Abstract
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.
Similar content being viewed by others
References
Shenker, S. H. & Stanford, D. Black holes and the butterfly effect. J. High Energy Phys. 2014, 1–25 (2014).
Hayden, P. & Preskill, J. Black holes as mirrors: quantum information in random subsystems. J. High Energy Phys. 2007, 120 (2007).
Sekino, Y. & Susskind, L. Fast scramblers. J. High Energy Phys. 2008, 065–065 (2008).
Shenker, S. H. & Stanford, D. Stringy effects in scrambling. J. High Energy Phys. 2015, 1–34 (2015).
Maldacena, J. Eternal black holes in anti-de Sitter. J. High Energy Phys. 2003, 021 (2003).
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).
Qi, X.-L. Does gravity come from quantum information? Nat. Phys. 14, 984–987 (2018).
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).
Nandkishore, R. & Huse, D. A. Many-body localization and thermalization in quantum statistical mechanics. Annu. Rev. Condens. Matter Phys. 6, 15–38 (2015).
Maldacena, J., Shenker, S. H. & Stanford, D. A bound on chaos. J. High Energy Phys. 2016, 106 (2016).
Hosur, P., Qi, X.-L., Roberts, D. A. & Yoshida, B. Chaos in quantum channels. J. High Energy Phys. 2016, 1–49 (2016).
Susskind, L. Computational complexity and black hole horizons. Fortschr. Phys. 64, 24–43 (2015).
Lieb, E. H. & Robinson, D. W. The finite group velocity of quantum spin systems. Commun. Math. Phys. 28, 251–257 (1972).
Cheneau, M. et al. Light-cone-like spreading of correlations in a quantum many-body system. Nature 481, 484–487 (2012).
Jurcevic, P. et al. Quasiparticle engineering and entanglement propagation in a quantum many-body system. Nature 511, 202–205 (2014).
Richerme, P. et al. Non-local propagation of correlations in quantum systems with long-range interactions. Nature 511, 198–201 (2014).
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).
Schweigler, T. et al. Experimental characterization of a quantum many-body system via higher-order correlations. Nature 545, 323–326 (2017).
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).
Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).
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).
Cheuk, L. W. et al. Quantum-gas microscope for fermionic atoms. Phys. Rev. Lett. 114, 193001 (2015).
Edge, G. J. A. et al. Imaging and addressing of individual fermionic atoms in an optical lattice. Phys. Rev. A 92, 063406 (2015).
Mitra, D. et al. Quantum gas microscopy of an attractive Fermi–Hubbard system. Nat. Phys. 14, 173–177 (2017).
Gross, C. & Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017).
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).
Brydges, T. et al. Probing Renyi entanglement entropy via randomized measurements. Science 364, 260–263 (2019).
Islam, R. et al. Measuring entanglement entropy in a quantum many-body system. Nature 528, 77–83 (2015).
Kaufman, A. M. et al. Quantum thermalization through entanglement in an isolated many-body system. Science 353, 794–800 (2016).
Smith, J. et al. Many-body localization in a quantum simulator with programmable random disorder. Nat. Phys. 12, 907–911 (2016).
Lukin, A et al. Probing entanglement in a many-body-localized system. Science 364, 256–260 (2018).
Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).
Choi, J.-y et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016).
Lüschen, H. P. et al. Signatures of many-body localization in a controlled open quantum system. Phys. Rev. X 7, 011034 (2017).
Swingle, B. Unscrambling the physics of out-of-time-order correlators. Nat. Phys. 14, 988–990 (2018).
Hastings, M. B. & Koma, T. Spectral gap and exponential decay of correlations. Commun. Math. Phys. 265, 781–804 (2006).
Hauke, P. & Tagliacozzo, L. Spread of correlations in long-range interacting quantum systems. Phys. Rev. Lett. 111, 207202 (2013).
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).
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).
Else, D. V., Machado, F., Nayak, C. & Yao, Y. An improved Lieb–Robinson bound for many-body Hamiltonians with power-law interactions. Preprint at https://arxiv.org/abs/1809.06369 (2018).
Altman, E. Many-body localization and quantum thermalization. Nat. Phys. 14, 979–983 (2018).
Žnidarič, M., Prosen, Tcv & Prelovšek, P. Many-body localization in the Heisenberg xxz magnet in a random field. Phys. Rev. B 77, 064426 (2008).
Bardarson, J. H., Pollmann, F. & Moore, J. E. Unbounded growth of entanglement in models of many-body localization. Phys. Rev. Lett. 109, 017202 (2012).
Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).
Kaufman, A. M. et al. Entangling two transportable neutral atoms via local spin exchange. Nature 527, 208–211 (2015).
Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604 (2017).
Friis, N. et al. Observation of entangled states of a fully controlled 20-qubit system. Phys. Rev. X 8, 021012 (2018).
Zeiher, J. et al. Coherent many-body spin dynamics in a long-range interacting Ising chain. Phys. Rev. X 7, 041063 (2017).
Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).
Labuhn, H. et al. Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models. Nature 534, 667–670 (2016).
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).
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).
Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225–1286 (2010).
Lahaye, T., Menotti, C., Santos, L., Lewenstein, M. & Pfau, T. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009).
