Experimental quantification of spatial correlations in quantum dynamics

Lukas Postler1, Ángel Rivas2,3, Philipp Schindler1, Alexander Erhard1, Roman Stricker1, Daniel Nigg1, Thomas Monz1, Rainer Blatt1,4, 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

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.

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[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.
https://doi.org/PhysRevLett.113.140401

[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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