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

摘要

Entanglement has been studied extensively for unveiling the mysteries ofnon-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 beincreased via local operations. It was found that for sets of non-maximallyentangled states of two qubits, comparing these entanglement measures may leadto different entanglement orderings of the states. On the other hand, althoughit is not an entanglement measure and not monotonic under local operations, dueto its ability of detecting multipartite entanglement, quantum Fisherinformation (QFI) has recently received an intense attraction generally withentanglement in the focus. In this work, we revisit the state ordering problemof general two qubit states. Generating a thousand random quantum states andperforming an optimization based on local general rotations of each qubit, wecalculate the maximal QFI for each state. We analyze the maximized QFI incomparison with concurrence, REE and negativity and obtain new state orderings.We show that there are pairs of states having equal maximized QFI but differentvalues for concurrence, REE and negativity and vice versa.