A Geometric Theory of Quantum Entanglement

@misc{capra2026geometric,
  title = {{A Geometric Theory of Quantum Entanglement}},
  author = {Lorenzo Capra and Lucio de Simone and Roberto Franzosi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11720},
  eprint = {2609.11720},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11720},
}

TY  - UNPB
TI  - A Geometric Theory of Quantum Entanglement
AU  - Lorenzo Capra
AU  - Lucio de Simone
AU  - Roberto Franzosi
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11720
UR  - https://arxiv.org/abs/2609.11720
AB  - Entanglement Distance (ED) was originally proposed as a geometric measure of entanglement derived from the Fubini-Study metric on the projective Hilbert space. Independently, the Meyer-Wallach and Scott measures quantify multipartite entanglement via linear entropy. In this work, we demonstrate that these two seemingly distinct frameworks are mathematically identical for pure states of arbitrary finite dimensions. We prove that ED arises naturally as the trace of the Fubini-Study metric tensor over the local subalgebra of observables. Crucially, this geometric unification yields a direct operational interpretation: the global entanglement of a pure state is exactly proportional to the total Quantum Fisher Information (QFI) available for local unitary estimation. This bridges abstract information geometry with quantum metrology, demonstrating that ED dynamically quantifies resourcefulness for distributed quantum sensing, identifying Heisenberg-limited sensitivity in regimes where standard variance-based witnesses fail.
ER  -