Majorization entropic uncertainty relations

Understand

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 R\'enyi entropies describing probability distributions associated with a given pure state expanded in eigenbases of two observables.
• Obtained bounds are expressed in terms of the largest singular values of submatrices of the unitary rotation matrix.
• Numerical simulations show that for a generic unitary matrix of size N = 5 our bound is stronger than the well known result of Maassen and Uffink (MU) with a probability larger than 98%.