Signatures of avoided energy-level crossings in entanglement indicators obtained from quantum tomograms

TL;DR

This paper explores how entanglement indicators derived from quantum tomograms behave near avoided energy-level crossings in various quantum systems, showing they align well with traditional entanglement measures.

Contribution

It demonstrates that entanglement indicators calculated directly from quantum tomograms effectively identify entanglement near avoided crossings across multiple quantum systems.

Findings

Entanglement indicators agree with subsystem von Neumann entropy near avoided crossings.

Indicators capturing nonlinear correlations match traditional entanglement measures.

Quantum tomogram-based indicators are effective for entanglement estimation.

Abstract

Extensive theoretical and experimental investigations on multipartite systems close to an avoided energy-level crossing reveal interesting features such as the extremisation of entanglement. Conventionally, the estimation of entanglement directly from experimental observation involves either one of two approaches: Uncertainty-relation-based estimation that captures the linear correlation between relevant observables, or rigorous but error-prone quantum state reconstruction on tomograms obtained from homodyne measurements. We investigate the behaviour, close to avoided crossings, of entanglement indicators that can be calculated directly from a numerically-generated tomogram. The systems we study are two generic bipartite continuous-variable systems: a Bose-Einstein condensate trapped in a double-well potential, and a multi-level atom interacting with a radiation field. We also consider a multipartite hybrid quantum system of superconducting qubits interacting with microwave photons. We carry out a quantitative comparison of the indicators with a standard measure of entanglement, the subsystem von Neumann entropy (SVNE). It is shown that the indicators that capture the nonlinear correlation between relevant subsystem observables are in excellent agreement with the SVNE.