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Characterization of classical static noise via qubit as probe

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Abstract

The dynamics of quantum Fisher information (QFI) of a single qubit coupled to classical static noise is investigated. The analytical relation for QFI fixes the optimal initial state of the qubit that maximizes it. An approximate limit for the time of coupling that leads to physically useful results is identified. Moreover, using the approach of quantum estimation theory and the analytical relation for QFI, the qubit is used as a probe to precisely estimate the disordered parameter of the environment. Relation for optimal interaction time with the environment is obtained, and condition for the optimal measurement of the noise parameter of the environment is given. It is shown that all values, in the mentioned range, of the noise parameter are estimable with equal precision. A comparison of our results with the previous studies in different classical environments is made.

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References

  1. Beneti, G., Casati, G., Strini, G.: Principles of Quantum Computation and Information. World Scientific Publishing, Toh Tuck Link (2005)

    Google Scholar 

  2. Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)

    Article  ADS  Google Scholar 

  3. Khan, S.: Generation and sudden death of entanglement in qubit-qutrit systems with depolarising noise. Math. Struct. Comput. Sci. 23, 1220 (2013)

    Article  MATH  Google Scholar 

  4. Sharma, K.K., Awasthi, S.K., Pandey, S.N.: Entanglement sudden death and birth in qubit-qutrit systems under Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 12, 3437–3447 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Khan, S., Khan, M.K.: Nondistillability of distillable qutrit–qutrit states under depolarising noise. J. Mod. Opt. 58, 918–923 (2011)

    Article  ADS  Google Scholar 

  6. Neder, I., Rudner, M.S., Bluhm, H., Foletti, S., Halperin, B.I., Yacoby, A.: Semiclassical model for the dephasing of a two-electron spin qubit coupled to a coherently evolving nuclear spin bath. Phys. Rev. B 84, 035441 (2011)

    Article  ADS  Google Scholar 

  7. Biercuck, M.J., Bluhm, H.: Phenomenological study of decoherence in solid-state spin qubits due to nuclear spin diffusion. Phys. Rev. B 83, 235316 (2011)

    Article  ADS  Google Scholar 

  8. Neng, G.Y., Fa, F.M., Xiang, L., Yuan, Y.B.: Dynamics of quantum discord in a two-qubit system under classical noise. Chin. Phys. B 23, 034204 (2014)

    Article  ADS  Google Scholar 

  9. Crow, D., Joynt, R.: Classical simulation of quantum dephasing and depolarizing noise. Phys. Rev. A 89, 042123 (2014)

    Article  ADS  Google Scholar 

  10. Witzel, W.M., Young, K., Sarma, S.D.: Converting a real quantum spin bath to an effective classical noise acting on a central spin. Phys. Rev. B 90, 115431 (2014)

    Article  ADS  Google Scholar 

  11. Yu, T., Eberly, J.H.: Entanglement evolution in a non-Markovian environment. Opt. Commun. 283, 676–680 (2010)

    Article  ADS  Google Scholar 

  12. Li, J.Q., Liang, J.Q.: Quantum and classical correlations in a classical dephasing environment. Phys. Lett. A 375, 1496–1503 (2011)

    Article  ADS  MATH  Google Scholar 

  13. Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.A.: Dynamics of quantum correlations in colored-noise environments. Phys. Rev. A 87, 052328 (2013)

    Article  ADS  Google Scholar 

  14. Javed, M., Khan, S., Ullah, S.A.: The dynamics of quantum correlations in mixed classical environments. J. Rus. Laser Res. 37, 562–571 (2016)

    Article  Google Scholar 

  15. Bylander, J., Gustavsson, S., Yan, F., Yoshihara, F., Harrabi, K., Fitch, G., Cory, D.G., Nakamura, Y., Tsai, J.S., Oliver, W.D.: Noise spectroscopy through dynamical decoupling with a superconducting flux qubit. Nat. Phys. 7, 565–570 (2011)

    Article  Google Scholar 

  16. Zhang, J., Peng, X., Rajendran, N., Suter, D.: Effect of system level structure and spectral distribution of the environment on the decoherence rate. Phys. Rev. A 75, 042314 (2007)

    Article  ADS  Google Scholar 

  17. Alvarez, G.A., Suter, D.: Measuring the spectrum of colored noise by dynamical decoupling. Phys. Rev. Lett. 107, 230501 (2011)

    Article  ADS  Google Scholar 

  18. Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.A.: Quantum probes for the spectral properties of a classical environment. Phys. Rev. A 89, 032114 (2014)

    Article  ADS  Google Scholar 

  19. Almog, I., Sagi, Y., Gordon, G., Bensky, G., Kurizki, G., Davidson, N.: Direct measurement of the system-environment coupling as a tool for understanding decoherence and dynamical decoupling. J. Phys. B 44, 154006 (2011)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  22. Pairs, M.G.A.: Quantum estimation for quantum technology. Int. J. Quantum Inf. 7, 125–137 (2009)

    Article  Google Scholar 

  23. Escher, B.M., de Matos Fillo, 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 

  24. Joo, J., Munro, W.J., Spiller, T.P.: Quantum metrology with entangled coherent states. Phys. Rev. Lett. 107, 083601 (2011)

