Delocalization of quantum information in long-range interacting systems (2105.06346v2)

Abstract: We investigate the delocalization of quantum information in the nonequilibrium dynamics of the $XY$ spin chain with asymptotically decaying interactions $\sim 1/r^{\alpha}$. As a figure of merit, we employ the tripartite mutual information (TMI), whose sign indicates if quantum information is predominantly shared globally. Interestingly, the sign of the TMI distinguishes regimes of the exponent $\alpha$ that are known for different behaviour of information propagation. While an effective causal region bounds the propagation of information, if interactions decay sufficiently fast, this information is mainly delocalized, which leads to the necessity of global measurements. Furthermore, the results indicate that mutual information is monogamous for all possible partitionings in this case, implying that quantum entanglement is the dominant correlation. If interactions decay sufficiently slow, though information can propagate (quasi-)instantaneously, it is mainly accessible by local measurements at early times. Furthermore, it takes some finite time until correlations start to become monogamous, which suggests that apart from entanglement, other nonmonogamous correlations are sizeable at early times. Our findings give new insights into the dynamics, and structure of quantum information in many-body systems with long-range interactions, and might get verified on state-of-the-art experimental platforms.

• The paper uses tripartite mutual information (TMI) to study quantum information delocalization in long-range interacting XY spin chains, focusing on how interaction decay ($\alpha$) influences information distribution.
• Distinct regimes of information propagation are identified based on the interaction decay exponent $\alpha$; small $\alpha$ allows local accessibility and late delocalization, sometimes without initial monogamy of mutual information.
• Numerical simulations and results show a transition in multipartite correlations marked by TMI's sign change over time, suggesting experimental verification using trapped ions or other quantum simulation platforms is feasible.

Delocalization of Quantum Information in Long-Range Interacting Systems

The paper "Delocalization of Quantum Information in Long-Range Interacting Systems" investigates the dynamics of quantum information in the context of long-range interactions within many-body systems. A central theme is understanding how an $XY$ spin chain, influenced by interactions that decay as a power law ($\sim 1/r^{\alpha}$), controls the delocalization of quantum information.

Study Overview

The authors utilize the tripartite mutual information (TMI) as a key metric for examining quantum information distribution. This paper illuminates the conditions under which quantum information becomes delocalized, meaning it is shared more globally rather than being confined to specific subsystems. The sign and behavior of the TMI, particularly in relation to the exponent $\alpha$ of the interaction decay, reveal different regimes of information propagation.

Main Findings

1. Information Propagation Regimes: The paper identifies distinct regimes based on the exponent $\alpha$. When interactions decay quickly with distance ($\alpha$ is large), a well-defined causal region limits information propagation, which results in delocalization observable only after a certain time. In contrast, slower-decaying interactions allow information to be quasi-instantaneously accessible locally at early times, and delocalization occurs at a later stage.
2. Delocalization and Monogamy: For small exponents, the time when quantum information begins to exhibit delocalized behavior implies regimes where monogamy of mutual information does not initially hold. This means that at early times, entanglement is not the dominant correlation form, contrasting with regimes where $\alpha$ is large, and mutual information is mainly monogamous.
3. Numerical Results: Through numerical simulations of $N=20$ to $N=24$ spin systems, the paper quantitatively examines how TMI evolves over time and different $\alpha$ values. The results indicate a distinct transition in the nature of multipartite correlations, demonstrated by the TMI's sign change over time.
4. Experimental Feasibility: The authors propose using trapped ions and other quantum simulation platforms for experimental verification of their results. They acknowledge the feasibility constraints due to system size and the necessity of techniques like quantum state tomography for entropy measurement.

Implications and Future Directions

Theoretical insights from this research suggest potential opportunities for optimizing quantum information distribution in long-range interacting systems. The findings have implications for quantum computing, particularly in understanding how information spreads through quantum networks or during quantum simulations.

The research opens avenues for further exploration of quantum information structure beyond bipartite entanglement, particularly in quantum systems with more complex interaction patterns. Identifying conditions under which entanglement becomes the dominant correlation reveals fundamental differences in how quantum systems might process and transmit information on a large scale.

Future work might explore the effects of system dimensionality, analyze different initial states, or expand to interactions that combine long-range and local terms. By experimenting with real systems, researchers can test theoretical predictions and refine our understanding of information dynamics in quantum mechanics.

The paper establishes a foundation for exploring how complex entanglements evolve, offering valuable insights into many-body quantum dynamics and their numerous applications in quantum technology development.