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arXiv · 2508.03781

The Cost of Nonlocality: A Dynamical Performance Equation of Energy-Entanglement-Complexity

HongZheng Liu·YiNuo Tian·Zhiyue Wu
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Abstract

This work aims to quantify the physical cost of generating non-local entanglement in systems governed by local interactions. By unifying the quantum speed limit and Lieb-Robinson bounds, we establish an "energy-entanglement performance equation." This framework connects theoretical computational complexity with experimental observables by introducing a measurable proxy for complexity, thereby revealing a performance trade-off among the "energy variance-entanglement product," the strength of local interactions, and dynamical efficiency. Our work not only defines a "performance frontier"-constrained by theoretical bounds and amenable to experimental benchmarking-but also provides a novel diagnostic tool for identifying the performance bottlenecks of a process.

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HongZheng Liu, YiNuo Tian, Zhiyue Wu. 2025-08-05. The Cost of Nonlocality: A Dynamical Performance Equation of Energy-Entanglement-Complexity. https://arxiv.org/abs/2508.03781

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