Roto-Reflection Geometry of Pure Two-Qubit Entanglement

Stanislav Filatov; Marcis Auzinsh

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arXiv · 2606.12637

Roto-Reflection Geometry of Pure Two-Qubit Entanglement

Stanislav Filatov·Marcis Auzinsh

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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.

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Stanislav Filatov, Marcis Auzinsh. 2026-06-10. Roto-Reflection Geometry of Pure Two-Qubit Entanglement. https://arxiv.org/abs/2606.12637

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