Title | Majorization entropic uncertainty relations |
Publication Type | Journal Article |
Year of Publication | 2013 |
Authors | Puchała Z , Rudnicki Ł. , Życzkowski K |
Journal | J. Phys. A: Math. Theor. |
Volume | 46 |
Abstract | Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of Renyi entropies describing probability distributions associated with a given pure state expanded in eigenbases of two observables. The bounds obtained are expressed in terms of the largest singular values of submatrices of the unitary rotation matrix. For a generic unitary matrix of size N = 5 the bound obtained is stronger than the one of Maassen and Uffink (MU) with probability larger than 98%, and this ratio increases with N. We show also that the bounds investigated are invariant for unitary matrices equivalent up to dephasing and permutation and derive a classical analogue of the MU uncertainty relation formulated for stochastic transition matrices. |