The techniques of quantum information processing have recently made their way into high energy physics opening the door to new type of measurements at particle colliders. Last year a pioneering measurement of entanglement between the spins of a top-antitop pair was done by the ATLAS experiment at LHC. It was followed by a similar measurement at CMS, which carried out the complete quantum tomography of the tt spin density matrix. In my talk I will explain the prospects and benefits of the quantum *process* tomography in high energy experiments. Not only it offers a new window for possible BSM physics, but allows to test the very foundations of quantum theory, such as linearity of complete positivity. As an illustrative example, I will discuss the process of top-antitop pair production from polarised electron-positron collisions. The talk is based on the recent works: arXiv:2103.12000 [quant-ph], arXiv:2412.01892 [hep-ph].