1307.4265 (Patrick J. Coles et al.)

Improved entropic uncertainty relations and information exclusion
relations    [PDF]

Patrick J. Coles, Marco Piani

We prove a stronger version of the uncertainty principle with quantum memory from Berta et al. [Nature Physics 6, 659 (2010)]. While the degree of strengthening depends on the quantum state, for some choices of measurements our bound is strictly stronger \emph{for all states}. As a corollary, we prove a main conjecture of Grudka et al. [ArXiv:1210.8317], which strengthens Hall's information exclusion principle [Phys. Rev. Lett. 74, 3307 (1995)] - an upper bound on the mutual informations for complementary observables. In addition to proving Grudka et al.'s conjecture, we provide a mutual information bound that is stronger and is generalised to the case of quantum memory. Our results highlight a fundamental distinction between the complementarity of information versus that of uncertainty, and also have application in witnessing of entanglement and quantum channel capacity.

View original: http://arxiv.org/abs/1307.4265