Uncertainty-reality complementarity and entropic uncertainty relations

Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified and deeply studied by means of entropic measures (Dieguez and Angelo 2018 Phys. Rev. A 97 022107). However, there is no state-independent 'reality trade-off' between non-commuting observables, as in certain systems all observables are real (Bilobran and Angelo 2015 Europhys. Lett. 112 40005). We show that the entropic uncertainty relation in the presence of quantum memory (Berta et al 2010 Nat. Phys. 6 659) perfectly supplements the discussed notion of reality, rendering trade-offs between reality and quantum uncertainty. State-independent complementarity inequalities involving entropic measures of both, uncertainty and reality, for two observables are presented.