    Article  ADS  Google Scholar 

  25. Dobrzanski, R.D., Kolodynski, J., Guta, M.: The elusive Heisenberg limit in quantum-enhanced metrology. Nat. Commun. 3, 1063 (2012)

    Article  Google Scholar 

  26. Shaji, A., Caves, C.M.: Qubit metrology and decoherence. Phys. Rev. A 76, 032111 (2007)

    Article  ADS  Google Scholar 

  27. Benedetti, C., Shurupov, A.P., Paris, M.G.A., Brida, G., Genovese, M.: Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations. Phys. Rev. A 87, 052136 (2013)

    Article  ADS  Google Scholar 

  28. Blandino, R., Genoni, M.G., Etesse, J., Barbieri, M., Paris, M.G.A., Grangier, P., Brouri, R.T.: Homodyne estimation of Gaussian quantum discord. Phys. Rev. Lett. 109, 180402 (2012)

    Article  ADS  Google Scholar 

  29. Durkin, G.A.: Preferred measurements: optimality and stability in quantum parameter estimation. New J. Phys. 12, 023010 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Spagnolo, N., Vitelli, C., Lucivero, V.G., Giovannetti, V., Maccone, L., Sciarrino, F.: Phase estimation via quantum interferometry for noisy detectors. Phys. Rev. Lett. 108, 233602 (2012)

    Article  ADS  Google Scholar 

  31. Monras, A.: Optimal phase measurements with pure Gaussian states. Phys. Rev. A 73, 033821 (2006)

    Article  ADS  Google Scholar 

  32. Benedetti, C., Paris, M.G.A.: Characterization of classical Gaussian processes using quantum probes. Phys. Lett. A 378, 2495–2500 (2014)

    Article  ADS  MATH  Google Scholar 

  33. Hotta, M., Karasawa, T., Ozawa, M.: Ancilla-assisted enhancement of channel estimation for low-noise parameters. Phys. Rev. A 72, 052334 (2005)

    Article  ADS  Google Scholar 

  34. Monras, A., Paris, M.G.A.: Optimal quantum estimation of loss in bosonic channels. Phys. Rev. Lett. 98, 160401 (2007)

    Article  ADS  Google Scholar 

  35. Fujiwara, A.: Quantum channel identification problem. Phys. Rev. A 63, 042304 (2001)

    Article  ADS  Google Scholar 

  36. Fujiwara, A., Imai, H.: Quantum parameter estimation of a generalized Pauli channel. J. Phys. A 36, 8093 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Ji, Z., Wang, G., Duan, R., Feng, Y., Ying, M.: Parameter estimation of quantum channels. IEEE Trans. Inf. Theory 54, 5172–5185 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  38. D’Auria, V., de Lisio, C., Porzio, A., Solimeno, S., Paris, M.G.A.: Transmittivity measurements by means of squeezed vacuum light. J. Phys. B 39, 1187–1198 (2006)

    Article  ADS  Google Scholar 

  39. Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23, 357–362 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  40. 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 

  41. Lu, X.M., Wang, X.G., Sun, C.P.: Quantum Fisher information flow and non-Markovian processes of open systems. Phys. Rev. A 82, 042103 (2010)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  43. Paris, M.G.A.: Quantum probes for fractional Gaussian processes. Phys. A 413, 256–265 (2014)

    Article  MathSciNet  Google Scholar 

  44. Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.A.: Effects of classical environmental noise on entanglement and quantum discord. Int. J. Quantum Inform. 10, 1241005 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Thompson, C., Vemuri, G., Agarwal, G.S.: Anderson localization with second quantized fields in a coupled array of waveguides. Phys. Rev. A 82, 053805 (2010)

    Article  ADS  Google Scholar 

  46. Tchoffo, M., Kenfack, L.T., Fouokeng, G.C., Fai, L.C.: Quantum correlations dynamics and decoherence of a three-qubit system subject to classical environmental noise. Eur. Phys. J. Plus 131, 380 (2016)

    Article  Google Scholar 

  47. Hao, X.N., Hou, J.C., Li, J.Q.: Dynamics of quantum correlation for a qubit-qutrit system in the presence of the dephasing environments. Quantum Inf. Process. 15, 2819–2838 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Oppenheim, A.V., Verghese, G.C.: Signals, Systems and Inference, p. 0133944212. Pearson Education, London (2015)

    Google Scholar 

  49. Didenko V.I., Ivanov, A.V.: Distribution laws of quantization noise for sigma-delta modulator. In: Proceedings of the 16th IMECO TC4 Symposium and 13th Workshop on ADC Modelling and Testing, Florence, Italy, pp. 995–1000 (2008)

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

    Article  ADS  Google Scholar 

  51. Dittmann, J.: Explicit formulae for the Bures metric. J. Phys. A 32, 2663–2670 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, COMSATS Institute of Information Technology, Park road, Islamabad, 45550, Pakistan

    Salman Khan

  2. Department of Physics, University of Malakand, Chakdara Dir, Pakistan

    Muhammad Javed & Sayed Arif Ullah

Authors
  1. Muhammad Javed
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  2. Salman Khan
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  3. Sayed Arif Ullah
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Correspondence to Salman Khan.

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Javed, M., Khan, S. & Ullah, S.A. Characterization of classical static noise via qubit as probe. Quantum Inf Process 17, 53 (2018). https://doi.org/10.1007/s11128-018-1817-x

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