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Quantum Fisher Information of Decohered W and GHZ Superposition States with Arbitrary Relative Phase

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Abstract

Quantum Fisher Information (QFI) is a very useful concept for analyzing situations that require phase sensitivity. It become a popular topic especially in Quantum Metrology domain. In this work, we study the changes in quantum Fisher information (QFI) values for one relative arbitrary phased quantum system consisting of a superposition of N Qubits W and GHZ states. In a recent work (Ozaydin et al. Int. J. Theor. Phys. 52, 2977, 2013), QFI values of this mentioned system for N qubits were studied. In this work, we extend this problem for the changes of QFI values in some noisy channels for the studied system. We show the changes in QFI depending on noise parameters. We report interesting results for different type of decoherence channels. We show the general case results for this problem.

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References

  1. Erol, V.: Quantum Fisher Information of W and GHZ state superposition under decoherence. Preprints 2017, 2017040147 (10.20944/preprints201704.0147.v1) (2017)

  2. Ji, Z., et al.: Parameter estimation of quantum channels. IEEE Trans. Inf. Theory 54(5172), 5172–5185 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  4. Yi, X., Huang, G., Wang, J.: Quantum fisher information of a 3-qubit state. Int. J. Theor. Phys. 51, 3458 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Spagnolo, N., et al.: Quantum interferometry with three-dimensional geometry. Nat. Sci Rep. 2(862) (2010)

  6. Liu, Z.: Spin squeezing in superposition of four-Kübit symmetric state and W states. Int. J. Theor. Phys. 52, 820 (2013)

    Article  ADS  MATH  Google Scholar 

  7. Ozaydin, F., Altintas, A.A., Bugu, S., Yesilyurt, C.: Quantum fisher information of N particles in the superposition of W and GHZ states. Int. J. Theor. Phys. 52, 2977 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ozaydin, F., Altintas, A.A., Bugu, S., Yesilyurt, C., Arik, M.: Quantum fisher information of several qubits in the superposition of a GHZ and two W states with arbitrary relative phase. Int. J. Theor. Phys. 53, 3259 (2014)

    Article  MATH  Google Scholar 

  9. Gibilisco, P., Imparato, D., Isola, T.: Uncertainty principle and Quantum Fisher Information. J. Math. Phys. 48(072109) (2007)

  10. Andai, A.: Uncertainty principle with Quantum Fisher Information. J. Math. Phys. 49(012106) (2008)

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

  12. Toth, et al.: Spin squeezing and entanglement. Phys. Rev. A 79(042334) (2009)

  13. Ozaydin, F., Altintas, A.A., Bugu, S., Yesilyurt, C.: Behavior of Quantum Fisher Information of bell pairs under decoherence channels. Acta Phys. Pol. A 125(2), 606 (2014)

    Article  Google Scholar 

  14. Ang, S.Z., Harris, G.I., Bowen, W.P., Tsang, M.: Optomechanical parameter estimation. New J. Phys. 15(103028) (2013)

  15. Iwasawa, K., et al.: Quantum-limited mirror-motion estimation. Phys. Rev. Lett. 111(163602) (2013)

  16. Tsang, M.: Quantum metrology with open dynamical systems. New J. Phys. 15(073005) (2013)

  17. Tsang, M., Ranjith, N.: Fundamental quantum limits to waveform detection. Phys. Rev. A 86(042115) (2012)

  18. Tsang, M.: Ziv-Zakai error bounds for quantum parameter estimation. Phys. Rev. Lett. 108(230401) (2012)

  19. Tsang, M., Wiseman, H.M., Caves, C.M.: Fundamental quantum limit to waveform estimation. In: IEEE Conference on Lasers and Electro-Optics (CLEO) (2011)

  20. Tsang, M., Shapiro, J.H., Lloyd, S.: Quantum optical temporal phase estimation by homodyne phase-locked loops. In: IEEE Conference on Lasers and Electro-Optics (CLEO) (2009)

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

    Article  ADS  MATH  Google Scholar 

  22. Erol, V., Ozaydin, F., Altintas, A.A.: Analysis of entanglement measures and locc maximized quantum fisher information of general two qubit systems. Sci. Rep. 4, 5422 (2014)

