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

Abstract

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.

6 pages, 1 figure, and 1 table; Close to published version

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• Upper bounds on the private capacity for bosonic Gaussian channels
• Universal upper bounds for Gaussian information capacity
• Quantum Rényi Entropy Functionals for Bosonic Gaussian Systems
• Weighted $p$-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory
• Quantifying coherence with quantum addition