Vaidya, V. D. et al. Tunable-range, photon-mediated atomic interactions in multimode cavity QED. Phys. Rev. X 8, 011002 (2018).
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).
Norcia, M. A. et al. Cavity mediated collective spin exchange interactions in a strontium superradiant laser. Science 361, 259–262 (2017).
Jurcevic, P. et al. Spectroscopy of interacting quasiparticles in trapped ions. Phys. Rev. Lett. 115, 100501 (2015).
Langen, T. et al. Experimental observation of a generalized Gibbs ensemble. Science 348, 207–211 (2015).
Keesling, A. et al. Probing quantum critical dynamics on a programmable Rydberg simulator. Preprint at https://arxiv.org/abs/1809.05540 (2018).
Calabrese, P. & Cardy, J. Entanglement entropy and quantum field theory. J. Stat. Mech. Theory Exp. 2004, P06002 (2004).
Calabrese, P. & Cardy, J. Evolution of entanglement entropy in one-dimensional systems. J. Stat. Mech. Theory Exp. 2005, P04010 (2005).
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).
Kitaev, A. & Preskill, J. Topological entanglement entropy. Phys. Rev. Lett. 96, 110404 (2006).
Levin, M. & Wen, X.-G. Detecting topological order in a ground state wavefunction. Phys. Rev. Lett. 96, 110405 (2006).
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).
Hahn, E. L. Spin echoes. Phys. Rev. 80, 580–594 (1950).
Larkin, A. & Ovchinnikov, Y. N. Quasiclassical method in the theory of superconductivity. Sov. Phys. JETP 28, 1200 (1969).
Fan, R., Zhang, P., Shen, H. & Zhai, H. Out-of-time-order correlation for many-body localization. Sci. Bull. 62, 707–711 (2017).
Swingle, B. & Chowdhury, D. Slow scrambling in disordered quantum systems. Phys. Rev. B 95, 060201 (2017).
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).
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).
Li, J. et al. Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator. Phys. Rev. X 7, 031011 (2017).
Wei, K. X., Ramanathan, C. & Cappellaro, P. Exploring localization in nuclear spin chains. Phys. Rev. Lett. 120, 070501 (2018).
Meier, E. J., Ang’ong’a, J., An, F. A. & Gadway, B. Exploring quantum signatures of chaos on a Floquet synthetic lattice. Preprint at https://arxiv.org/abs/1705.06714v1 (2018).
Landsman, K. A. et al. Verified quantum information scrambling. Nature 567, 61–65 (2019).
Sachdev, S. & Ye, J. Gapless spin-fluid ground state in a random quantum Heisenberg magnet. Phys. Rev. Lett. 70, 3339–3342 (1993).
Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011).
Lucas, A. Quantum many-body dynamics on the star graph. Preprint at https://arxiv.org/abs/1903.01468 (2019).
Martinez, E. A. et al. Real-time dynamics of lattice gauge theories with a few-qubit quantum computer. Nature 534, 516 (2016).
Preskill, J. Quantum computing and the entanglement frontier. Preprint at https://arxiv.org/abs/1203.5813 (2012).
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).
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).
Nahum, A., Vijay, S. & Haah, J. Operator spreading in random unitary circuits. Phys. Rev. X 8, 021014 (2018).
Eckardt, A. Colloquium: Atomic quantum gases in periodically driven optical lattices. Rev. Mod. Phys. 89, 011004 (2017).
Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217–220 (2017).
Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).
Deutsch, C. et al. Spin self-rephasing and very long coherence times in a trapped atomic ensemble. Phys. Rev. Lett. 105, 020401 (2010).
Solaro, C. et al. Competition between spin echo and spin self-rephasing in a trapped atom interferometer. Phys. Rev. Lett. 117, 163003 (2016).
Piéchon, F., Fuchs, J. N. & Laloë, F. Cumulative identical spin rotation effects in collisionless trapped atomic gases. Phys. Rev. Lett. 102, 215301 (2009).
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).
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).
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).
Li, J. et al. A stripe phase with supersolid properties in spin–orbit coupled Bose–Einstein condensates. Nature 543, 91–94 (2017).
Jurcevic, P. et al. Direct observation of dynamical quantum phase transitions in an interacting many-body system. Phys. Rev. Lett. 119, 080501 (2017).
Smale, S. et al. Observation of a dynamical phase transition in a quantum degenerate Fermi gas. Preprint at https://arxiv.org/abs/1806.11044 (2018).
Acknowledgements
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
Authors and Affiliations
Contributions
All authors worked together on preparing and writing this Perspective.
Corresponding author
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
About this article
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). https://doi.org/10.1038/s42254-019-0090-y
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s42254-019-0090-y
- Springer Nature Limited
This article is cited by
-
Measuring statistics-induced entanglement entropy with a Hong–Ou–Mandel interferometer
Nature Communications (2024)
-
Open system approach to neutrino oscillations in a quantum walk framework
Quantum Information Processing (2024)
-
Information dissemination
Nature Physics (2022)
-
Fluctuation relations for irreversible emergence of information
Scientific Reports (2022)
-
The randomized measurement toolbox
Nature Reviews Physics (2022)