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  • Letter
  • Open Access

Direct evaluation of measurement uncertainties by feedback compensation of decoherence

Holger F. Hofmann*

  • Graduate School of Advanced Science and Engineering, Hiroshima University, Kagamiyama 1-3-1, Higashi Hiroshima 739-8530, Japan

  • *hofmann@hiroshima-u.ac.jp
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Phys. Rev. Research 3, L012011 – Published 3 February, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012011

Abstract

It is shown that measurement uncertainties can be observed directly by evaluating the feedback compensation of the decoherence induced by the measured system on a probe qubit in a weak interaction occurring between state preparation and measurement. The uncompensated decoherence is described by the measurement uncertainties introduced by Ozawa in Phys. Rev. A 67, 042105 (2003), confirming the empirical validity of measurement theories that combine the initial information of the input state with the additional information provided by each measurement outcome.

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References (30)

  1. W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Phys. 43, 172 (1927).
  2. P. Busch, T. Heinonen, and P. Lahti, Heisenberg's uncertainty principle, Phys. Rep. 452, 155 (2007).
  3. E. Benitez Rodriguez and L. M. Arevalo Aguilar, A survey of the concept of disturbance in quantum mechanics, Entropy 21, 142 (2019).
  4. M. Ozawa, Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement, Phys. Rev. A 67, 042105 (2003).
  5. Y. Watanabe, T. Sagawa, and M. Ueda, Uncertainty relation revisited from quantum estimation theory, Phys. Rev. A 84, 042121 (2011).
  6. P. Busch, P. Lahti, and R. F. Werner, Proof of Heisenberg's Error-Disturbance Relation, Phys. Rev. Lett. 111, 160405 (2013).
  7. J. Dressel and F. Nori, Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance, Phys. Rev. A 89, 022106 (2014).
  8. P. Busch, P. Lahti, and R. F. Werner, Colloquium: Quantum root-mean-square error and measurement uncertainty relations, Rev. Mod. Phys. 86, 1261 (2014).
  9. L. A. Rozema, D. H. Mahler, A. Hayat, and A. M. Steinberg, A note on different definitions of momentum disturbance, Quantum Stud.: Math. Found. 2, 17 (2015).
  10. A. P. Lund and H. M. Wiseman, Measuring measurement-disturbance relationships with weak values, New J. Phys. 12, 093011 (2010).
  11. J. Lee and I. Tsutsuim, Uncertainty relations for approximation and estimation, Phys. Lett. A 380, 2045 (2016).
  12. M. Iinuma, Y. Suzuki, T. Nii, R. Kinoshita, and H. F. Hofmann, Experimental evaluation of nonclassical correlations between measurement outcomes and target observable in a quantum measurement, Phys. Rev. A 93, 032104 (2016).
  13. G. S. Thekkadath, F. Hufnagel, and J. S. Lundeen, Determining complementary properties using weak-measurement: Uncertainty, predictability, and disturbance, New J. Phys. 20, 113034 (2019).
  14. J. Dressel, Weak values as interference phenomena, Phys. Rev. A 91, 032116 (2015).
  15. D. Sokolovski, Weak measurements measure probability amplitudes (and very little else), Phys. Lett. A 380, 1593 (2016).
  16. R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature (London) 490, 77 (2012).
  17. A. Bolund and K. Molmer, Stochastic excitation during the decay of a two-level emitter subject to homodyne and heterodyne detection, Phys. Rev. A 89, 023827 (2014).
  18. A. Soare, H. Ball, D. Hayes, X. Zhen, M. C. Jarratt, J. Sastrawan, H. Uys, and M. J. Biercuk, Experimental bath engineering for quantitative studies of quantum control, Phys. Rev. A 89, 042329 (2014).
  19. H. Wakamura, R. Kawakubo, and T. Koike, State protection by quantum control before and after noise processes, Phys. Rev. A 96, 022325 (2017).
  20. S. Mavadia, V. Frey, J. Sastrawan, S. Dona, and M. J. Biercuk, Prediction and real-time compensation of qubit decoherence via machine learning, Nat. Commun. 8, 14106 (2017).
  21. M. Naghiloo, D. Tan, P. M. Harrington, J. J. Alonso, E. Lutz, A. Romito, and K. W. Murch, Heat and Work Along Individual Trajectories of a Quantum Bit, Phys. Rev. Lett. 124, 110604 (2020).
  22. J. Tollaksen, Pre- and post-selection, weak values, and contextuality, J. Phys. A: Math. Theor. 40, 9033 (2007).
  23. H. F. Hofmann, Contextuality of quantum fluctuations characterized by conditional weak values of entangled states, Phys. Rev. A 102, 062215 (2020).
  24. C. Branciard, Error-tradeoff and error-disturbance relations for incompatible quantum measurements, Proc. Natl. Acad. Sci. U.S.A. 110, 6742 (2013).
  25. M. J. W. Hall, Prior information: How to circumvent the standard joint-measurement uncertainty relation, Phys. Rev. A 69, 052113 (2004).
  26. J. M. Renes, V. B. Scholz, and S. Huber, Uncertainty relations: An operational approach to the error-disturbance trade-off, Quantum 1, 20 (2017).
  27. J. Erhart, S. Sponar, G. Sulyok, G. Badurek, M. Ozawa, and Y. Hasegawa, Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin measurements, Nat. Phys. 8, 185 (2012).
  28. F. Kaneda, S.-Y. Baek, M. Ozawa, and K. Edamatsu, Experimental Test of Error-Disturbance Uncertainty Relations by Weak Measurement, Phys. Rev. Lett. 112, 020402 (2014).
  29. G. Sulyok and S. Sponar, Heisenberg's error-disturbance uncertainty relation: Experimental study of competing approaches, Phys. Rev. A 96, 022137 (2017).
  30. H. F. Hofmann, Uncertainty limits for quantum metrology obtained from the statistics of weak measurements, Phys. Rev. A 83, 022106 (2011).

Outline

Information

Phys. Rev. Research 3, L012011– Published 3 February, 2021
  • Received 23 June 2020
  • Revised 15 November 2020
  • Accepted 25 January 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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