mgr Marek Miller

Positive maps and the problem of entanglement detection

Positive maps on operator algebras, specifically on matrix algebras, are extremely useful mathematical tools in the study of entanglement in quantum information theory. A surprising correspondence between positive maps and the so-called entanglement witnesses, i.e. observables that in principle could facilitate detecting entanglement of a quantum state, was established in 1990s and since then, it has been the starting point in any attempt to solve the non-trivial problem of deciding whether a density matrix of a composite quantum system exhibits entanglement. In my talk, I will focus on trying to formulate that problem precisely, as well as presenting generally known answers to it and my own results in this matter that I have been working on during my graduate studies.