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Dynamics of quantum information
R. J. Lewis-Swan, A. Safavi-Naini, A. M. Kaufman, A. M. Rey
TL;DR
Entangled many-body systems are difficult to create and characterize, yet understanding their dynamics matters across quantum technologies and complex-system physics. This Perspective reviews propagation bounds and experimental tools for probing entanglement and scrambling. In reviewed experiments, correlation dynamics were approximately consistent with a linear light cone for interaction exponent α > 1.41, with strong deviations below that value.
Problem
Entangled many-body systems are difficult to create, characterize experimentally, and model theoretically, and systems with even a few tens of interacting particles can exhibit behavior inaccessible to classical simulations.
Source: §1 · p. 2Method
The Perspective surveys propagation bounds and experimental approaches to measuring correlations, entanglement dynamics, and information scrambling in quantum many-body systems.
Source: §1 · p. 2Results
For α > 1.41, correlation dynamics were approximately consistent with a linear light cone, while smaller α showed strong deviations from a linear wavefront.
Source: §3 · p. 6Takeaways & Limitations
New in-situ techniques have enabled direct measurements of entanglement between parts of a quantum system and studies of its role in the emergence of statistical mechanics.
Source: §1 · p. 2Entanglement measurements remain constrained to a handful of particles, and detailed studies in systems of many tens to hundreds of particles remain an open challenge.
Source: §6 · p. 15
Abstract
from arXiv · showhide
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 unify and confront common problems in otherwise disparate fields in physics, such as quantum statistical mechanics and cosmology. On the experimental side the impressive developments on the manipulation of neutral atoms and trapped ions are providing new capabilities 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 great insight into the intrinsic connection between entanglement and thermodynamics, bounds on information transport and computational complexity of interacting systems. In turn this understanding should enable the realization of quantum technologies.
1 Introduction
The Perspective connects entanglement to questions spanning quantum information, many-body physics, and black-hole physics. It outlines how experimental control now enables studies of entanglement and correlations in systems that are difficult to characterize or model.
1 Introduction
- Entanglement links atomic, molecular and optical physics, condensed matter, general relativity, and high-energy physics, including questions about black-hole horizons and emergent space-time [1] [2] [4].Entangled states also appear in non-equilibrium dynamics of isolated many-body systems [8], while entanglement distribution is related to quantum chaos and complexity [11] [12].Source: §1 · pp. 1–2
- Creating, characterizing, and theoretically modeling entangled many-body systems is difficult, and systems of even a few tens of interacting particles can exhibit behavior inaccessible to classical simulations.Advances in quantum gas microscopes, optical tweezers, and trapped-ion arrays now make it possible to probe entanglement and many-body correlations.Source: §1 · p. 2
- The Perspective reviews information-propagation speed, measurements of higher-order correlations and entanglement, many-body localization, and scrambling through out-of-time-order correlations.It proceeds from propagation after a quench to measurement techniques, entanglement dynamics, and scrambling.Source: §1 · p. 2
Theoretical developments
The section frames information propagation and entanglement dynamics as questions about thermalization and fundamental spreading bounds. It contrasts short-range bounds with unresolved long-range behavior and describes scrambling as a route to thermalization.
Theoretical developments
- The spread and distribution of entanglement in non-equilibrium many-body systems matter for quantum technologies, quantum-circuit design, and the emergence of thermodynamics in isolated systems [8, 9].Interactions can build entanglement, motivating questions about how quickly it spreads.Source: Theoretical developments · p. 3
- Entanglement growth can accompany information scrambling, allowing smaller subsystems to reach steady states described by statistical ensembles and thus thermalize.This connects microscopic quantum dynamics with behavior consistent with macroscopic statistical mechanics.Source: Theoretical developments · p. 3
- For short-range interactions, the Lieb-Robinson bound limits correlations to a linear effective light cone, while propagation speeds and possible fundamental bounds for generic long-range interactions remain uncertain.It is also unclear whether cold-atom systems saturate the conjectured bounds.Source: Theoretical developments · p. 3
- Many-body localized systems can retain retrievable quantum correlations and avoid information spreading for arbitrarily long times, typically through strong disorder together with interactions.This contrasts with the thermalization behavior discussed for generic systems.Source: Theoretical developments · pp. 3–4
Experimental platforms
Synthetic AMO platforms provide microscopic control and tunable interactions for studying many-body information dynamics. The section describes interaction types and how their range and implementation vary across platforms.
Experimental platforms
- Ultracold neutral atoms and trapped-ion arrays are synthetic quantum many-body platforms used to study information propagation, thermalization, scrambling, and many-body localization.Experiments are beginning to achieve microscopic control over individual qubits and tunable interactions.Source: Experimental platforms · p. 4
- Collisions dominate interactions in ultracold gases and are controlled by tuning scattering length [53]; van der Waals interactions ∝1/r6 occur in Rydberg atoms, while dipolar interactions ∝1/r3 occur in magnetic atoms, polar molecules, and Rydberg atoms [54].Dipolar interactions additionally depend on the relative orientation of the interacting dipoles.Source: Experimental platforms · p. 5
- In trapped ions, laser-induced spin-dependent forces virtually excite phonons that mediate spin-spin couplings through collective modes [55] [56] [57].The resulting couplings inherit the non-local structure of those modes.Source: Experimental platforms · p. 5
3 Measuring correlation functions
Across cold-atom and trapped-ion platforms, spatial correlations reveal finite-speed propagation and departures from a linear light cone; higher-order correlations extend these measurements to relaxation and many-body-state complexity.
