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This research introduces the Entanglement Roto-Reflection Plane (ERRP), offering a geometric framework to characterize pure two-qubit entanglement beyond traditional scalar metrics like concurrence. By mapping maximally entangled states as roto-reflections between local Bloch spheres, the study provides new covariant tools for analyzing quantum correlations in fundamental systems.
Roto-Reflection Geometry of Pure Two-Qubit Entanglement
arXiv:2606.12637v1 Announce Type: new 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.
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.
arXiv:2606.12637 [quant-ph]
(or arXiv:2606.12637v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.12637 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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