Experimental quantification of spatial correlations in quantum dynamics

Lukas Postler; Ángel Rivas; Philipp Schindler; Alexander Erhard; Roman Stricker; Daniel Nigg; Thomas Monz; Rainer Blatt; Markus Müller

doi:10.22331/q-2018-09-03-90

Experimental quantification of spatial correlations in quantum dynamics

Lukas Postler¹, Ángel Rivas^2,3, Philipp Schindler¹, Alexander Erhard¹, Roman Stricker¹, Daniel Nigg¹, Thomas Monz¹, Rainer Blatt^1,4, and Markus Müller⁵

¹Institut für Experimentalphysik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria
²Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
³CCS-Center for Computational Simulation, Campus de Montegancedo UPM, 28660 Boadilla del Monte, Madrid, Spain
⁴Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Otto-Hittmair-Platz 1, A-6020 Innsbruck, Austria
⁵Department of Physics, College of Science, Swansea University, Singleton Park, Swansea - SA2 8PP, United Kingdom

Published:	2018-09-03, volume 2, page 90
Eprint:	arXiv:1806.08088v2
Doi:	https://doi.org/10.22331/q-2018-09-03-90
Citation:	Quantum 2, 90 (2018).

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Abstract

Correlations between different partitions of quantum systems play a central role in a variety of many-body quantum systems, and they have been studied exhaustively in experimental and theoretical research. Here, we investigate dynamical correlations in the time evolution of multiple parts of a composite quantum system. A rigorous measure to quantify correlations in quantum dynamics based on a full tomographic reconstruction of the quantum process has been introduced recently [Á. Rivas et al., New Journal of Physics, 17(6) 062001 (2015).]. In this work, we derive a lower bound for this correlation measure, which does not require full knowledge of the quantum dynamics. Furthermore we also extend the correlation measure to multipartite systems. We directly apply the developed methods to a trapped ion quantum information processor to experimentally characterize the correlations in quantum dynamics for two- and four-qubit systems. The method proposed and demonstrated in this work is scalable, platform-independent and applicable to other composite quantum systems and quantum information processing architectures. We apply the method to estimate spatial correlations in environmental noise processes, which are crucial for the performance of quantum error correction procedures.

► BibTeX data

@article{Postler2018experimental,
  doi = {10.22331/q-2018-09-03-90},
  url = {https://doi.org/10.22331/q-2018-09-03-90},
  title = {Experimental quantification of spatial correlations in quantum dynamics},
  author = {Postler, Lukas and Rivas, {\'{A}}ngel and Schindler, Philipp and Erhard, Alexander and Stricker, Roman and Nigg, Daniel and Monz, Thomas and Blatt, Rainer and M{\"{u}}ller, Markus},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {90},
  month = sep,
  year = {2018}
}

► References

[1] M. B. Plenio and S. Virmani. Quantum Information and Computation, 7(1):1–51, 2007.

[2] K. Modi, A. Brodutch, C. Cable, T. Paterek, and V. Vedral. Reviews of Modern Physics, 84:1655, 2012.
https://doi.org/10.1103/RevModPhys.84.1655

[3] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki. Reviews of Modern Physics, 81:865, 2009.
https://doi.org/10.1103/RevModPhys.81.865

[4] R. H. Dicke. Physical Review, 93:99–110, 1954.
https://doi.org/10.1103/PhysRev.93.99

[5] T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt. Physical Review Letters, 106:130506, 2011.
https://doi.org/10.1103/PhysRevLett.106.130506

[6] A. Crubellier, S. Liberman, D. Pavolini, and P. Pillet. Journal of Physics B: Atomic and Molecular Physics, 18(18):3811, 1985.
https://doi.org/10.1088/0022-3700/18/18/022

[7] F. Caruso, A. W. Chin, A. Datta, S. F. Huelga, and M. B. Plenio. Journal of Chemical Physics, 131:105106, 2009.
https://doi.org/10.1063/1.3223548

