Weakly invasive metrology: quantum advantage and physical implementations

M. Perarnau-Llobet; D. Malz; J. I. Cirac

doi:10.22331/q-2021-04-28-446

Weakly invasive metrology: quantum advantage and physical implementations

M. Perarnau-Llobet^1,2,3, D. Malz^1,2, and J. I. Cirac^1,2

¹Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany.
²Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München
³Département de Physique Appliquée, Université de Genève, Genève, Switzerland

Published:	2021-04-28, volume 5, page 446
Eprint:	arXiv:2006.12114v4
Doi:	https://doi.org/10.22331/q-2021-04-28-446
Citation:	Quantum 5, 446 (2021).

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Abstract

We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons $N_{\rm abs}$ are absorbed, for a total time $T$. The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with $N_{\rm abs}$ and $T$, whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of $N_{\rm abs}$ and $T$, as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.

Featured image: Two interacting cavities are individually coupled to two atomic arrays, which are used to prepare and measure quantum states of light in the cavities.

► BibTeX data

@article{PerarnauLlobet2021weaklyinvasive,
  doi = {10.22331/q-2021-04-28-446},
  url = {https://doi.org/10.22331/q-2021-04-28-446},
  title = {Weakly invasive metrology: quantum advantage and physical implementations},
  author = {Perarnau-Llobet, M. and Malz, D. and Cirac, J. I.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {446},
  month = apr,
  year = {2021}
}

► References

[1] V. Giovannetti, S. Lloyd, and L. Maccone, Nature Photonics 5, 222 (2011).
https://doi.org/10.1038/nphoton.2011.35

[2] G. Tóth and I. Apellaniz, Journal of Physics A: Mathematical and Theoretical 47, 424006 (2014).
https://doi.org/10.1088/1751-8113/47/42/424006

[3] R. Demkowicz-Dobrzański, M. Jarzyna, and J. Kołodyński, in Progress in Optics (Elsevier, 2015) pp. 345–435.
https://doi.org/10.1016/bs.po.2015.02.003

[4] J. P. Dowling and K. P. Seshadreesan, Journal of Lightwave Technology 33, 2359 (2015).
https://doi.org/10.1109/jlt.2014.2386795

[5] E. Polino, M. Valeri, N. Spagnolo, and F. Sciarrino, AVS Quantum Science 2, 024703 (2020).
https://doi.org/10.1116/5.0007577

[6] C. M. Caves, Phys. Rev. D 23, 1693 (1981).
https://doi.org/10.1103/PhysRevD.23.1693

[7] M. J. Holland and K. Burnett, Phys. Rev. Lett. 71, 1355 (1993).
https://doi.org/10.1103/PhysRevLett.71.1355

[8] J. J. . Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).
https://doi.org/10.1103/PhysRevA.54.R4649

[9] K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, Biophysical Journal 77, 2856 (1999).
https://doi.org/10.1016/s0006-3495(99)77117-1

[10] E. J. Peterman, F. Gittes, and C. F. Schmidt, Biophysical Journal 84, 1308 (2003).
https://doi.org/10.1016/s0006-3495(03)74946-7

[11] R. Cole, Cell Adhesion & Migration 8, 452 (2014).
https://doi.org/10.4161/cam.28348

[12] M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, Nature Photonics 7, 229 (2013).
https://doi.org/10.1038/nphoton.2012.346

[13] M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, Phys. Rev. X 4, 011017 (2014).
https://doi.org/10.1103/PhysRevX.4.011017

[14] M. A. Taylor and W. P. Bowen, Physics Reports 615, 1 (2016).
https://doi.org/10.1016/j.physrep.2015.12.002

[15] R. Whittaker, C. Erven, A. Neville, M. Berry, J. L. O'Brien, H. Cable, and J. C. F. Matthews, New Journal of Physics 19, 023013 (2017).
https://doi.org/10.1088/1367-2630/aa5512

