Single-shot energetic-based estimator for entanglement in a half-parity measurement setup

Cyril Elouard1,2, Alexia Auffèves2, and Géraldine Haack3

1Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
2CNRS and Université Grenoble Alpes, Institut Néel, F-38042 Grenoble, France
3Université de Genève, Department of Applied Physics, Chemin de Pinchat 22, CH-1211 Genève 4, Switzerland

Producing and certifying entanglement between distant qubits is a highly desirable skill for quantum information technologies. Here we propose a new strategy to monitor and characterize entanglement genesis in a half parity measurement setup, that relies on the continuous readout of an energetic observable which is the half-parity observable itself. Based on a quantum-trajectory approach, we theoretically analyze the statistics of energetic fluctuations for a pair of continuously monitored qubits. We quantitatively relate these energetic fluctuations to the rate of entanglement produced between the qubits, and build an energetic-based estimator to assess the presence of entanglement in the circuit. Remarkably, this estimator is valid at the single-trajectory level and shows to be robust against finite detection efficiency. Our work paves the road towards a fundamental understanding of the stochastic energetic processes associated with entanglement genesis, and opens new perspectives for witnessing quantum correlations thanks to quantum thermodynamic quantities.

► BibTeX data

► References

[1] A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
https:/​/​doi.org/​10.1103/​PhysRevLett.67.661

[2] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
https:/​/​doi.org/​10.1103/​PhysRevLett.70.1895

[3] H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).
https:/​/​doi.org/​10.1103/​PhysRevLett.81.5932

[4] R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).
https:/​/​doi.org/​10.1103/​PhysRevLett.86.5188

[5] C. I. Nielsen M., Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge: Cambridge University Press, 2010).

[6] K. Lalumière, J. M. Gambetta, and A. Blais, Phys. Rev. A 81, 040301 (2010).
https:/​/​doi.org/​10.1103/​PhysRevA.81.040301

[7] L. Tornberg and G. Johansson, Physical Review A 82, 012329 (2010).
https:/​/​doi.org/​10.1103/​physreva.82.012329

[8] A. Chantasri, M. E. Kimchi-Schwartz, N. Roch, I. Siddiqi, and A. N. Jordan, Phys. Rev. X 6, 041052 (2016).
https:/​/​doi.org/​10.1103/​PhysRevX.6.041052

[9] B. Royer, S. Puri, and A. Blais, Science Advances 4, eaau1695 (2018).
https:/​/​doi.org/​10.1126/​sciadv.aau1695

[10] B. Trauzettel, A. N. Jordan, C. W. J. Beenakker, and M. Büttiker, Phys. Rev. B 73, 235331 (2006).
https:/​/​doi.org/​10.1103/​PhysRevB.73.235331

[11] N. S. Williams and A. N. Jordan, Phys. Rev. A 78, 062322 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.78.062322

[12] G. Haack, H. Förster, and M. Büttiker, Phys. Rev. B 82, 155303 (2010).
https:/​/​doi.org/​10.1103/​PhysRevB.82.155303

[13] C. Meyer zu Rheda, G. Haack, and A. Romito, Phys. Rev. B 90, 155438 (2014).
https:/​/​doi.org/​10.1103/​PhysRevB.90.155438

[14] D. Ristè, M. Dukalski, C. A. Watson, G. de Lange, M. J. Tiggelman, Y. M. Blanter, K. W. Lehnert, R. N. Schouten, and L. DiCarlo, Nature 502, 350 (2013).
https:/​/​doi.org/​10.1038/​nature12513

[15] N. Roch, M. E. Schwartz, F. Motzoi, C. Macklin, R. Vijay, A. W. Eddins, A. N. Korotkov, K. B. Whaley, M. Sarovar, and I. Siddiqi, Phys. Rev. Lett. 112, 170501 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.170501

[16] S. J. Weber, A. Chantasri, J. Dressel, A. N. Jordan, K. W. Murch, and I. Siddiqi, Nature 511, 570 (2014).
https:/​/​doi.org/​10.1038/​nature13559

[17] Q. Ficheux, S. Jezouin, P. Campagne-Ibarcq, P. Rouchon, and B. Huard, in Quantum Information and Measurement (QIM) 2017 (Optical Society of America, 2017) p. QF5A.2.
https:/​/​doi.org/​10.1364/​QIM.2017.QF5A.2

[18] M. Naghiloo, J. J. Alonso, A. Romito, E. Lutz, and K. W. Murch, Phys. Rev. Lett. 121, 030604 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.030604

[19] C. Elouard, D. Herrera-Martí, B. Huard, and A. Auffèves, Phys. Rev. Lett. 118, 260603 (2017a).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.260603

[20] C. Elouard and A. N. Jordan, Phys. Rev. Lett. 120, 260601 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.260601

[21] L. Buffoni, A. Solfanelli, P. Verrucchi, A. Cuccoli, and M. Campisi, (2018), arXiv:1806.07814.
https:/​/​doi.org/​10.1103/​PhysRevLett.122.070603
arXiv:1806.07814

[22] X. Ding, J. Yi, Y. W. Kim, and P. Talkner, Phys. Rev. E 98, 042122 (2018).
https:/​/​doi.org/​10.1103/​PhysRevE.98.042122

[23] C. Elouard, D. A. Herrera-Martí, M. Clusel, and A. Auffèves, npj Quantum Information 3, 9 (2017b).
https:/​/​doi.org/​10.1038/​s41534-017-0008-4

[24] G. Manzano, J. M. Horowitz, and J. M. R. Parrondo, Phys. Rev. E 92, 032129 (2015).
https:/​/​doi.org/​10.1103/​PhysRevE.92.032129

[25] J. J. Alonso, E. Lutz, and A. Romito, Phys. Rev. Lett. 116, 080403 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.116.080403

