01221nas a2200157   4500000000100000000000100001008004100002100002200043700002100065700002300086700002200109245006400131856004500195490000700240520081600247       2018                            d1 aZbigniew Puchała1 aŁukasz Rudnicki1 aAleksandra Krawiec1 aKarol Życzkowski00aMajorization uncertainty relations for mixed quantum states  uhttps://doi.org/10.1088/1751-8121/aab66c0 v513 a<p>Majorization uncertainty relations are generalized for an arbitrary mixed quantum state <span style="font-size:129%"><em>ρ</em></span> of a finite size <span style="font-size:129%"><em>N</em></span>. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to measurements with respect to arbitrary two orthogonal bases is derived in terms of the spectrum of <span style="font-size:129%"><em>ρ</em></span> and the entries of a unitary matrix <span style="font-size:129%"><em>U</em></span> relating both bases. The obtained results can also be formulated for two measurements performed on a single subsystem of a bipartite system described by a pure state, and consequently expressed as uncertainty relation for the sum of conditional entropies.</p>