[16] M. Pototschnig, Y. Chassagneux, J. Hwang, G. Zumofen, A. Renn, and V. Sandoghdar, Phys. Rev. Lett. 107, 063001 (2011).
https://doi.org/10.1103/PhysRevLett.107.063001

[17] K. Eckert, O. Romero-Isart, M. Rodriguez, M. Lewenstein, E. S. Polzik, and A. Sanpera, Nature Physics 4, 50 (2007).
https://doi.org/10.1038/nphys776

[18] F. Wolfgramm, C. Vitelli, F. A. Beduini, N. Godbout, and M. W. Mitchell, Nature Photonics 7, 28 (2012).
https://doi.org/10.1038/nphoton.2012.300

[19] T. Ono, R. Okamoto, and S. Takeuchi, Nature Communications 4 (2013), 10.1038/ncomms3426.
https://doi.org/10.1038/ncomms3426

[20] S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Phys. Rev. Lett. 79, 3865 (1997).
https://doi.org/10.1103/PhysRevLett.79.3865

[21] A. Shaji and C. M. Caves, Phys. Rev. A 76, 032111 (2007).
https://doi.org/10.1103/PhysRevA.76.032111

[22] A. J. Hayes, S. Dooley, W. J. Munro, K. Nemoto, and J. Dunningham, Quantum Science and Technology 3, 035007 (2018).
https://doi.org/10.1088/2058-9565/aac30b

[23] Y. Matsuzaki, S. C. Benjamin, and J. Fitzsimons, Phys. Rev. A 84, 012103 (2011).
https://doi.org/10.1103/PhysRevA.84.012103

[24] A. W. Chin, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 109, 233601 (2012).
https://doi.org/10.1103/PhysRevLett.109.233601

[25] R. Chaves, J. B. Brask, M. Markiewicz, J. Kołodyński, and A. Acín, Phys. Rev. Lett. 111, 120401 (2013).
https://doi.org/10.1103/PhysRevLett.111.120401

[26] J. B. Brask, R. Chaves, and J. Kołodyński, Phys. Rev. X 5, 031010 (2015).
https://doi.org/10.1103/PhysRevX.5.031010

[27] A. Smirne, J. Kołodyński, S. F. Huelga, and R. Demkowicz-Dobrzański, Phys. Rev. Lett. 116, 120801 (2016).
https://doi.org/10.1103/PhysRevLett.116.120801

[28] M. J. Woolley, G. J. Milburn, and C. M. Caves, New Journal of Physics 10, 125018 (2008).
https://doi.org/10.1088/1367-2630/10/12/125018

[29] M. Beau and A. del Campo, Phys. Rev. Lett. 119, 010403 (2017).
https://doi.org/10.1103/PhysRevLett.119.010403

[30] M. Naghiloo, A. N. Jordan, and K. W. Murch, Phys. Rev. Lett. 119, 180801 (2017).
https://doi.org/10.1103/PhysRevLett.119.180801

[31] S. Pang and A. N. Jordan, Nature Communications 8 (2017), 10.1038/ncomms14695.
https://doi.org/10.1038/ncomms14695

[32] L. Sun, X. He, C. You, C. Lv, B. Li, S. Lloyd, and X. Wang, arXiv preprint arXiv:2004.01216 (2020).
arXiv:2004.01216

[33] U. Dorner, New Journal of Physics 14, 043011 (2012).
https://doi.org/10.1088/1367-2630/14/4/043011

[34] W. Dür, M. Skotiniotis, F. Fröwis, and B. Kraus, Phys. Rev. Lett. 112, 080801 (2014).
https://doi.org/10.1103/PhysRevLett.112.080801

[35] E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin, Phys. Rev. Lett. 112, 150802 (2014).
https://doi.org/10.1103/PhysRevLett.112.150802

[36] G. Arrad, Y. Vinkler, D. Aharonov, and A. Retzker, Phys. Rev. Lett. 112, 150801 (2014).
https://doi.org/10.1103/PhysRevLett.112.150801

