Topological Quantum Metrology: Measuring Entanglement Topology via Persistent Homology with Quadratic Scaling
Year: 2025
Type: preprint
Abstract: We introduce τ_topo — a topological quantum metric derived from persistent homology of entanglement morphism graphs — that quantifies global entanglement structure invariant under local unitaries and scalable to N-qubit systems with O(N²) measurement complexity. Unlike bipartite entropy, τ_topo captures higher-order connectivity via β₁-barcode length in Rips filtrations of Pauli-weighted state distributions.
Author: Udo Granops
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4415109688
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