| Issue |
EPL
Volume 151, Number 6, September 2025
|
|
|---|---|---|
| Article Number | 68001 | |
| Number of page(s) | 7 | |
| Section | Quantum information | |
| DOI | https://doi.org/10.1209/0295-5075/adffb5 | |
| Published online | 11 September 2025 | |
Quantifying entanglement from the geometric perspective
Naturwissenschaftlich-Technische Fakultät, Universität Siegen - Walter-Flex-Straße 3, 57068 Siegen, Germany
Received: 26 May 2025
Accepted: 26 August 2025
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.
© 2025 The author(s)
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