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.
 M. B. Plenio and S. Virmani. Quantum Information and Computation, 7(1):1–51, 2007.
 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.
 A. Crubellier, S. Liberman, D. Pavolini, and P. Pillet. Journal of Physics B: Atomic and Molecular Physics, 18(18):3811, 1985.
 A. Nazir. Physical Review Letters, 103:146404, 2009.
 P. Nalbach, J. Eckel, and M. Thorwart. New Journal of Physics, 12:065043, 2010.
 J. Jeske, J. H. Cole, and S. F. Huelga. New Journal of Physics, 16(7):073039, 2014.
 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.
 J. Preskill. Quantum Information and Computation, 13:181, 2013.
 E. Novais and E. R. Mucciolo. Physical Review Letters, 110:010502, 2013.
 Á. Rivas and M. Müller. New Journal of Physics, 17(6):062001, 2015.
 G. Gour and R. W. Spekkens. New Journal of Physics, 10(3):033023, 2008.
 F. G. S. L. Brandao, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens. Physical Review Letters, 111(25):250404, 2013.
 V. Veitch, S. A. H. Mousavian, D. Gottesman, and J. Emerson. New Journal of Physics, 16(1):013009, 2014.
 J. I. De Vicente. Journal of Physics A: Mathematical and Theoretical, 47(42):424017, 2014.
 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.
 B. Schumacher and M. D. Westmoreland. Contemporary Mathematics, 305:265–290, 2002.
 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.
 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.
 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.
 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.
 C. L. Edmunds, C. Hempel, R. J. Harris, V. Frey, T. M. Stace, and M. J. Biercuk, "Dynamically corrected gates suppressing spatiotemporal error correlations as measured by randomized benchmarking", Physical Review Research 2 1, 013156 (2020).
 Daniel Manzano, "Measuring correlations in quantum systems", Quantum Views 3, 12 (2019).
 Eric Chitambar and Gilad Gour, "Quantum resource theories", Reviews of Modern Physics 91 2, 025001 (2019).
 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.
 Riddhi S. Gupta and Michael J. Biercuk, "Convergence analysis for autonomous adaptive learning applied to quantum architectures", arXiv:1911.05752.
 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.
The above citations are from Crossref's cited-by service (last updated successfully 2020-04-03 19:54:30) and SAO/NASA ADS (last updated successfully 2020-04-03 19:54:31). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.