Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Dynamics of quantum information


The ability to harness the dynamics of quantum information and entanglement is necessary for the development of quantum technologies and the study of complex quantum systems. On the theoretical side, the dynamics of quantum information is a topic that is helping us to unify and confront common problems in otherwise disparate fields in physics, such as quantum statistical mechanics and cosmology. On the experimental side, impressive developments in the manipulation of neutral atoms and trapped ions are providing new ways to probe their quantum dynamics. Here, we overview and discuss progress in characterizing and understanding the dynamics of quantum entanglement and information scrambling in quantum many-body systems. The level of control attainable over both the internal and external degrees of freedom of individual particles in these systems provides insight into the intrinsic connection between entanglement and thermodynamics, and between bounds on information transport and computational complexity of interacting systems. In turn, this understanding should enable the realization of quantum technologies.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Tools to control single atoms and ions enable us to probe, almost in real time, the dynamics of quantum information.
Fig. 2: Propagation and build-up of quantum correlations in non-equilibrium dynamics.
Fig. 3: Thermalization dynamics of an isolated quantum system accompanied by the build-up of entanglement entropy.
Fig. 4: Measurement and analysis of out-of-time-order correlations.


  1. 1.

    Shenker, S. H. & Stanford, D. Black holes and the butterfly effect. J. High Energy Phys. 2014, 1–25 (2014).

    MathSciNet  MATH  Google Scholar 

  2. 2.

    Hayden, P. & Preskill, J. Black holes as mirrors: quantum information in random subsystems. J. High Energy Phys. 2007, 120 (2007).

    Article  MathSciNet  Google Scholar 

  3. 3.

    Sekino, Y. & Susskind, L. Fast scramblers. J. High Energy Phys. 2008, 065–065 (2008).

    Article  Google Scholar 

  4. 4.

    Shenker, S. H. & Stanford, D. Stringy effects in scrambling. J. High Energy Phys. 2015, 1–34 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  5. 5.

    Maldacena, J. Eternal black holes in anti-de Sitter. J. High Energy Phys. 2003, 021 (2003).

    Article  MathSciNet  Google Scholar 

  6. 6.

    Ryu, S. & Takayanagi, T. Holographic derivation of entanglement entropy from the anti–de Sitter space/conformal field theory correspondence. Phys. Rev. Lett. 96, 181602 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. 7.

    Qi, X.-L. Does gravity come from quantum information? Nat. Phys. 14, 984–987 (2018).

    Article  Google Scholar 

  8. 8.

    D’Alessio, L., Kafri, Y., Polkovnikov, A. & Rigol, M. From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239–362 (2016).

    Article  ADS  Google Scholar 

  9. 9.

    Nandkishore, R. & Huse, D. A. Many-body localization and thermalization in quantum statistical mechanics. Annu. Rev. Condens. Matter Phys. 6, 15–38 (2015).

    Article  ADS  Google Scholar 

  10. 10.

    Maldacena, J., Shenker, S. H. & Stanford, D. A bound on chaos. J. High Energy Phys. 2016, 106 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  11. 11.

    Hosur, P., Qi, X.-L., Roberts, D. A. & Yoshida, B. Chaos in quantum channels. J. High Energy Phys. 2016, 1–49 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  12. 12.

    Susskind, L. Computational complexity and black hole horizons. Fortschr. Phys. 64, 24–43 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  13. 13.

    Lieb, E. H. & Robinson, D. W. The finite group velocity of quantum spin systems. Commun. Math. Phys. 28, 251–257 (1972).

    Article  ADS  MathSciNet  Google Scholar 

  14. 14.

    Cheneau, M. et al. Light-cone-like spreading of correlations in a quantum many-body system. Nature 481, 484–487 (2012).

    Article  ADS  Google Scholar 

  15. 15.

    Jurcevic, P. et al. Quasiparticle engineering and entanglement propagation in a quantum many-body system. Nature 511, 202–205 (2014).

