01050nas a2200157   4500000000100000000000100001008004100002100001900043700001900062700002200081245006900103856004600172300000800218490000700226520065900233       2018                            d1 aDariusz Kurzyk1 aŁukasz Pawela1 aZbigniew Puchała00aConditional entropic uncertainty relations for Tsallis entropies  uhttps://doi.org/10.1007/s11128-018-1955-1  a1930 v173 a<p>The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find state-independent entropic uncertainty relations in terms of the Tsallis entropies for states with a fixed amount of entanglement. Our main result is stated as Theorem. Taking the special case of von Neumann entropy and utilizing the concavity of conditional von Neumann entropies, we extend our result to mixed states. Finally we provide a lower bound on the amount of extractable key in a quantum cryptographic scenario.</p>