[37] B. Escher, R. de Matos Filho, and L. Davidovich, Nature Physics 7, 406 (2011).
https://doi.org/10.1038/nphys1958
https://www.nature.com/articles/nphys1958

[38] R. Demkowicz-Dobrzański, J. Kołodyński, and M. Guţă, Nature Communications 3 (2012), 10.1038/ncomms2067.
https://doi.org/10.1038/ncomms2067

[39] J. Kołodyński and R. Demkowicz-Dobrzański, New Journal of Physics 15, 073043 (2013).
https://doi.org/10.1088/1367-2630/15/7/073043

[40] S. I. Knysh, E. H. Chen, and G. A. Durkin, arXiv preprint arXiv:1402.0495 (2014).
arXiv:1402.0495

[41] S. Haroche and J.-M. Raimond, Exploring the Quantum, Vol. 5 (Oxford University Press, 2006) p. 11.
https://doi.org/10.1093/acprof:oso/9780198509141.001.0001

[42] A. Blais, S. M. Girvin, and W. D. Oliver, Nature Physics 16, 247 (2020).
https://doi.org/10.1038/s41567-020-0806-z

[43] R. H. Dicke, Phys. Rev. 93, 99 (1954).
https://doi.org/10.1103/physrev.93.99

[44] F. Haas, J. Volz, R. Gehr, J. Reichel, and J. Esteve, Science 344, 180 (2014).
https://doi.org/10.1126/science.1248905

[45] M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, Science Advances 2, e1601231 (2016).
https://doi.org/10.1126/sciadv.1601231

[46] M. Hosseini, Y. Duan, K. M. Beck, Y.-T. Chen, and V. Vuletić, Phys. Rev. Lett. 118, 183601 (2017).
https://doi.org/10.1103/PhysRevLett.118.183601

[47] J. Kim, D. Yang, S.-h. Oh, and K. An, Science 359, 662 (2018).
https://doi.org/10.1126/science.aar2179

[48] A. Frisk Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Nature Reviews Physics 1, 19 (2019), arXiv:1807.11636.
https://doi.org/10.1038/s42254-018-0006-2
arXiv:1807.11636

[49] J. A. Mlynek, A. A. Abdumalikov, C. Eichler, and A. Wallraff, Nat. Commun. 5, 5186 (2014).
https://doi.org/10.1038/ncomms6186

[50] A. Goban, C.-L. Hung, J. Hood, S.-P. Yu, J. Muniz, O. Painter, and H. Kimble, Phys. Rev. Lett. 115, 063601 (2015).
https://doi.org/10.1103/physrevlett.115.063601

[51] P. Solano, P. Barberis-Blostein, F. K. Fatemi, L. A. Orozco, and S. L. Rolston, Nature Communications 8, 1857 (2017).
https://doi.org/10.1038/s41467-017-01994-3

[52] J. L. O'Brien, A. Furusawa, and J. Vučković, Nature Photonics 3, 687 (2009).
https://doi.org/10.1038/nphoton.2009.229

[53] A. González-Tudela, V. Paulisch, H. J. Kimble, and J. I. Cirac, Phys. Rev. Lett. 118, 213601 (2017).
https://doi.org/10.1103/PhysRevLett.118.213601

[54] V. Paulisch, H. J. Kimble, J. I. Cirac, and A. González-Tudela, Phys. Rev. A 97, 053831 (2018).
https://doi.org/10.1103/PhysRevA.97.053831

[55] M. Uria, P. Solano, and C. Hermann-Avigliano, Phys. Rev. Lett. 125, 093603 (2020).
https://doi.org/10.1103/PhysRevLett.125.093603

[56] C. Groiseau, A. E. Elliott, S. J. Masson, and S. Parkins, arXiv preprint arXiv:2012.00246 (2020).
arXiv:2012.00246

[57] G. Romero, J. J. García-Ripoll, and E. Solano, Physical Review Letters 102, 173602 (2009).
https://doi.org/10.1103/PhysRevLett.102.173602