    Article  ADS  Google Scholar 

  16. 16.

    Richerme, P. et al. Non-local propagation of correlations in quantum systems with long-range interactions. Nature 511, 198–201 (2014).

    Article  ADS  Google Scholar 

  17. 17.

    Langen, T., Geiger, R., Kuhnert, M., Rauer, B. & Schmiedmayer, J. Local emergence of thermal correlations in an isolated quantum many-body system. Nat. Phys. 9, 640–643 (2013).

    Article  Google Scholar 

  18. 18.

    Schweigler, T. et al. Experimental characterization of a quantum many-body system via higher-order correlations. Nature 545, 323–326 (2017).

    Article  ADS  Google Scholar 

  19. 19.

    Bakr, W. S., Gillen, J. I., Peng, A., Fölling, S. & Greiner, M. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 74–77 (2009).

    Article  ADS  Google Scholar 

  20. 20.

    Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).

    Article  ADS  Google Scholar 

  21. 21.

    Gericke, T., Würtz, P., Reitz, D., Langen, T. & Ott, H. High-resolution scanning electron microscopy of an ultracold quantum gas. Nat. Phys. 4, 949–953 (2008).

    Article  Google Scholar 

  22. 22.

    Cheuk, L. W. et al. Quantum-gas microscope for fermionic atoms. Phys. Rev. Lett. 114, 193001 (2015).

    Article  ADS  Google Scholar 

  23. 23.

    Edge, G. J. A. et al. Imaging and addressing of individual fermionic atoms in an optical lattice. Phys. Rev. A 92, 063406 (2015).

    Article  ADS  Google Scholar 

  24. 24.

    Mitra, D. et al. Quantum gas microscopy of an attractive Fermi–Hubbard system. Nat. Phys. 14, 173–177 (2017).

    Article  Google Scholar 

  25. 25.

    Gross, C. & Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017).

    Article  ADS  Google Scholar 

  26. 26.

    Yamamoto, R., Kobayashi, J., Kuno, T., Kato, K. & Takahashi, Y. An ytterbium quantum gas microscope with narrow-line laser cooling. New J. Phys. 18, 023016 (2016).

    Article  ADS  Google Scholar 

  27. 27.

    Brydges, T. et al. Probing Renyi entanglement entropy via randomized measurements. Science 364, 260–263 (2019).

    ADS  Google Scholar 

  28. 28.

    Islam, R. et al. Measuring entanglement entropy in a quantum many-body system. Nature 528, 77–83 (2015).

    Article  ADS  Google Scholar 

  29. 29.

    Kaufman, A. M. et al. Quantum thermalization through entanglement in an isolated many-body system. Science 353, 794–800 (2016).

    Article  ADS  Google Scholar 

  30. 30.

    Smith, J. et al. Many-body localization in a quantum simulator with programmable random disorder. Nat. Phys. 12, 907–911 (2016).

    Article  Google Scholar 

  31. 31.

    Lukin, A et al. Probing entanglement in a many-body-localized system. Science 364, 256–260 (2018).

    ADS  Google Scholar 

  32. 32.

    Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. 33.

    Choi, J.-y et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. 34.

    Lüschen, H. P. et al. Signatures of many-body localization in a controlled open quantum system. Phys. Rev. X 7, 011034 (2017).

    Google Scholar 

  35. 35.

    Swingle, B. Unscrambling the physics of out-of-time-order correlators. Nat. Phys. 14, 988–990 (2018).

    Article  Google Scholar 

  36. 36.

    Hastings, M. B. & Koma, T. Spectral gap and exponential decay of correlations. Commun. Math. Phys. 265, 781–804 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. 37.

    Hauke, P. & Tagliacozzo, L. Spread of correlations in long-range interacting quantum systems. Phys. Rev. Lett. 111, 207202 (2013).

    Article  ADS  Google Scholar 

  38. 38.