[26] C. Elouard and H. Mohammady, Work, heat and entropy production along quantum trajectories (2018) arXiv:1805.08305.
https:/​/​doi.org/​10.1007/​978-3-319-99046-0_15
arXiv:1805.08305

[27] M. Riebe, H. Häffner, C. F. Roos, W. Hänsel, J. Benhelm, G. P. T. Lancaster, T. W. Körber, C. Becher, F. Schmidt-Kaler, D. F. V. James, and R. Blatt, Nature 429, 734 EP (2004).
https:/​/​doi.org/​10.1038/​nature02570

[28] H. M. Wiseman, Quantum and Semiclassical Optics: Journal of the European Optical Society Part B 8, 205 (1996).
https:/​/​doi.org/​10.1088/​1355-5111/​8/​1/​015

[29] K. Jacobs and D. A. Steck, Contemporary Physics 47, 279 (2006).
https:/​/​doi.org/​10.1080/​00107510601101934

[30] S. Pilgram and M. Büttiker, Phys. Rev. Lett. 89, 200401 (2002).
https:/​/​doi.org/​10.1103/​PhysRevLett.89.200401

[31] A. N. Korotkov, Phys. Rev. B 60, 5737 (1999).
https:/​/​doi.org/​10.1103/​PhysRevB.60.5737

[32] C. Gardiner, Handbook of Stochastic Methods (Springer-Verlag Berlin Heidelberg, 1985).

[33] D. T. Gillespie, American Journal of Physics 64, 225 (1996).
https:/​/​doi.org/​10.1119/​1.18210

[34] W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
https:/​/​doi.org/​10.1103/​PhysRevLett.80.2245

[35] K. Brandner, K. Saito, and U. Seifert, Phys. Rev. X 5, 031019 (2015).
https:/​/​doi.org/​10.1103/​PhysRevX.5.031019

[36] K. Abdelkhalek, Y. Nakata, and D. Reeb, Fundamental energy cost for quantum measurement, ArXiv:1609.06981.
arXiv:1609.06981

[37] C. Elouard, D. Herrera-Martí, B. Huard, and A. Auffèves, Physical Review Letters 118, 260603 (2017c).
https:/​/​doi.org/​10.1103/​physrevlett.118.260603

[38] J. Yi, P. Talkner, and Y. W. Kim, Phys. Rev. E 96, 022108 (2017).
https:/​/​doi.org/​10.1103/​PhysRevE.96.022108

[39] M. B. Plenio and S. Virmani, Quantum Info. Comput. 7, 1 (2007).
http:/​/​dl.acm.org/​citation.cfm?id=2011706.2011707

[40] J. Anders, D. Kaszlikowski, C. Lunkes, T. Ohshima, and V. Vedral, New Journal of Physics 8, 140 (2006).
https:/​/​doi.org/​10.1088/​1367-2630/​8/​8/​140

[41] J. Anders, Phys. Rev. A 77, 062102 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.77.062102

[42] M. Huber, M. Perarnau-Llobet, K. V. Hovhannisyan, P. Skrzypczyk, C. Klöckl, N. Brunner, and A. Acín, New Journal of Physics 17, 065008 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​6/​065008
http:/​/​stacks.iop.org/​1367-2630/​17/​i=6/​a=065008

[43] D. E. Bruschi, M. Perarnau-Llobet, N. Friis, K. V. Hovhannisyan, and M. Huber, Phys. Rev. E 91, 032118 (2015).
https:/​/​doi.org/​10.1103/​PhysRevE.91.032118

[44] N. Friis, M. Huber, and M. Perarnau-Llobet, Phys. Rev. E 93, 042135 (2016).
https:/​/​doi.org/​10.1103/​PhysRevE.93.042135

[45] F. Giazotto and M. J. Martínez-Pérez, Nature 492, 401 (2012).
https:/​/​doi.org/​10.1038/​nature11702

[46] S. Jezouin, F. D. Parmentier, A. Anthore, U. Gennser, A. Cavanna, Y. Jin, and F. Pierre, Science 342, 601 (2013).
https:/​/​doi.org/​10.1126/​science.1241912

[47] S. Gasparinetti, K. Viisanen, O.-P. Saira, T. Faivre, M. Arzeo, M. Meschke, and J. Pekola, Physical Review Applied 3, 014007 (2015).
https:/​/​doi.org/​10.1103/​PhysRevApplied.3.014007

[48] Z. Iftikhar, A. Anthore, S. Jezouin, F. D. Parmentier, Y. Jin, A. Cavanna, A. Ouerghi, U. Gennser, and F. Pierre, Nature Communications 7, 12908 (2016).
https:/​/​doi.org/​10.1038/​ncomms12908

[49] A. Fornieri and F. Giazotto, Nature Nanotechnology 12, 944 (2017).
https:/​/​doi.org/​10.1038/​nnano.2017.204

[50] M. Banerjee, M. Heiblum, A. Rosenblatt, Y. Oreg, D. E. Feldman, A. Stern, and V. Umansky, Nature 545, 75 (2017).
https:/​/​doi.org/​10.1038/​nature22052

[51] D. M. T. van Zanten, D. M. Basko, I. M. Khaymovich, J. P. Pekola, H. Courtois, and C. B. Winkelmann, Phys. Rev. Lett. 116, 166801 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.116.166801

Cited by

[1] Teng Ma, Ming-Jing Zhao, Shao-Ming Fei, and Man-Hong Yung, "Necessity for quantum coherence of nondegeneracy in energy flow", Physical Review A 99 6, 062303 (2019).

The above citations are from SAO/NASA ADS (last updated 2019-08-18 05:45:56). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2019-08-18 05:45:55).