A class of symmetric Bell diagonal entanglement witnesses - a geometric perspective

Abstract

We provide a class of Bell diagonal entanglement witnesses displaying an additional local symmetry -- a maximal commutative subgroup of the unitary group U(n). Remarkably, this class of witnesses is parameterized by a torus being a maximal commutative subgroup of an orthogonal group SO(n-1). It is shown that a generic element from the class defines an indecomposable entanglement witness. The paper provides a geometric perspective for some aspects of the entanglement theory and an interesting interplay between group theory and block-positive operators.

14 pages; Submission to Special Issue of J. Phys. A celebrating 50 years of Bell-nonlocality

References in corpus (6)

• Entanglement detection
• Geometric entanglement witnesses and bound entanglement
• Entanglement witnesses and geometry of entanglement of two--qutrit states
• A new class of states with positive partial transposition
• Detection and typicality of bound entangled states
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Cited by in corpus (2)

• A class of Bell diagonal entanglement witnesses in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$: optimization and the spanning property
• Detecting Entanglement by State Preparation and Local Measurements