J. Eli Bourassa1,* and Hoi-Kwong Lo1,2,3
2Center for Quantum Information and Quantum Control, University of Toronto, 80 St. George St., Toronto, Ontario M5S 3H6, Canada
*Corresponding author: bourassa@physics.utoronto.ca
J Eli Bourassa
J. Eli Bourassa and Hoi-Kwong Lo, "Entropic uncertainty relations and the measurement range problem, with consequences for high-dimensional quantum key distribution," J. Opt. Soc. Am. B 36, B65-B76 (2019)
The measurement range problem, where one cannot determine the data outside the range of the detector, limits the characterization of entanglement in high-dimensional quantum systems when employing, among other tools from information theory, the entropic uncertainty relations. Practically, the measurement range problem weakens the security of entanglement-based large-alphabet quantum key distribution (QKD) employing degrees of freedom including time-frequency or electric field quadrature. We present a modified entropic uncertainty relation that circumvents the measurement range problem under certain conditions and apply it to well-known QKD protocols. For time-frequency QKD, although our bound is an improvement, we find that high channel loss poses a problem for its feasibility. In homodyne-based continuous variable QKD, we find our bound provides a quantitative way to monitor for saturation attacks.