We present entropic uncertainty relations for continuous variable systems in the presence of a quantum memory. These uncertainty relations account for the reduction of the uncertainty due to entanglement present between the measured system and the quantum memory. The entropic inequalities are stated in terms of the (differential) conditional (smooth) min- and max-entropies. While the uncertainty relations are derived for arbitrary measurements, we discuss them in details for position and momentum operators. We further discuss how they can be used to prove security of a squeezed state quantum key distribution protocol against arbitrary coherent attacks including finite-size effects.
(英)
We present entropic uncertainty relations for continuous variable systems in the presence of a quantum memory. These uncertainty relations account for the reduction of the uncertainty due to entanglement present between the measured system and the quantum memory. The entropic inequalities are stated in terms of the (differential) conditional (smooth) min- and max-entropies. While the uncertainty relations are derived for arbitrary measurements, we discuss them in details for position and momentum operators. We further discuss how they can be used to prove security of a squeezed state quantum key distribution protocol against arbitrary coherent attacks including finite-size effects.