XXXVI Workshop on Geometric Methods in Physics | 2-8.07.2017 |

VI School on Geometry and Physics | 26-30.06.2017 |

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## Shahriar Salimi## Entropic uncertainty relation with quantum memoryHeisenberg’s uncertainty principle sets a lower bound on the uncertainties of two incompatible observables measured on a particle. The uncertainty lower bound can be reduced by considering a particle as a quantum memory correlating with the measured particle. Beside fundamental importance, the lower bound of entropic uncertainty relation in the presence of quantum memory has various applications, ranging from entanglement detection to quantum cryptography. In this paper, we obtain a lower bound for the entropic uncertainty in the presence of quantum memory which is tighter than the previous lower bounds. Also, we consider a tripartite scenario in which an entangled quantum state has been shared among Alice, Bob, and Charlie. Bob and Charlie want to know the Alice’s measurement outcomes. Because of entanglement monogamy, no one can guess Alice’s measurement outcomes exactly. So, they concentrate their correlation with Alice in Charlie’s side by local operations and classical communication. By this strategy, Charlie can guess the Alice’s measurement outcomes with better accuracy. We obtain a lower bound for Charlie’s uncertainty about Alice’s measurement outcomes after concentrating information and compare it with the lower bound without concentrating information in some examples. |

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University of Bialystok |

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