[8] P. Rebentrost, M. Mohseni, and A. Aspuru-Guzik. Journal of Physical Chemistry B, 113:9942, 2009.
https://doi.org/10.1021/jp901724d

[9] A. Nazir. Physical Review Letters, 103:146404, 2009.
https://doi.org/10.1103/PhysRevLett.103.146404

[10] P. Nalbach, J. Eckel, and M. Thorwart. New Journal of Physics, 12:065043, 2010.
https://doi.org/10.1088/1367-2630/12/6/065043

[11] C. Olbrich, J. Strümpfer, K. Schulten, and U. Kleinekathöfer. Journal of Physical Chemistry B, 115:758, 2011.
https://doi.org/10.1021/jp1099514

[12] J. Jeske, A. Rivas, M. H. Ahmed, M. A. Martin-Delgado, and J. H. Cole. arXiv:1802.10258, 2018.
arXiv:1802.10258

[13] S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. Büchler, and P. Zoller. Nature Physics, 4(11):878, 2008.
https://doi.org/10.1038/nphys1073

[14] F. Verstraete, M. M. Wolf, and J. I. Cirac. Nature Physics, 5(9):633, 2009.
https://doi.org/10.1038/nphys1342

[15] B. Olmos, D. Yu, and I. Lesanovsky. Physical Review A, 89:023616, 2014.
https://doi.org/10.1103/PhysRevA.89.023616

[16] T. E. Lee, C.-K. Chan, and S. F. Yelin. Physical Review A, 90:052109, 2014.
https://doi.org/10.1103/PhysRevA.90.052109

[17] P. Schindler, M. Müller, D. Nigg, J. T. Barreiro, E. A. Martinez, M. Hennrich, T. Monz, S. Diehl, P. Zoller, and R. Blatt. Nature Physics, 9(6):361, 2013.
https://doi.org/10.1038/nphys2630

[18] J. Jeske, J. H. Cole, and S. F. Huelga. New Journal of Physics, 16(7):073039, 2014.
https://doi.org/10.1088/1367-2630/16/7/073039

[19] D. A. Lidar and T. A. Brun. Quantum error correction. Cambridge University Press, 2013.
https://doi.org/10.1017/CBO9781139034807

[20] P. Zanardi and M. Rasetti. Physical Review Letters, 79:3306–3309, 1997.
https://doi.org/10.1103/PhysRevLett.79.3306

[21] D. A. Lidar, I. L. Chuang, and K. B. Whaley. Physical Review Letters, 81:2594–2597, 1998.
https://doi.org/10.1103/PhysRevLett.81.2594

[22] D. A. Lidar, D. Bacon, J. Kempe, and K. B. Whaley. Physical Review A, 63:022306, 2001.
https://doi.org/10.1103/PhysRevA.63.022307

[23] D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland. Science, 291(5506):1013–1015, 2001.
https://doi.org/10.1126/science.1057357

[24] H. Häffner, F. Schmidt-Kaler, W. Hänsel, C. F. Roos, T. Körber, M. Chwalla, M. Riebe, J. Benhelm, U. D. Rapol, C. Becher, and R. Blatt. Applied Physics B, 81(2):151–153, 2005.
https://doi.org/10.1007/s00340-005-1917-z

[25] J. Preskill. "Fault-Tolerant Quantum Computation" in "Introduction to Quantum Computation and Information". World Scientific, 1998.
https://doi.org/10.1142/9789812385253_0008

[26] J. P. Clemens, S. Siddiqui, and J. Gea-Banacloche. Physical Review A, 69:062313, 2004.
https://doi.org/10.1103/PhysRevA.69.062313

[27] R. Klesse and S. Frank. Phyical Review Letters, 95:230503, 2005.
https://doi.org/10.1103/PhysRevLett.95.230503

[28] D. Aharonov, A. Kitaev, and J. Preskill. Physical Review Letters, 96:050504, 2006.
https://doi.org/10.1103/PhysRevLett.96.050504

[29] E. Novais and H. U. Baranger. Physical Review Letters, 97:040501, 2006.
https://doi.org/10.1103/PhysRevLett.97.040501

[30] E. Novais, E. R. Mucciolo, and H. U. Baranger. Physical Review Letters, 98:040501, 2007.
https://doi.org/10.1103/PhysRevLett.98.040501

[31] J. Preskill. Quantum Information and Computation, 13:181, 2013.

