Quantifying entanglement in macroscopic systems

Benjamin Yadin, Matteo Fadel

The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with multiple approaches having varying interpretations and levels of computability and measurability. Here, we introduce two measures that capture independent macroscopic properties: i) extensive size, measuring the degree of coherence in position or momentum observables relative to atomic-scale units, and ii) entangled size, quantifying the number of entangled subsystems. These measures unify many desirable features of past proposals while having rigorously justified interpretations from quantum information theory in terms of coherence and multipartite entanglement. We demonstrate how to estimate them and obtain lower-bounds using experimental data from micro-mechanical oscillators and diffracting molecules. Notably, we find evidence for genuine multipartite entanglement of 10 5 to 10 7 atoms in recent mechanical superposition states.

Neha Pathania, Tabish Qureshi

Jincheng Zhang

Quantum entanglement, a fundamental phenomenon in quantum mechanics, exhibits a remarkable degree of correlation between particles, defying classical intuition. However, its practical implications, particularly regarding macroscopic systems, remain largely unexplored. This research investigates the Quantum Entanglement Gradient Field (QEFG) – a novel framework for quantifying the evolution of entanglement through a gradient field, leveraging both quantum mechanics and statistical thermodynamics. The QEFG offers a new lens for understanding the impact of quantum correlations on macroscopic systems, moving beyond simple entanglement measurements. This paper presents a mathematically rigorous model for modeling entanglement as a gradient, incorporating both quantum mechanical principles and statistical thermodynamics to predict entanglement decay and stability. The core mechanism aims to provide a quantitative tool for analyzing entanglement dynamics, opening avenues for potentially significant advancements in our comprehension of quantum phenomena.

David S. Simon

Jie‐Qiao Liao, WU Qin-Qin, Franco Nori

We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should work in the single-photon strong-coupling regime and the deep-resolved-sideband regime.