    Article  ADS  Google Scholar 

  23. Ozaydin, F., Altintas, A.A., Yesilyurt, C., Bugu, S., Erol, V.: Quantum Fisher Information of bipartitions of W states. Acta Phys. Pol. A 127, 1233–1235 (2015)

    Article  Google Scholar 

  24. Erol, V., Bugu, S., Ozaydin, F., Altintas, A.A.: An analysis of concurrence entanglement measure and quantum fisher information of quantum communication networks of two-qubits. In: Proceedings of IEEE 22nd Signal Processing and Communications Applications Conference (SIU2014), pp. 317–320 (2014)

  25. Erol, V.: A comparative study of concurrence and negativity of general three-level quantum systems of two particles. AIP Conf. Proc. 1653(020037) (2015)

    Google Scholar 

  26. Erol, V., Ozaydin, F., Altintas, A.A.: Analysis of negativity and relative entropy of entanglement measures for qubit-qutrit quantum communication systems. In: Proceedings of IEEE 23rd Signal Processing and Communications Applications Conference (SIU2015), pp. 116–119 (2014)

  27. Erol, V.: Detecting violation of bell inequalities using LOCC maximized Quantum Fisher Information and entanglement measures, Preprints 2017, 2017030223 (doi:10.20944/preprints201703.0223.v1) (2017)

  28. Erol, V.: Analysis of negativity and relative entropy of entanglement measures for two qutrit Quantum Communication Systems, Preprints 2017, 2017030217 (doi:10.20944/preprints201703.0217.v1) (2017)

  29. Erol, V.: The relation between majorization theory and quantum information from entanglement monotones perspective. AIP Conf. Proc. 1727(020007) (2016)

  30. Erol, V.: A proposal for Quantum Fisher Information optimization and its relation with entanglement measures, PhD Thesis, Okan University, Institute of Science (2015)

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

    Article  ADS  Google Scholar 

  32. Altintas, A.A.: Quantum Fisher Information of an open and noisy system in the steady state. Ann. Phys. 362, 192–198 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  33. Ozaydin, F.: Quantum Fisher Information of a 3 × 3 bound entangled state and its relation with geometric discord. Int. J. Theor. Phys. 54 (9), 3304–3310 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  34. Frieden, B.R., Gatenby, R.A.: Exploratory Data Analysis Using Fisher Information. Springer, Arizona (2007)

    Book  MATH  Google Scholar 

  35. Pezze, L., Smerzi, A.: Entanglement, nonlinear dynamics, and the Heisenberg limit. Phys. Rev. Lett. 102(100401) (2009)

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

  37. Hyllus, P., Gühne, O., Smerzi, A.: Not all pure entangled states are useful for sub-shot-noise interferometry. Phys. Rev. A 82(012337) (2010)

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  40. Xiong, H.N., Ma, J., Liu, W.F., Wang, X.: Quantum Fisher Information for Superpositions of Spin States. Quantum Inf. Comput. 10(5&6) (2010)

  41. Jozsa, R., Abrams, D. S., Dowling, J. P., Williams, C. P.: Quantum clock synchronization based on shared prior entanglement. Phys. Rev. Lett. 85(2010) (2000)

  42. Bollinger, J.J., Itano, W.M., Wineland, D.J., Heinzen, D.J.: Optimal frequency measurements with maximally correlated states. Phys. Rev. A 54(R 4649) (1996)

  43. Erol, V.: Quantum Fisher Information: Theory and Applications. Preprints 2017, 2017040134 (doi:10.20944/preprints201704.0134.v1) (2017)

  44. Erol, V.: Entanglement Monotones and Measures: An Overview. Preprints 2017, 2017040098 (doi:10.20944/preprints201704.0098.v3) (2017)

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  1. Computer Engineering Department, Okan University, Istanbul, Turkey

    Volkan Erol

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  1. Volkan Erol
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Erol, V. Quantum Fisher Information of Decohered W and GHZ Superposition States with Arbitrary Relative Phase. Int J Theor Phys 56, 3202–3208 (2017). https://doi.org/10.1007/s10773-017-3487-3

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  • DOI: https://doi.org/10.1007/s10773-017-3487-3

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