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

Conditional quantum entropy power inequality for $d$-level quantum systems