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arXiv:2505.01394 · Europhysics Letters (EPL)

Quantifying entanglement from the geometric perspective

Lisa T. Weinbrenner, Otfried Gühne

Published Aug 27, 2025• 4 citations
arXivHTMLPDF

Abstract

Abstract Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of quantifying the amount of entanglement in a quantum state. We present a review on the geometric measure of entanglement, being a quantifier based on the distance of a state to the nearest separable state. We explain basic properties, existing methods to compute it, its operational interpretations, as well as scaling and complexity issues. We point out intimate relations to fundamental problems in mathematics concerning eigenvalues and norms of tensors. Consequently, the geometric measure of entanglement provides a playground where physical intuition and mathematical rigor benefit from each other.

DOI
10.1209/0295-5075/adffb5

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Quantum entanglement, a cornerstone of quantum mechanics, exhibits a profound connection to geometry. This research explores the potential of leveraging this entanglement to develop a novel geometric measurement technique for quantifying quantum system non-locality. We propose a method that translates the inherent properties of entangled states into measurable geometric quantities, offering a pathway towards more precise and insightful interpretations of quantum states. The core claim is that this approach provides a new perspective on evaluating and characterizing quantum systems' non-local behavior. This work investigates the theoretical underpinnings of this measurement method and demonstrates its potential for significant advancements in quantum state analysis.
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