Experimental investigation of conditional majorization uncertainty relations in the presence of quantum memory

We report an experimental investigation of conditional majorization uncertainty relations (CMURs) in the presence of quantum memory. We find that the CMUR bounds are always physically nontrivial even if the particle of interest is strongly entangled with a quantum memory, whereas the previous conditional entropic uncertainty relation bounds may be trivial and physically unreachable. We deploy vectorized measures of uncertainty relations and quantum correlations, and the result reveals the sophisticated structures of them. In addition, we demonstrate an application of the CMURs, to witness steerability of bipartite states. Such a method applies to an arbitrary number of measurement settings and can be efficiently implemented. Aside from the CMURs' fundamental significance, our result also shows its impact on the development of future quantum technologies.