    Eisert, J., van den Worm, M., Manmana, S. R. & Kastner, M. Breakdown of quasilocality in long-range quantum lattice models. Phys. Rev. Lett. 111, 260401 (2013).

    Article  ADS  Google Scholar 

  39. 39.

    Foss-Feig, M., Gong, Z.-X., Clark, C. W. & Gorshkov, A. V. Nearly linear light cones in long-range interacting quantum systems. Phys. Rev. Lett. 114, 157201 (2015).

    Article  ADS  Google Scholar 

  40. 40.

    Else, D. V., Machado, F., Nayak, C. & Yao, Y. An improved Lieb–Robinson bound for many-body Hamiltonians with power-law interactions. Preprint at (2018).

  41. 41.

    Altman, E. Many-body localization and quantum thermalization. Nat. Phys. 14, 979–983 (2018).

    Article  Google Scholar 

  42. 42.

    Žnidarič, M., Prosen, Tcv & Prelovšek, P. Many-body localization in the Heisenberg xxz magnet in a random field. Phys. Rev. B 77, 064426 (2008).

    Article  ADS  Google Scholar 

  43. 43.

    Bardarson, J. H., Pollmann, F. & Moore, J. E. Unbounded growth of entanglement in models of many-body localization. Phys. Rev. Lett. 109, 017202 (2012).

    Article  ADS  Google Scholar 

  44. 44.

    Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).

    Article  Google Scholar 

  45. 45.

    Kaufman, A. M. et al. Entangling two transportable neutral atoms via local spin exchange. Nature 527, 208–211 (2015).

    Article  ADS  Google Scholar 

  46. 46.

    Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604 (2017).

    Article  ADS  Google Scholar 

  47. 47.

    Friis, N. et al. Observation of entangled states of a fully controlled 20-qubit system. Phys. Rev. X 8, 021012 (2018).

    Google Scholar 

  48. 48.

    Zeiher, J. et al. Coherent many-body spin dynamics in a long-range interacting Ising chain. Phys. Rev. X 7, 041063 (2017).

    Google Scholar 

  49. 49.

    Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).

    Article  ADS  Google Scholar 

  50. 50.

    Labuhn, H. et al. Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models. Nature 534, 667–670 (2016).

    Article  ADS  Google Scholar 

  51. 51.

    Lienhard, V. et al. Observing the space- and time-dependent growth of correlations in dynamically tuned synthetic Ising models with antiferromagnetic interactions. Phys. Rev. X 8, 021070 (2018).

    Google Scholar 

  52. 52.

    Guardado-Sanchez, E. et al. Probing the quench dynamics of antiferromagnetic correlations in a 2D quantum Ising spin system. Phys. Rev. X 8, 021069 (2018).

    Google Scholar 

  53. 53.

    Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225–1286 (2010).

    Article  ADS  Google Scholar 

  54. 54.

    Lahaye, T., Menotti, C., Santos, L., Lewenstein, M. & Pfau, T. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009).

    Article  ADS  Google Scholar 

  55. 55.

    Vaidya, V. D. et al. Tunable-range, photon-mediated atomic interactions in multimode cavity QED. Phys. Rev. X 8, 011002 (2018).

    Google Scholar 

  56. 56.

    Davis, E. J., Bentsen, G., Homeier, L., Li, T. & Schleier-Smith, M. H. Photon-mediated spin-exchange dynamics of spin-1 atoms. Phys. Rev. Lett. 122, 010405 (2019).

    Article  ADS  Google Scholar 

  57. 57.

    Norcia, M. A. et al. Cavity mediated collective spin exchange interactions in a strontium superradiant laser. Science 361, 259–262 (2017).

    Article  ADS  Google Scholar 

  58. 58.

    Jurcevic, P. et al. Spectroscopy of interacting quasiparticles in trapped ions. Phys. Rev. Lett. 115, 100501 (2015).

    Article  ADS  Google Scholar 

  59. 59.

    Langen, T. et al. Experimental observation of a generalized Gibbs ensemble. Science 348, 207–211 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  60. 60.

