Tensorial characterization and quantum estimation of weakly entangled qubits

TL;DR

This paper introduces a new class of entanglement monotones for two qubits, improving quantum estimation in weakly entangled regimes through a geometric tensor-based approach.

Contribution

It proposes a novel geometric framework for defining entanglement monotones that enhances estimation efficiency for weakly entangled qubits.

Findings

New entanglement monotones outperform linear entropy in weak entanglement regimes

Tensorial characterization provides a more accurate quantum estimation method

Geometric approach links invariant tensor fields to entanglement measures

Abstract

In the case of two qubits, standard entanglement monotones like the linear entropy fail to provide an efficient quantum estimation in the regime of weak entanglement. In this paper, a more efficient entanglement estimation, by means of a novel class of entanglement monotones, is proposed. Following an approach based on the geometric formulation of quantum mechanics, these entanglement monotones are defined by inner products on invariant tensor fields on bipartite qubit orbits of the group SU(2)xSU(2).