# Schmidt number of pure bi-partite entangled states and methods of its calculation

**Authors:** Mikalai Karelin  
**arXiv:** [quant-ph/0606055](https://arxiv.org/abs/quant-ph/0606055)  
**Date:** 2006-06-07  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/quant-ph--0606055v2/

## Key points

- Study by Mikalai Karelin focuses on calculating the Schmidt number, an entanglement measure for pure-state continuous-variable bi-partite systems
- Research delves into a simple model of atom-field scattering
- Analytically determines the Schmidt number for this scenario
- Findings provide insights into entangled states in such systems and effective quantification methods
- Contributes to understanding of entanglement in quantum systems and showcases practical application in real-world scenarios like atom-field interactions
- Adds significant knowledge to quantum optics and entanglement theory with potential implications for future studies in quantum information processing and communication

## Summary

The study by Mikalai Karelin focuses on the calculation of the Schmidt number, an entanglement measure for pure-state continuous-variable bi-partite systems. Specifically delving into a simple model of atom-field scattering, Karelin's research analytically determines the Schmidt number for this scenario. The findings provide valuable insights into the entangled states present in such systems and highlight effective methods for quantifying their entanglement. This work not only contributes to our understanding of entanglement in quantum systems but also showcases the practical application of theoretical calculations in real-world scenarios, such as atom-field interactions. Overall, Karelin's research adds significant knowledge to the field of quantum optics and entanglement theory with potential implications for future studies in quantum information processing and communication.