Measurement incompatibility cannot be stochastically distilled

Huan-Yu Ku^1*, Chung-Yun Hsieh², Costantino Budroni³

¹Department of Physics, NTNU, Taipei, Taiwan
²H.H. Wills Physics Laboratory, University of Bristol, Bristol, UK
³Department of Physics “E. Fermi”, University of Pisa, Pisa, Italy

* Presenter:Huan-Yu Ku, email:huan_yu@phys.ncku.edu.tw

We show that the incompatibility of a set of measurements cannot be increased by subjecting them to a filter, namely, by combining them with a device that post-selects the incoming states on a fixed outcome of a stochastic transformation. This result holds for several measures of incompatibility, such as those based on robustness and convex weight. Expanding these ideas to Einstein-Podolsky-Rosen steering experiments, we are able to solve the problem of the maximum steerability obtained with respect to the most general local filters in a way that allows for an explicit calculation of the filter operation. Moreover, our results generalize to nonphysical maps, i.e., positive but not completely positive linear maps.

Keywords: Resource theory , nonlocality, Quantum correlations, entanglement