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

TL;DR

This paper introduces an energy-entanglement performance equation that quantifies the physical cost of generating non-local entanglement, linking theoretical bounds with experimental observables and revealing a fundamental performance trade-off.

Contribution

It unifies quantum speed limits and Lieb-Robinson bounds into a new framework that measures the cost of entanglement generation and identifies performance bottlenecks.

Findings

Establishes a measurable proxy for complexity in quantum systems.

Defines a performance frontier constrained by theoretical bounds.

Provides a diagnostic tool for optimizing entanglement generation processes.

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.