Measurement - induced qudit geometric discord

TL;DR

This paper investigates the measurement-induced geometric discord for qudits using the trace norm, extending known properties from qutrits to arbitrary dimensions, and highlights fundamental differences between qubits and higher-dimensional systems.

Contribution

It generalizes properties of measurement-induced geometric discord from qutrits to all qudits, providing rigorous proofs and insights into the geometric structure of quantum correlations.

Findings

Systems with d ≥ 3 exhibit similar quantum correlation behavior.

Qubit systems are uniquely simple due to underlying geometry.

Pronounced differences exist between d=2 and d=3 systems.

Abstract

We study the measurement-induced geometric discord based on the trace norm and generalize some properties known for qutrits to qudits. Previous preliminary results for bipartite qutrit systems (i.e. d=3 systems) are here strictly proved for arbitrary d. Present study supports observations, coming also from other approaches, that systems with $d \geq 3$ show similar behaviour when quantum correlations are concerned, but there is pronounced difference between d=2 and d=3. Qubit systems are exceptionally simple. Underlying geometry of state spaces and related Lie groups are responsible for that.