Analysis of Entanglement Measures and LOCC Maximized Quantum Fisher Information of General Two Qubit Systems

TL;DR

This paper investigates the relationships between quantum entanglement measures and quantum Fisher information in two-qubit systems, revealing that different measures can order states differently and highlighting the unique role of QFI.

Contribution

The study compares maximized quantum Fisher information with traditional entanglement measures, providing new insights into state ordering and the distinct information each measure captures.

Findings

Maximized QFI can be equal for states with different entanglement measures.

Different entanglement measures can produce different state orderings.

QFI reveals unique aspects of quantum correlations beyond traditional measures.

Abstract

Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa.