|Tytuł||Majorization uncertainty relations for mixed quantum states|
|Publication Type||Journal Article|
|Autorzy||Puchała Z, Rudnicki Ł, Krawiec A, Życzkowski K|
|Journal||Journal of Physics A: Mathematical and Theoretical|
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state ρ of a finite size N. 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 ρ and the entries of a unitary matrix U 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.