In this talk, I will present randomized measurement protocols to measure quantities associated with entanglement in quantum processors [1].

I will focus in particular on recent upgrades to the measurement toolbox:

 - How to increase the system sizes where the protocols can be applied [2]

 - How to measure new physical quantities with controlled statistical errors and efficient data processing [3,4]?

[1] https://arxiv.org/abs/2203.11374

[2] Phys. Rev. Lett. 127, 200503

[3] Phys. Rev. Lett. 127, 260501

[4] https://arxiv.org/abs/2209.04393