Entanglement at Avoided Level Crossings

We introduce various bipartite entanglement indicators that are defined entirely from optical and spin tomograms, circumventing reconstruction of the density matrix. Some of these indicators are adapted from the manner in which the distance between two classical probability distributions is estimated. We also indicate how spin squeezing can be related to the tomographic entanglement indicators. A comparison is made of the performance of these tomographic indicators with standard entanglement measures based on the density matrix, with two objectives: to gauge the utility of specific indicators in different situations both in bipartite continuous variable systems and in hybrid quantum systems; and to assess how far ideas from classical probability theory and its role in information processing can be used to understand quantum entanglement. These investigations are conducted specifically in systems in which, with the variation of an appropriate parameter, some of the energy levels move close to each other and then move apart, avoiding level crossing. We summarize known results pointing out that standard quantum entanglement measures extremize at avoided energy-level crossings. Hence such systems provide an ideal platform for our investigations on the utility and limitations of tomographic entanglement indicators.