Abstract:
Computing accessible information for an ensemble of quantum states is a basic problem
in quantum information theory coming back to its origin and important in particular for
applications in quantum cryptography. The problem is solved in some special cases but in
general remains open. In this talk we show that recently obtained optimality criterion
when applied to specific ensembles of states leads to nontrivial entropy inequalities that
are discrete relatives of the log-Sobolev inequality. In this light, the hypothesis of an
information-optimal measurement for an ensemble of equiangular equiprobable states –
the quantum pyramids – is reconsidered and the corresponding tight entropy inequalities
are proposed.
