS  Google Scholar 

  9. Aasi, J., et al.: Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photonics 7, 613 (2013)

    Article  ADS  Google Scholar 

  10. Taylor, J.M., Cappellaro, P., Childress, L., Jiang, L., Budker, D., Hemmer, P.R., Yacoby, A., Walsworth, R., Lukin, M.D.: High-sensitivity diamond magnetometer with nanoscale resolution. Nat. Phys. 4, 810 (2008)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  12. Baumgratz, T., Datta, A.: Quantum enhanced estimation of a multidimensional field. Phys. Rev. Lett. 116, 030801 (2016)

    Article  ADS  Google Scholar 

  13. Kolobov, M.I.: Quantum Imaging. Springer, New York (2007)

    Book  Google Scholar 

  14. Spagnolo, N., Aparo, L., Vitelli, C., Crespi, A., Ramponi, R., Osellame, R., Mataloni, P., Sciarrino, F.: Quantum interferometry with three-dimensional geometry. Sci. Rep. 2, 862 (2012)

    Article  ADS  Google Scholar 

  15. Genovese, M.: Real applications of quantum imaging. J. Opt. 18, 073002 (2016)

    Article  ADS  Google Scholar 

  16. Ang, S.Z., Nair, R., Tsang, M.: Quantum limit for two-dimensional resolution of two incoherent optical point sources. Phys. Rev. A 95, 063847 (2017)

    Article  ADS  Google Scholar 

  17. R̆ehac̆ek, J., Hradil, Z., Stoklasa, B., Paúr, M., Grover, J., Krzic, A., Sanchez-Soto, L. L.: Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution. Phys. Rev. A 96, 062107 (2017)

  18. Kómar, P., Kessler, E.M., Bishof, M., Jiang, L., Sørensen, A.S., Ye, J., Lukin, M.D.: A quantum network of clocks. Nat. Phys. 10, 582 (2014)

    Article  Google Scholar 

  19. Nokkala, J., Arzani, F., Galve, F., Zambrini, R., Maniscalco, S., Piilo, J., Treps, N., Parigi, V.: Reconfigurable optical implementation of quantum complex networks. New J. Phys. 20, 053024 (2018)

    Article  ADS  Google Scholar 

  20. Genoni, M.G., Paris, M.G.A., Adesso, G., Nha, H., Knight, P.L., Kim, M.S.: Optimal estimation of joint parameters in phase space. Phys. Rev. A 87, 012107 (2013)

    Article  ADS  Google Scholar 

  21. Humphreys, P.C., Barbieri, M., Datta, A., Walmsley, I.A.: Quantum enhanced multiple phase estimation. Phys. Rev. Lett. 111, 070403 (2013)

    Article  ADS  Google Scholar 

  22. Gagatsos, C.N., Branford, D., Datta, A.: Gaussian systems for quantum-enhanced multiple phase estimation. Phys. Rev. A 94, 042342 (2016)

    Article  ADS  Google Scholar 

  23. Ragy, S., Jarzyna, M., Demkowicz-Dobrzanski, R.: Compatibility in multiparameter quantum metrology. Phys. Rev. A 94, 052108 (2016)

    Article  ADS  Google Scholar 

  24. Ciampini, M.A., Spagnolo, N., Vitelli, C., Pezze, L., Smerzi, A., Sciarrino, F.: Quantum-enhanced multiparameter estimation in multiarm interferometers. Sci. Rep. 6, 28881 (2016)

    Article  ADS  Google Scholar 

  25. Liu, J., Lu, X.-M., Sun, Z., Wang, X.: Quantum multiparameter metrology with generalized entangled coherent state. J. Phys. A Math. Theor. 49, 115302 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  26. Kok, P., Dunningham, J., Ralph, J.F.: Role of entanglement in calibrating optical quantum gyroscopes. Phys. Rev. A 95, 012326 (2017)

    Article  ADS  Google Scholar 

  27. Dominic, B., Haixing, M., Animesh, D.: Fundamental quantum limits of multicarrier optomechanical sensors. Phys. Rev. Lett. 121, 110505 (2018)

    Article  Google Scholar 

  28. Ge, W., Jacobs, K., Eldredge, Z., Gorshkov, A.V., Foss-Feig, M.: Distributed quantum metrology with linear networks and separable inputs. Phys. Rev. Lett. 121, 043604 (2018)

    Article  ADS  Google Scholar 

  29. Zhuang, Q., Zhang, Z., Shapiro, J.H.: Distributed quantum sensing using continuous-variable multipartite entanglement. Phys. Rev. A 97, 032329 (2018)

    Article  ADS  Google Scholar 

  30. Brask, J.B., Chaves, R., Kołodyński, J.: Improved quantum magnetometry beyond the standard quantum limit. Phys. Rev. X 5, 031010 (2015)

    Google Scholar 

  31. Mamin, H.J., Sherwood, M.H., Kim, M., Rettner, C.T., Ohno, K., Awschalom, D.D., Rugar, D.: Multipulse double-quantum magnetometry with near-surface nitrogen-vacancy centers. Phys. Rev. Lett. 113, 030803 (2014)