[32] E. Novais and E. R. Mucciolo. Physical Review Letters, 110:010502, 2013.
https://doi.org/10.1103/PhysRevLett.110.010502

[33] P. W. Shor. Fault-tolerant quantum computation, pages 56–65. IEEE, 1996.
https://doi.org/10.1109/SFCS.1996.548464

[34] J. Preskill. Fault-Tolerant Quantum Computation, pages 213–269. World Scientific, 2011.
https://doi.org/10.1142/9789812385253_0008

[35] Á. Rivas and M. Müller. New Journal of Physics, 17(6):062001, 2015.
https://doi.org/10.1088/1367-2630/17/7/079602

[36] F. G. S. L. Brandao and M. B. Plenio. Nature Physics, 4(11):873, 2008.
https://doi.org/10.1038/nphys1100

[37] G. Gour and R. W. Spekkens. New Journal of Physics, 10(3):033023, 2008.
https://doi.org/10.1088/1367-2630/10/3/033023

[38] F. G. S. L. Brandao, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens. Physical Review Letters, 111(25):250404, 2013.
https://doi.org/10.1103/PhysRevLett.111.250404

[39] V. Veitch, S. A. H. Mousavian, D. Gottesman, and J. Emerson. New Journal of Physics, 16(1):013009, 2014.
https://doi.org/10.1088/1367-2630/16/1/013009

[40] T. Baumgratz, M. Cramer, and M. B. Plenio. Physical Review Letters, 113:140401, 2014.

[41] J. I. De Vicente. Journal of Physics A: Mathematical and Theoretical, 47(42):424017, 2014.
https://doi.org/10.1088/1751-8113/47/42/424017

[42] G. Gour, M. P. Müller, V. Narasimhachar, R. W. Spekkens, and N. Y. Halpern. Physics Reports, 583:1–58, 2015.
https://doi.org/10.1016/j.physrep.2015.04.003

[43] T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt. Physical Review Letters, 102:040501, 2009.
https://doi.org/10.1103/PhysRevLett.102.040501

[44] M.-D. Choi. Linear Algebra and its Applications, 10(3):285 – 290, 1975.
https://doi.org/10.1016/0024-3795(75)90075-0

[45] A. Jamiołkowski. Reports on Mathematical Physics, 3(4):275 – 278, 1972.
https://doi.org/10.1016/0034-4877(72)90011-0

[46] M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010.
https://doi.org/10.1017/CBO9780511976667

[47] B. Schumacher and M. D. Westmoreland. Contemporary Mathematics, 305:265–290, 2002.

[48] M. Ježek, J. Fiurášek, and Z. Hradil. Physical Review A, 68:012305, 2003.
https://doi.org/10.1103/PhysRevA.68.012305

[49] V. Vedral. Reviews of Modern Physics, 74:197–234, 2002.
https://doi.org/10.1103/RevModPhys.74.197

[50] M. M. Wilde. Quantum information theory. Cambridge University Press, 2013.
https://doi.org/10.1017/CBO9781139525343

[51] P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. Martinez, S. X. Wang, S. Quint, M. F. Brandl, V. Nebendahl, C. F. Roos, M. Chwalla, M. Hennrich, and R. Blatt. New Journal of Physics, 15(12):123012, 2013.
https://doi.org/10.1088/1367-2630/15/12/123012