    Keesling, A. et al. Probing quantum critical dynamics on a programmable Rydberg simulator. Preprint at (2018).

  61. 61.

    Calabrese, P. & Cardy, J. Entanglement entropy and quantum field theory. J. Stat. Mech. Theory Exp. 2004, P06002 (2004).

    MathSciNet  MATH  Google Scholar 

  62. 62.

    Calabrese, P. & Cardy, J. Evolution of entanglement entropy in one-dimensional systems. J. Stat. Mech. Theory Exp. 2005, P04010 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  63. 63.

    Khemani, V., Lim, S. P., Sheng, D. N. & Huse, D. A. Critical properties of the many-body localization transition. Phys. Rev. X 7, 021013 (2017).

    Google Scholar 

  64. 64.

    Kitaev, A. & Preskill, J. Topological entanglement entropy. Phys. Rev. Lett. 96, 110404 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  65. 65.

    Levin, M. & Wen, X.-G. Detecting topological order in a ground state wavefunction. Phys. Rev. Lett. 96, 110405 (2006).

    Article  ADS  Google Scholar 

  66. 66.

    Daley, A. J., Pichler, H., Schachenmayer, J. & Zoller, P. Measuring entanglement growth in quench dynamics of bosons in an optical lattice. Phys. Rev. Lett. 109, 020505 (2012).

    Article  ADS  Google Scholar 

  67. 67.

    Hahn, E. L. Spin echoes. Phys. Rev. 80, 580–594 (1950).

    Article  ADS  MATH  Google Scholar 

  68. 68.

    Larkin, A. & Ovchinnikov, Y. N. Quasiclassical method in the theory of superconductivity. Sov. Phys. JETP 28, 1200 (1969).

    ADS  Google Scholar 

  69. 69.

    Fan, R., Zhang, P., Shen, H. & Zhai, H. Out-of-time-order correlation for many-body localization. Sci. Bull. 62, 707–711 (2017).

    Article  Google Scholar 

  70. 70.

    Swingle, B. & Chowdhury, D. Slow scrambling in disordered quantum systems. Phys. Rev. B 95, 060201 (2017).

    Article  ADS  Google Scholar 

  71. 71.

    Heyl, M., Pollmann, F. & Dóra, B. Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators. Phys. Rev. Lett. 121, 016801 (2018).

    Article  ADS  Google Scholar 

  72. 72.

    Gärttner, M. et al. Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet. Nat. Phys. 13, 781–786 (2017).

    Article  Google Scholar 

  73. 73.

    Li, J. et al. Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator. Phys. Rev. X 7, 031011 (2017).

    Google Scholar 

  74. 74.

    Wei, K. X., Ramanathan, C. & Cappellaro, P. Exploring localization in nuclear spin chains. Phys. Rev. Lett. 120, 070501 (2018).

    Article  ADS  Google Scholar 

  75. 75.

    Meier, E. J., Ang’ong’a, J., An, F. A. & Gadway, B. Exploring quantum signatures of chaos on a Floquet synthetic lattice. Preprint at (2018).

  76. 76.

    Landsman, K. A. et al. Verified quantum information scrambling. Nature 567, 61–65 (2019).

    Article  ADS  Google Scholar 

  77. 77.

    Sachdev, S. & Ye, J. Gapless spin-fluid ground state in a random quantum Heisenberg magnet. Phys. Rev. Lett. 70, 3339–3342 (1993).

    Article  ADS  Google Scholar 

  78. 78.

    Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011).

    Article  ADS  Google Scholar 

  79. 79.

    Lucas, A. Quantum many-body dynamics on the star graph. Preprint at (2019).

  80. 80.

    Martinez, E. A. et al. Real-time dynamics of lattice gauge theories with a few-qubit quantum computer. Nature 534, 516 (2016).

    Article  ADS  Google Scholar 

  81. 81.

    Preskill, J. Quantum computing and the entanglement frontier. Preprint at (2012).

