From local to non local entanglement

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, exhibits a peculiar phenomenon – non-locality. This paper proposes a novel framework for verifying entanglement non-locality, leveraging precise modeling of entanglement's non-local properties and integrating it with a quantum topological measurement technique. The core claim is that this framework will provide a more rigorous and effective method for detecting and quantifying the non-local aspects of entangled systems. We introduce a new approach to entanglement testing, centered around a modified measurement protocol inspired by quantum topology. This approach seeks to circumvent traditional limitations of local measurement techniques by explicitly modeling the entanglement's inherent non-locality. This paper explores the theoretical foundations and experimental implications of this framework, aiming to advance our understanding of entanglement and its potential for broader applications.

Jordi Tura i Brugués

Wu, Xiaohua

Zhao-Yang Tong, Kuang Le-Man

We study the degree to which quantum entanglement survives when a three-qubit entangled state is copied by using local and non-local processes, respectively, and investigate iterating quantum copying for the three-qubit system. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system. We show that both local and non-local copying processes degrade quantum entanglement in the three-particle system due to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubit entanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find that non-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state via non-local cloning exhibits the fidelity better than local cloning.

André Allan Méthot, Valerio Scarani

Ever since the work of Bell, it has been known that entangled quantum states can rise non-local correlations. However, for almost forty years, it has been assumed that the most non-local states would be the maximally entangled ones. Surprisingly it is not the case: non-maximally entangled states are generally more non-local than maximally entangled states for all the measures of non-locality proposed to date: Bell inequalities, the Kullback-Leibler distance, entanglement simulation with communication or with non-local boxes, the detection loophole and efficiency of cryptography. In fact, one can even find simple examples in low dimensions, confirming that it is not an artefact of a specifically constructed Hilbert space or topology. This anomaly shows that entanglement and non-locality are not only different concepts, but also truly different resources. We review the present knowledge on this anomaly, point out that Hardy's theorem has the same feature, and discuss the perspectives opened by these discoveries.

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato +2 more