Tuesday, April 30, 2013

1304.7755 (Zbigniew Puchala et al.)

Entropic uncertainty relations and majorization    [PDF]

Zbigniew Puchala, Lukasz Rudnicki, Karol Zyczkowski
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.
View original: http://arxiv.org/abs/1304.7755

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