Majorization uncertainty relations for mixed quantum states

TytułMajorization uncertainty relations for mixed quantum states
Publication TypeJournal Article
Rok publikacji2018
AutorzyPuchała Z, Rudnicki Ł, Krawiec A, Życzkowski K
JournalJournal of Physics A: Mathematical and Theoretical
Start Page175306

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.