Quantum Discord and the Geometry of Bell-Diagonal States

TL;DR

This paper explores the geometric structure of Bell-diagonal states in two qubits, analyzing entanglement and quantum discord levels, revealing their nonanalytic behavior and non-convexity, providing insights into quantum correlations.

Contribution

It offers a geometric visualization of entanglement and discord for Bell-diagonal states, highlighting their nonanalytic and non-convex properties under decoherence.

Findings

Level surfaces of entanglement and discord are characterized geometrically.

Quantum discord is shown to be neither convex nor concave.

The structure of quantum correlations is visualized within a tetrahedral state space.

Abstract

The set of Bell-diagonal states for two qubits can be depicted as a tetrahedron in three dimensions. We consider the level surfaces of entanglement and quantum discord for Bell-diagonal states. This provides a complete picture of the structure of entanglement and discord for this simple case and, in particular, of their nonanalytic behavior under decoherence. The pictorial approach also indicates how to show that discord is neither convex nor concave.