Roto-Reflection Geometry of Pure Two-Qubit Entanglement

• URL: http://arxiv.org/abs/2606.12637v1
• Date: Wed, 10 Jun 2026 20:02:20 GMT
• Title: Roto-Reflection Geometry of Pure Two-Qubit Entanglement
• Abstract summary: In the Pauli correlation tensor, maximally entangled states appear as improper maps between two local Bloch spheres.<n>For partially entangled pure states, the same roto-reflection geometry is recovered after separating the contraction associated with concurrence.<n>We call the corresponding geometric object the Entanglement Roto-Reflection Plane (ERRP)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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