  82. 82.

    von Keyserlingk, C. W., Rakovszky, T., Pollmann, F. & Sondhi, S. L. Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws. Phys. Rev. X 8, 021013 (2018).

    Google Scholar 

  83. 83.

    Khemani, V., Vishwanath, A. & Huse, D. A. Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws. Phys. Rev. X 8, 031057 (2018).

    Google Scholar 

  84. 84.

    Nahum, A., Vijay, S. & Haah, J. Operator spreading in random unitary circuits. Phys. Rev. X 8, 021014 (2018).

    Google Scholar 

  85. 85.

    Eckardt, A. Colloquium: Atomic quantum gases in periodically driven optical lattices. Rev. Mod. Phys. 89, 011004 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  86. 86.

    Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217–220 (2017).

    Article  ADS  Google Scholar 

  87. 87.

    Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).

    Article  ADS  Google Scholar 

  88. 88.

    Deutsch, C. et al. Spin self-rephasing and very long coherence times in a trapped atomic ensemble. Phys. Rev. Lett. 105, 020401 (2010).

    Article  ADS  Google Scholar 

  89. 89.

    Solaro, C. et al. Competition between spin echo and spin self-rephasing in a trapped atom interferometer. Phys. Rev. Lett. 117, 163003 (2016).

    Article  ADS  Google Scholar 

  90. 90.

    Piéchon, F., Fuchs, J. N. & Laloë, F. Cumulative identical spin rotation effects in collisionless trapped atomic gases. Phys. Rev. Lett. 102, 215301 (2009).

    Article  ADS  Google Scholar 

  91. 91.

    Baumann, K., Guerlin, C., Brennecke, F. & Esslinger, T. Dicke quantum phase transition with a superfluid gas in an optical cavity. Nature 464, 1301–1306 (2010).

    Article  ADS  Google Scholar 

  92. 92.

    Klinder, J., Keßler, H., Wolke, M., Mathey, L. & Hemmerich, A. Dynamical phase transition in the open Dicke model. Proc. Natl Acad. Sci. USA 112, 3290–3295 (2015).

    Article  ADS  Google Scholar 

  93. 93.

    Leonard, J., Morales, A., Zupancic, P., Donner, T. & Esslinger, T. Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas. Science 358, 1415–1418 (2017).

    Article  ADS  Google Scholar 

  94. 94.

    Li, J. et al. A stripe phase with supersolid properties in spin–orbit coupled Bose–Einstein condensates. Nature 543, 91–94 (2017).

    Article  ADS  Google Scholar 

  95. 95.

    Jurcevic, P. et al. Direct observation of dynamical quantum phase transitions in an interacting many-body system. Phys. Rev. Lett. 119, 080501 (2017).

    Article  ADS  Google Scholar 

  96. 96.

    Smale, S. et al. Observation of a dynamical phase transition in a quantum degenerate Fermi gas. Preprint at (2018).

Download references


The authors thank M. Norcia and A. Shankar for their reading of the manuscript and feedback. This work is supported by the US Air Force Office of Scientific Research grant FA9550-18-1-0319 and its MURI Initiative, the US Defense Advanced Research Projects Agency (DARPA) and Army Research Office (ARO) grant W911NF-16-1-0576, the DARPA DRINQs programme, the ARO single investigator award W911NF-19-1-0210, the US National Science Foundation (NSF) PHY1820885 and NSF JILA-PFC PHY-1734006 grants, and the US National Institute of Standards and Technology.

Author information




All authors worked together on preparing and writing this Perspective.

Corresponding author

Correspondence to A. M. Rey.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Physics thanks M. Schleier-Smith, A. Polkovnikov and the other, anonymous, reviewer(s) for their contribution to the peer-review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lewis-Swan, R.J., Safavi-Naini, A., Kaufman, A.M. et al. Dynamics of quantum information. Nat Rev Phys 1, 627–634 (2019).

Download citation


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing