Measurement - induced qudit geometric discord
Piotr Lugiewicz, Andrzej Frydryszak, Lech Jakobczyk

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 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.
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