HOW TO DETECT ENTANGLEMENT IN QUANTUM SYSTEMS

摘要

The present paper is a brief, elementary introduction to the theory of entangled states in quantum systems, based on the lecture given by the author at the Suwa Satellite Conference of QBIC09, held at Tokyo University of Science in Suwa, March 6-8, 2009. We focus here on the mathematical problem of entanglement detection. The duality between positive maps and entanglement witnesses is emphasized. One particular class of experimentally relevant entanglement witnesses and the method of their construction is further discussed in another paper appearing in this volume.~1 An interested reader may find much more information about recent developments in the entanglement theory and applications in a review paper [2].