Local Quantum Uncertainty and Bounds on Quantumness for Orthogonally invariant class of states

TL;DR

This paper investigates the local quantum uncertainty and other quantum correlation measures for orthogonally invariant states, including Werner and Isotropic states, aiming to find closed-form formulas and compare bounds with entanglement.

Contribution

It derives potential closed-form formulas for LQU, geometric discord, and measurement-induced nonlocality for orthogonally invariant states, and compares quantum correlation bounds with entanglement.

Findings

Derived bounds for quantum correlations in orthogonally invariant states.

Compared quantum correlation measures with entanglement for specific subclasses.

Explored the possibility of closed-form expressions for LQU and other measures.

Abstract

Local quantum uncertainty (in short LQU) was introduced by Girolami et. al.(Phy. Rev. Lett. \textbf{110}, 240402) as a measure of quantum uncertainty in a quantum state as achievable on single local measurement. However, such quantity do satisfy all necessary criteria to serve as measure of discord like quantum correlation and it has no closed formula except only for $2\otimes n$ system. Here, we consider orthogonal invariant class of states which includes both the Werner and Isotropic class of states and explore the possibility of closed form formula. Further, we extend our quest to the possibility of closed form of geometric discord and measurement induced nonlocality for this class. We also provide a comparative study of the bounds of general quantum correlations with entanglement, as measured by negativity, for an interesting subclass of states.