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 quantifyingthe amount of entanglement in a quantum state. We presenta 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 geometricmeasure of entanglement provides a playground where physical intuition and mathematical rigor benefit from each other.
Weinbrenner et al. (Wed,) studied this question.