Tomographic entanglement indicators in multipartite systems

TL;DR

This paper evaluates a tomographic entanglement indicator's effectiveness in hybrid quantum systems, demonstrating it accurately estimates entanglement dynamics in atomic and field subsystems through numerical and experimental analysis.

Contribution

It extends the application of a tomographic entanglement indicator to hybrid systems, comparing its performance with quantum mutual information.

Findings

The indicator accurately estimates entanglement in atomic and field subsystems.

An approximation of the indicator is effective for field but not atomic subsystems.

Numerical simulations and IBM experiments support the indicator's reliability.

Abstract

We assess the performance of an entanglement indicator which can be obtained directly from tomograms, avoiding state reconstruction procedures. In earlier work, we have examined this tomographic entanglement indicator, and a variant obtained from it, in the context of continuous variable systems. It has been shown that, in multipartite systems of radiation fields, these indicators fare as well as standard measures of entanglement. In this paper, we assess these indicators in the case of two generic hybrid quantum systems, the double Jaynes-Cummings model and the double Tavis-Cummings model using, for purposes of comparison, the quantum mutual information as a standard reference for both quantum correlations and entanglement. The dynamics of entanglement is investigated in both models over a sufficiently long time interval. We establish that the tomographic indicator provides a good estimate of the extent of entanglement both in the atomic subsystems and in the field subsystems. An indicator obtained from the tomographic indicator as an approximation, however, does not capture the entanglement properties of atomic subsystems, although it is useful for field subsystems. Our results are inferred from numerical calculations based on the two models, simulations of relevant equivalent circuits in both cases, and experiments performed on the IBM computing platform.