[58] B. Peropadre, G. Romero, G. Johansson, C. M. Wilson, E. Solano, and J. J. García-Ripoll, Physical Review A 84, 063834 (2011).
https://doi.org/10.1103/PhysRevA.84.063834

[59] D. Malz and J. I. Cirac, Phys. Rev. Research 2, 033091 (2020).
https://doi.org/10.1103/PhysRevResearch.2.033091

[60] V. Paulisch, M. Perarnau-Llobet, A. González-Tudela, and J. I. Cirac, Physical Review A 99, 043807 (2019a).
https://doi.org/10.1103/PhysRevA.99.043807

[61] M. Perarnau-Llobet, A. González-Tudela, and J. I. Cirac, Quantum Science and Technology 5, 025003 (2020).
https://doi.org/10.1088/2058-9565/ab6ce5

[62] C. W. Helstrom, Quantum Detection and Estimation Theory (Elsevier Science, 1976).
http://www.ebook.de/de/product/15210504/quantum_detection_and_estimation_theory.html

[63] A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (Statistics & Probability) (English and Russian Edition) (Elsevier Science, 1982).
https://www.amazon.com/Probabilistic-Statistical-Aspects-Statistics-Probability/dp/0444863338?SubscriptionId=0JYN1NVW651KCA56C102&tag=techkie-20&linkCode=xm2&camp=2025&creative=165953&creativeASIN=0444863338

[64] S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. 72, 3439 (1994).
https://doi.org/10.1103/PhysRevLett.72.3439

[65] A. Fujiwara and H. Imai, Journal of Physics A: Mathematical and Theoretical 41, 255304 (2008).
https://doi.org/10.1088/1751-8113/41/25/255304

[66] S. Knysh, V. N. Smelyanskiy, and G. A. Durkin, Phys. Rev. A 83, 021804 (2011).
https://doi.org/10.1103/PhysRevA.83.021804

[67] R. A. Campos, C. C. Gerry, and A. Benmoussa, Phys. Rev. A 68, 023810 (2003).
https://doi.org/10.1103/physreva.68.023810

[68] A. Datta, L. Zhang, N. Thomas-Peter, U. Dorner, B. J. Smith, and I. A. Walmsley, Phys. Rev. A 83, 063836 (2011).
https://doi.org/10.1103/PhysRevA.83.063836

[69] M. G. A. Paris, International Journal of Quantum Information 07, 125 (2009).
https://doi.org/10.1142/s0219749909004839

[70] T. Kim, O. Pfister, M. J. Holland, J. Noh, and J. L. Hall, Phys. Rev. A 57, 4004 (1998).
https://doi.org/10.1103/PhysRevA.57.4004

[71] L. Pezzé and A. Smerzi, Phys. Rev. Lett. 110, 163604 (2013).
https://doi.org/10.1103/PhysRevLett.110.163604

[72] W. Zhong, Y. Huang, X. Wang, and S.-L. Zhu, Phys. Rev. A 95, 052304 (2017).
https://doi.org/10.1103/PhysRevA.95.052304

[73] B. Yurke, S. L. McCall, and J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
https://doi.org/10.1103/PhysRevA.33.4033

[74] S. Olivares and M. G. A. Paris, Optics and Spectroscopy 103, 231 (2007).
https://doi.org/10.1134/S0030400X07080103

[75] D. Šafránek and I. Fuentes, Phys. Rev. A 94, 062313 (2016).
https://doi.org/10.1103/PhysRevA.94.062313

[76] S. D. Huver, C. F. Wildfeuer, and J. P. Dowling, Phys. Rev. A 78, 063828 (2008).
https://doi.org/10.1103/PhysRevA.78.063828

[77] U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, Phys. Rev. Lett. 102, 040403 (2009).
https://doi.org/10.1103/PhysRevLett.102.040403

[78] R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, Phys. Rev. A 80, 013825 (2009).
https://doi.org/10.1103/PhysRevA.80.013825

[79] H. Cable and G. A. Durkin, Phys. Rev. Lett. 105, 013603 (2010).
https://doi.org/10.1103/PhysRevLett.105.013603

