  We propose an extension of the quantum entropy power inequality for finite
dimensional quantum systems, and prove a conditional quantum entropy power
inequality by using the majorization relation as well as the concavity of
entropic functions also given by Audenaert, Datta, and Ozols [J. Math. Phys.
57, 052202 (2016)]. Here, we make particular use of the fact that a specific
local measurement after a partial swap operation (or partial swap quantum
channel) acting only on finite dimensional bipartite subsystems does not affect
the majorization relation for the conditional output states when a separable
ancillary subsystem is involved. We expect our conditional quantum entropy
power inequality to be useful, and applicable in bounding and analyzing several
capacity problems for quantum channels.
