Geometric Aspects of Entanglement

@misc{simone2026geometric,
  title = {{Geometric Aspects of Entanglement}},
  author = {Lucio De Simone and Lorenzo Capra and Arthur Vesperini and Leonardo Rossi and Loris Di Cairano and Roberto Franzosi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03446},
  eprint = {2610.03446},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03446},
}

TY  - UNPB
TI  - Geometric Aspects of Entanglement
AU  - Lucio De Simone
AU  - Lorenzo Capra
AU  - Arthur Vesperini
AU  - Leonardo Rossi
AU  - Loris Di Cairano
AU  - Roberto Franzosi
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03446
UR  - https://arxiv.org/abs/2610.03446
AB  - Quantum entanglement is a fundamental resource in quantum information theory, yet its general characterization and quantification remain challenging, especially in multipartite systems. In this work we investigate entanglement from a geometric perspective, focusing on the Riemannian structure induced by the Fubini--Study metric on the projective Hilbert space of multi-qubit quantum states. By exploiting the local-unitary invariance of this metric, we derive the entanglement distance (ED), a geometric measure that quantifies entanglement as an obstruction to locally minimizing the sum of squared Fubini--Study distances generated by local operations. We analyze the properties of ED for pure multi-qubit states and discuss its behavior under local operations and classical communication. In particular, we show that ED reproduces established entanglement measures in well-defined and restricted settings. For pure states of two qubits, ED reduces to an exact monotone function of the concurrence and, independently, to an explicit monotone function of the entropy of entanglement. These results provide a clear geometric interpretation of standard bipartite entanglement measures within the present framework, while highlighting the limitations of such correspondences beyond the two-qubit case.
ER  -