[52] C. F. Roos, G. P. T. Lancaster, M. Riebe, H. Häffner, W. Hänsel, S. Gulde, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt. Physical Review Letters, 92:220402, 2004.
https://doi.org/10.1103/PhysRevLett.92.220402

[53] A. Bermudez, X. Xu, R. Nigmatullin, J. O'Gorman, V. Negnevitsky, P. Schindler, T. Monz, U. G. Poschinger, C. Hempel, J. Home, F. Schmidt-Kaler, M. Biercuk, R. Blatt, S. Benjamin, and M. Müller. Physical Review X, 7:041061, 2017.
https://doi.org/10.1103/PhysRevX.7.041061

[54] T. Ruster, H. Kaufmann, M. A. Luda, V. Kaushal, C. T. Schmiegelow, F. Schmidt-Kaler, and U. G. Poschinger. Physical Review X, 7:031050, 2017.
https://doi.org/10.1103/PhysRevX.7.031050

[55] P. Schindler, J. T. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, and R. Blatt. Science, 332(6033):1059–1061, 2011.
https://doi.org/10.1126/science.1203329

[56] D. Nigg, M. Müller, E. A. Martinez, P. Schindler, M. Hennrich, T. Monz, M. A. Martin-Delgado, and R. Blatt. Science, 345(6194):302–305, 2014.
https://doi.org/10.1126/science.1253742

[57] 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 Blatt R. Nature, 429(6993):734, 2004.
https://doi.org/10.1038/nature02570

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[2] Daniel Manzano, "Measuring correlations in quantum systems", Quantum Views 3, 12 (2019).

[3] Riddhi Swaroop Gupta, Claire L. Edmunds, Alistair R. Milne, Cornelius Hempel, and Michael J. Biercuk, "Adaptive characterization of spatially inhomogeneous fields and errors in qubit registers", npj Quantum Information 6 1, 53 (2020).

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[5] Simon J. D Phoenix, Faisal Shah Khan, and Berihu Teklu, "Partitions of correlated N-qubit systems", Quantum Information Processing 20 2, 62 (2021).

[6] Francisco Riberi, Leigh M Norris, Félix Beaudoin, and Lorenza Viola, "Frequency estimation under non-Markovian spatially correlated quantum noise", New Journal of Physics 24 10, 103011 (2022).

[7] Eric Chitambar and Gilad Gour, "Quantum resource theories", Reviews of Modern Physics 91 2, 025001 (2019).

[8] Jelmer M. Boter, Xiao Xue, Tobias Krähenmann, Thomas F. Watson, Vickram N. Premakumar, Daniel R. Ward, Donald E. Savage, Max G. Lagally, Mark Friesen, Susan N. Coppersmith, Mark A. Eriksson, Robert Joynt, and Lieven M. K. Vandersypen, "Spatial noise correlations in a Si/SiGe two-qubit device from Bell state coherences", Physical Review B 101 23, 235133 (2020).

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[11] Marco Cattaneo, Gian Luca Giorgi, Sabrina Maniscalco, Gheorghe Sorin Paraoanu, and Roberta Zambrini, "Bath‐Induced Collective Phenomena on Superconducting Qubits: Synchronization, Subradiance, and Entanglement Generation", Annalen der Physik 533 5, 2100038 (2021).

[12] Riddhi Swaroop Gupta, Alistair R. Milne, Claire L. Edmunds, Cornelius Hempel, and Michael J. Biercuk, "Autonomous adaptive noise characterization in quantum computers", arXiv:1904.07225, (2019).

[13] Uwe von Lüpke, Félix Beaudoin, Leigh M. Norris, Youngkyu Sung, Roni Winik, Jack Y. Qiu, Morten Kjaergaard, David Kim, Jonilyn Yoder, Simon Gustavsson, Lorenza Viola, and William D. Oliver, "Two-qubit spectroscopy of spatiotemporally correlated quantum noise in superconducting qubits", arXiv:1912.04982, (2019).

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Experimental quantification of spatial correlations in quantum dynamics

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