Year: 2026
Type: preprint
Abstract: Pure two-qubit entanglement is usually characterized by scalar quantities such as concurrence. Here we show that it also has a natural geometric form. In the Pauli correlation tensor, maximally entangled states appear as improper orthogonal maps between two local Bloch spheres. These maps are roto-reflections. For partially entangled pure states, the same roto-reflection geometry is recovered after separating the contraction associated with concurrence. We call the corresponding geometric object the Entanglement Roto-Reflection Plane (ERRP). It organizes the maximally correlated directions of the two-qubit state and provides a covariant geometric complement to the scalar magnitude of entanglement. We further illustrate the usefulness of this geometry through partial transposition, where it provides a direct construction of the maximally entangled negative eigenvector and a geometric interpretation of negativity.
Source: arXiv (Cornell University)
Authors: Filatov, Stanislav, Auzinsh, Marcis
Institution: University of Latvia
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G4951683367
OpenAlex ID: W7164499987