Estimation of entanglement in bipartite systems directly from tomograms

TL;DR

This paper explores a direct method to estimate bipartite entanglement from experimental tomograms, avoiding complex state reconstruction, and validates its effectiveness on two nonlinear models through comparison with standard entanglement measures.

Contribution

It introduces and assesses a direct entanglement indicator from tomograms, demonstrating its accuracy and efficiency compared to traditional methods in bipartite quantum systems.

Findings

The tomographic entanglement indicator correlates well with standard measures.

The method performs effectively across different initial states.

It provides a practical alternative for experimental entanglement estimation.

Abstract

We investigate the advantages of extracting the degree of entanglement in bipartite systems directly from tomograms, as it is the latter that are readily obtained from experiments. This would provide a superior alternative to the standard procedure of assessing the extent of entanglement between subsystems after employing the machinery of state reconstruction from the tomogram. The latter is both cumbersome and involves statistical methods, while a direct inference about entanglement from the tomogram circumvents these limitations. In an earlier paper, we had identified a procedure to obtain a bipartite entanglement indicator directly from tomograms. To assess the efficacy of this indicator, we now carry out a detailed investigation using two nonlinear bipartite models by comparing this tomographic indicator with standard markers of entanglement such as the subsystem linear entropy and the subsystem von Neumann entropy and also with a commonly-used indicator obtained from inverse participation ratios. The two model systems selected for this purpose are a multilevel atom interacting with a radiation field, and a double-well Bose-Einstein condensate. The role played by the specific initial states of these two systems in the performance of the tomographic indicator is also examined. Further, the efficiency of the tomographic entanglement indicator during the dynamical evolution of the system is assessed from a time-series analysis of the difference between this indicator and the subsystem von Neumann entropy.