[80] J. Calsamiglia, B. Gendra, R. Muñoz-Tapia, and E. Bagan, New Journal of Physics 18, 103049 (2016).
https://doi.org/10.1088/1367-2630/18/10/103049

[81] T. Matsubara, P. Facchi, V. Giovannetti, and K. Yuasa, New Journal of Physics 21, 033014 (2019).
https://doi.org/10.1088/1367-2630/ab0604

[82] F. Wolf, C. Shi, J. C. Heip, M. Gessner, L. Pezzè, A. Smerzi, M. Schulte, K. Hammerer, and P. O. Schmidt, Nature Communications 10 (2019), 10.1038/s41467-019-10576-4.
https://doi.org/10.1038/s41467-019-10576-4

[83] V. Paulisch, M. Perarnau-Llobet, A. González-Tudela, and J. I. Cirac, Phys. Rev. A 99, 043807 (2019b).
https://doi.org/10.1103/PhysRevA.99.043807

[84] H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, Reports on Progress in Physics 69, 1325 (2006).
https://doi.org/10.1088/0034-4885/69/5/R02

[85] M. Hennrich, T. Legero, A. Kuhn, and G. Rempe, Physical Review Letters 85, 4872 (2000).
https://doi.org/10.1103/PhysRevLett.85.4872

[86] F. Mivehvar, F. Piazza, T. Donner, and H. Ritsch, (2021), arXiv:2102.04473.
arXiv:2102.04473

[87] H. Zhang, R. McConnell, S. Ć uk, Q. Lin, M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, Physical Review Letters 109, 133603 (2012).
https://doi.org/10.1103/PhysRevLett.109.133603

[88] D. B. Hume, I. Stroescu, M. Joos, W. Muessel, H. Strobel, and M. K. Oberthaler, Physical Review Letters 111, 253001 (2013), arXiv:1307.7598.
https://doi.org/10.1103/PhysRevLett.111.253001
arXiv:1307.7598

[89] E. Jeffrey, D. Sank, J. Y. Mutus, T. C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P. J. J. O'Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, and J. M. Martinis, Physical Review Letters 112, 190504 (2014).
https://doi.org/10.1103/PhysRevLett.112.190504

[90] T. Walter, P. Kurpiers, S. Gasparinetti, P. Magnard, A. Potočnik, Y. Salathé, M. Pechal, M. Mondal, M. Oppliger, C. Eichler, and A. Wallraff, Physical Review Applied 7, 054020 (2017).
https://doi.org/10.1103/PhysRevApplied.7.054020

[91] R. Dassonneville, T. Ramos, V. Milchakov, L. Planat, Dumur, F. Foroughi, J. Puertas, S. Leger, K. Bharadwaj, J. Delaforce, C. Naud, W. Hasch-Guichard, J. J. García-Ripoll, N. Roch, and O. Buisson, Physical Review X 10, 11045 (2020).
https://doi.org/10.1103/PhysRevX.10.011045

[92] M. W. Mitchell, Quantum Science and Technology 2, 044005 (2017).
https://doi.org/10.1088/2058-9565/aa80c0

[93] R. J. Thompson, G. Rempe, and H. J. Kimble, Physical Review Letters 68, 1132 (1992).
https://doi.org/10.1103/PhysRevLett.68.1132

[94] M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, Physical Review Letters 76, 1800 (1996).
https://doi.org/10.1103/PhysRevLett.76.1800

[95] T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
https://doi.org/10.1038/nature03119

[96] A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Nature 431, 162 (2004).
https://doi.org/10.1038/nature02851

[97] J. P. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, Nature 432, 197 (2004).
https://doi.org/10.1038/nature02969

[98] I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, Nature 431, 159 (2004).
https://doi.org/10.1038/nature02831

[99] A. Reiserer and G. Rempe, Reviews of Modern Physics 87, 1379 (2015).
https://doi.org/10.1103/RevModPhys.87.1379

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