    Article  ADS  Google Scholar 

  32. Geremia, J.M., Stockton, J.K., Doherty, A.C., Mabuchi, H.: Quantum kalman filtering and the heisenberg limit in atomic magnetometry. Phys. Rev. Lett. 91, 250801 (2003)

    Article  ADS  Google Scholar 

  33. Wasilewski, W., Jensen, K., Krauter, H., Renema, J.J., Balabas, M.V., Polzik, E.S.: Quantum noise limited and entanglement-assisted magnetometry. Phys. Rev. Lett. 104, 133601 (2010)

    Article  ADS  Google Scholar 

  34. Stockton, J.K., Geremia, J.M., Doherty, A.C., Mabuchi, H.: Robust quantum parameter estimation: coherent magnetometry with feedback. Phys. Rev. A 69, 032109 (2004)

    Article  ADS  Google Scholar 

  35. Kitching, J., Knapper, S., Donley, E.: Atomic sensors—a review. IEEE Sens. J. 11, 1749 (2011)

    Article  ADS  Google Scholar 

  36. Vengalattore, M., Higbie, J.M., Leslie, S.R., Guzman, J., Sadler, L.E., Stamper-Kurn, D.M.: High-resolution magnetometry with a spinor Bose–Einstein condensate. Phys. Rev. Lett. 98, 200801 (2007)

    Article  ADS  Google Scholar 

  37. Maiwald, R., Leibfried, D., Britton, J., Bergquist, J.C., Leuchs, G., Wineland, D.J.: Stylus ion trap for enhanced access and sensing. Nat. Phys. 5, 551 (2009)

    Article  Google Scholar 

  38. Kominis, K., Kornack, T.W., Allred, J.C., Romalis, M.V.: A subfemtotesla multichannel atomic magnetometer. Nature (London) 422, 596 (2003)

    Article  ADS  Google Scholar 

  39. Savukov, I.M., Romalis, M.V.: NMR detection with an atomic magnetometer. Phys. Rev. Lett. 94, 123001 (2005)

    Article  ADS  Google Scholar 

  40. Rondin, L., Tetienne, J.P., Rohart, S., Thiaville, A., Hingant, T., Spinicelli, P., Roch, J.F., Jacques, V.: Nanoscale magnetic field mapping with a single spin scanning probe magnetometer. Appl. Phys. Lett. 100, 153118 (2012)

    Article  ADS  Google Scholar 

  41. Schirhagl, R., Chang, K., Loretz, M., Degen, C.L.: Nitrogen-vacancy centers in diamond: nanoscale sensors for physics and biology. Annu. Rev. Phys. Chem. 65, 83 (2014)

    Article  ADS  Google Scholar 

  42. Troiani, F., Paris, G.A.M.: Universal quantum magnetometry with spin states at equilibrium. Phys. Rev. Lett. 120, 260503 (2018)

    Article  ADS  Google Scholar 

  43. Xie, D., Xu, C., Wang, A.: Quantum metrology in coarsened measurement reference. Phys. Rev. A 95, 012117 (2017)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  45. Hayashi, M.: Asymptotic Theory of Quantum Statistical Inference. World Scientific, Singapore (2005)

    Book  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  47. Vidrighin, M.D., Donati, G., Genoni, M.G., Jin, X.-M., Kolthammer, W.S., Kim, M., Datta, A., Barbieri, M., Walmsley, I.A.: Joint estimation of phase and phase diffusion for quantum metrology. Nat. Commun. 5, 3532 (2014)

    Article  ADS  Google Scholar 

  48. Crowley, P.J., Datta, A., Barbieri, M., Walmsley, I.A.: Tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry. Phys. Rev. A 89, 023845 (2014)

    Article  ADS  Google Scholar 

  49. Jeong, H., Lim, Y., Kim, M.S.: Coarsening measurement references and the quantum-to-classical transition. Phys. Rev. Lett. 112, 010402 (2014)

    Article  ADS  Google Scholar 

  50. Safranek, D., Ahmadi, M., Fuentes, I.: Quantum parameter estimation with imperfect reference frames. New J. Phys. 17, 033012 (2015)

    Article  ADS  Google Scholar 

  51. Ghirardi, L., Siloi, I., Bordone, P., Troiani, F., Matteo, G.A.P.: Quantum metrology at level anticrossing. Phys. Rev. A 97, 012120 (2018)

    Article  ADS  Google Scholar 

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Acknowledgements

This research was supported by the National Natural Science Foundation of China under Grant No. 11747008 and the Guangxi Natural Science Foundation 2016GXNSFBA380227.

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  1. College of Science, Guilin University of Aerospace Technology, Guilin, Guangxi, People’s Republic of China

    Dong Xie & Chunling Xu

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  1. Dong Xie
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Correspondence to Dong Xie.

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Xie, D., Xu, C. Multi-parameter quantum magnetometry with spin states in coarsened measurement reference. Quantum Inf Process 18, 241 (2019). https://doi.org/10.1007/s11128-019-2351-1

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