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arXiv · 1707.09278

Conditional entropic uncertainty relations for Tsallis entropies

Dariusz Kurzyk·Łukasz Pawela·Zbigniew Puchała
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Abstract

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 entanglement-dependent entropic uncertainty relations in terms of the Tsallis entropies for states with a fixed amount of entanglement. Our main result is stated as Theorem~\ref{th:bound}. 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.

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Dariusz Kurzyk, Łukasz Pawela, Zbigniew Puchała. 2018-03-22. Conditional entropic uncertainty relations for Tsallis entropies. https://doi.org/10.1007/s11128-018-1955-1

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