3 Measuring correlation functions
- A Mott-to-superfluid quench produced doublon/holon pairs whose correlations propagated at a constant characteristic velocity, consistent with short-range Lieb-Robinson bounds [14].The experiment used a 1D Bose-Hubbard model of 87Rb in an optical lattice.Source: §3 · p. 5
- For α > 1.41, trapped-ion dynamics approximately followed a linear light cone, while smaller α produced strong deviations that motivated improved long-range bounds [39].The experiments used power-law spin couplings and different quench protocols, including a single local excitation and a global quench [58].Source: §3 · pp. 5–6
- z_c ∼ 2ct: a split 1D Bose gas developed a steady state first at short length scales, consistent with a generalized Gibbs ensemble accounting for conserved quantities.Two-point phase correlations were measured using matter-wave interference.Source: §3 · p. 6
- Atom-chip experiments reached up to 10-point correlations and full distribution functions, enabling characterization of many-body-state complexity through high-order correlations’ non-factorizability.The sine-Gordon experiment used tunnel-coupled 1D Bose gases.Source: §3 · p. 6
- In Rydberg arrays, non-trivial spatial spin correlations showed a characteristic delay used as an experimental signature of correlation-propagation bounds [52, 61].The experiments studied dynamics while tuning parameters in neutral-atom spin models.Source: §3 · p. 8
4 Probing entanglement entropy
This section surveys how entanglement entropy can be measured in AMO systems and used to characterize thermalization and many-body localization. It also explains why correlations alone and full-state tomography are insufficient for many-body entanglement measurements.
4 Probing entanglement entropy
- Correlations alone do not always certify entanglement, and full-state tomography scales poorly, motivating newer protocols for direct measurement of entanglement dynamics.These protocols leverage advances in microscopic control of large AMO systems.Source: §4 · p. 8
- For spatial subsystems, interactions can turn an initially unentangled product state into mixed reduced states whose entropy quantifies entanglement.The section describes this in terms of von Neumann and Rényi entropies.Source: §4 · pp. 8–9
- A quantum gas microscope protocol interferes two identically quenched copies and uses number-resolved measurements to obtain Tr(ρ²) for subsystems and the full system.It was applied to a six-site, unity-filled Bose-Hubbard chain quenched from the Mott insulator into the superfluid region.Source: §4 · p. 9
- Entanglement entropy rose from zero and saturated near the subsystem’s expected thermal entropy, while global entropy stayed near unity and local observables approached thermal predictions.The long-time entropy scaling was contrasted with that of the ground state at the same lattice parameters.Source: §4 · pp. 10–11
- Randomized measurements in a trapped-ion simulator measured Rényi entropy for partitions up to 10 of 20 ions, using a single system copy.Well-understood decoherence sources allowed local and global entropy to be distinguished.Source: §4 · pp. 10–11
- In many-body localization, entropy grows logarithmically, but direct measurements are size- and coherence-limited; experiments used imbalance, Hamming distance, and entanglement proxies to distinguish phases.A direct half-chain entropy measurement also showed marked differences between thermalizing and MBL phases.Source: §4 · p. 12
5 Scrambling of quantum information
Out-of-time-order correlations (OTOCs) probe information scrambling by tracking the non-commutativity of initially commuting operators. Experiments use effective time reversal to measure OTOCs, which also support entanglement and many-body-correlation analyses.
5 Scrambling of quantum information
- OTOCs quantify the non-commutativity of initially commuting operators and characterize quantum chaos, operator spreading, and information scrambling.They are expectations of products of operators at different times and are closely connected with spin-echo protocols.Source: §5 · p. 13
- Effective reversal of the Hamiltonian in spin-echo protocols enables OTOC measurements across trapped-ion, nuclear magnetic resonance, Bose-Einstein condensate, and ion-chain experiments.For the described optical-platform protocol, choosing V so the initial state is its eigenstate reduces the OTOC to measuring V† on the time-evolved state.Source: §5 · pp. 13–14
- OTOCs have been used to reconstruct entanglement entropy and to infer many-body correlations from Fourier decompositions.A seven-qubit ion-trap protocol also distinguished decoherence effects from scrambling.Source: §5 · pp. 13–14
- A nonzero Fourier amplitude A_m indicates m-body correlations among m spins.The trapped-ion analysis uses grouped ions to indicate the corresponding correlated spins.Source: §5 · p. 14
- Engineered AMO interactions may realize fast-scrambling models such as Sachdev-Ye-Kitaev, while black-hole scrambling saturates the bound λ ≤ 2πT.The paper describes tabletop analogue models as a way to explore these connections.Source: §5 · pp. 14–15
6 Outlook
The outlook identifies scaling entanglement measurements beyond a handful of particles as an open challenge. It also points to digital simulation and driven or dissipative dynamics as directions for extending the study.
6 Outlook
- Entanglement measurements in quantum gas microscopes, microtraps, and trapped-ion systems remain limited to a handful of particles; measurements across tens to hundreds remain an open challenge.The paper calls for efficient, scalable alternative protocols for creating or measuring entanglement.Source: §6 · p. 15
- Digital quantum simulators are expected to enable investigation of more tunable physical systems, including models for high-energy physics, fast scrambling, and random-unitary quantum supremacy demonstrations.The paper also notes possible studies of systems that saturate or, under specific conditions, violate the information-scrambling bound.Source: §6 · p. 15
- The discussion is restricted to time-independent Hamiltonians, while driven and dissipative phenomena offer regimes beyond unitary, time-independent dynamics.Examples include Floquet dynamics, time crystals, quantum synchronization, self-organization, and dynamical phase transitions.Source: §6 · p. 15