Coherently enhanced measurements in classical
mechanics

• Authors: Daniel Braun , Sandu Popescu
• Languages of publication: EN

Abstracts

EN

In all quantitative sciences, it is common practice
to increase the signal-to-noise ratio of noisy measurements
by measuring identically prepared systems N
times and averaging the measurement results. This leads
to a scaling of the sensitivity as 1/√N, known in quantum
measurement theory as the “standard quantum limit”
(SQL). It is known that if one puts the N systems into an
entangled state, a scaling as 1/N can be achieved, the socalled
“Heisenberg limit” (HL), but decoherence problems
have so far prevented implementation of such protocols
for large N. Here we show that a method of coherent averaging
inspired by a recent entanglement-free quantum
enhanced measurement protocol is capable of achieving a
sensitivity that scales as 1/N in a purely classical setup.
This may substantially improve the measurement of very
weak interactions in the classical realm, and, in particular,
open a novel route to measuring the gravitational constant
with enhanced precision.

• Publisher: Versita
• Journal: Quantum Measurements and Quantum Metrology
• Year: 2014
• Volume: 2
• Issue: 1

Dates

revised

13 - 6 - 2014

received

16 - 4 - 2014

accepted

3 - 7 - 2014

online

6 - 8 - 2014

Contributors

author

Daniel Braun

• Laboratoire de Physique Théorique, IRSAMC, UMR
  5152 du CNRS, and Université Paul Sabatier, Toulouse, France
  and Institut für Theoretische Physik, Universität Tübingen, Germany

author

Sandu Popescu

• H. H. Wills Physics Laboratory, University of Bristol,
  Tyndall Avenue, Bristol, BS8 1TL, United Kingdom

References

• [1] C. M. Caves, Phys. Rev. D 23, 1693 (1981).
• [2] S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. 72, 3439(1994).
• [3] V. Giovannetti, S. Loyd, and L. Maccone, Science 306, 1330(2004).
• [4] D. Leibfried, M. D. Barrett, T. Schaetz, J. Britton, J. Chiaverini,W. M. Itano, J. D. Jost, C. Langer, and D. J. Wineland, Science304, 1476 (2004).
• [5] V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. Lett. 96,010401 (2006).
• [6] D. Budker and M. Romalis, Nature Physics 3, 227 (2007).[Crossref]
• [7] K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari,K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala,Nature Physics 4, 472 (2008).[Crossref]
• [8] T. Nagata, R. Okamoto, J. L. O’Brien, and K. S. S. Takeuchi,Science 316, 726 (2007).
• [9] B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, andG. J. Pryde, Nature 450, 393 (2007).
• [10] M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A.Bachor, and W. P. Bowen, Biological measurement beyond thequantum limit, arXiv:1206.6928v1.
• [11] A. Luis, Physics Letters A 329, 8 (2004).
• [12] J. Beltrán and A. Luis, Phys. Rev. A 72, 045801 (2005).
• [13] S. M. Roy and S. L. Braunstein, quant-ph/0607152 (2006).
• [14] A. Luis, Phys. Rev. A 76, 035801 (2007).
• [15] A. M. Rey, L. Jiang, and M. D. Lukin, Phys. Rev. A 76, 053617(2007).
• [16] S. Choi and B. Sundaram, Phys. Rev. A 77, 053613 (2008).[Crossref]
• [17] M. Napolitano, M. Koschorreck, B. Dubost, N. Behbood, R. J.Sewell, and M. W. Mitchell, Nature 471, 486 (2011).
• [18] S. Boixo, S. T. Flammia, C. M. Caves, and J. M. Geremia, Phys.Rev. Lett. 98, 090401 (2007).
• [19] S. Boixo, A. Datta, S. T. Flammia, A. Shaji, E. Bagan, and C. M.Caves, Phys. Rev. A 77, 012317 (2008).[Crossref]
• [20] S. Boixo, A. Datta, M. J. Davis, S. T. Flammia, A. Shaji, andC. M. Caves, Phys. Rev. Lett. 101, 040403 (2008).
• [21] M. G. A. Paris, International Journal of Quantum Information 7,125 (2009).
• [22] V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantummetrology, arXiv:1102.2318.
• [23] J. J. . Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen,Phys. Rev. A 54, R4649 (1996).
• [24] H. Lee, P. Kok, and J. P. Dowling, J. Mod. Opt. 49, 2325 (2002).
• [25] S. Massar and E. S. Polzik, Phys. Rev. Lett. 91, 060401 (2003).
• [26] V. Giovannetti, S. Lloyd, and L. Maccone, Nature 412, 417(2001).
• [27] C. A. Santivanez, S. Guha, Z. Dutton, M. Annamalai, M. Vasilyev,B. J. Yen, R. Nair, and J. H. Shapiro (2011), vol. ConfernceProceedings SPIE 8613, (San Diego, CA, USA); Quantum Communicationsand Quantum Imaging IX, eds. Ronald E. Meyers;Yanhua Shih; Keith S. Deacon, pp. 81630Z–81630Z–16.
• [28] M. D’Angelo, M. V. Chekhova, and Y. Shih, Phys. Rev. Lett. 87,013602 (2001).
• [29] S. D. Huver, C. F. Wildfeuer, and J. P. Dowling, Phys. Rev. A 78,063828 (2008).[Crossref]
• [30] T. M. Stace, Quantum limits of thermometry (2010), arXiv:1206.6928v1.
• [31] U. Marzolino and D. Braun, Precision measurements withquantum gases (2013), arXiv:1308.2735.
• [32] J. Huang, S. Wu, H. Zhong, and C. Lee, Quantum metrologywith cold atoms (2013), arXiv:1308.6092.
• [33] O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, and C. Fabre, Phys.Rev. A 85, 010101 (2012).
• [34] T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, andS. Takeuchi, Science 316, 726 (2007).
• [35] K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari,K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala,Nature Physics 4, 472 (2008).[Crossref]
• [36] L. S. C. . T. V. Collaboration", Nature 460, 990 (2009).
• [37] S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B.Plenio, and J. I. Cirac, Phys. Rev. Lett. 79, 3865–3868 (1997).
• [38] J. Kołodynski and R. Demkowicz-Dobrzanski, Phys. Rev. A 82,053804 (2010).
• [39] B. M. Escher, R. L. de Matos Filho, and L. Davidovich, Nat Phys7, 406 (2011).[Crossref]
• [40] T. L. S. Collaboration, Nature Physics 7, 962 (2011).
• [41] T. L. S. Collaboration, Nat. Photon 7, 613 (2013).
• [42] R. Demkowicz-Dobrzanski, K. Banaszek, and R. Schnabel,Phys. Rev. A 88, 041802 (2013).
• [43] A. W. Chin, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 109,233601 (2012).
• [44] D. Braun and J. Martin, Nat. Commun. 2, 223 (2011).
• [45] D. Braun and J. Martin, Decoherence-enhanced measurements(2009), arXiv:0902.1213.
• [46] G. T. Gillies, Reports on Progress in Physics 60, 151 (1997).
• [47] D. J. Kapner, T. S. Cook, E. G. Adelberger, J. H. Gundlach, B. R.Heckel, C. D. Hoyle, and H. E. Swanson, Phys. Rev. Lett. 98,021101 (2007).

Identifiers

DOI

10.2478/qmetro-2014-0003