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In most communication schemes information is transmitted via travelling modesof electromagnetic radiation. These modes are unavoidably subject toenvironmental noise along any physical transmission medium and the quality ofthe communication channel strongly depends on the minimum noise achievable atthe output. For classical signals such noise can be rigorously quantified interms of the associated Shannon entropy and it is subject to a fundamentallower bound called entropy power inequality. Electromagnetic fields are howeverquantum mechanical systems and then, especially in low intensity signals, thequantum nature of the information carrier cannot be neglected and manyimportant results derived within classical information theory requirenon-trivial extensions to the quantum regime. Here we prove one possiblegeneralization of the Entropy Power Inequality to quantum bosonic systems. Theimpact of this inequality in quantum information theory is potentially largeand some relevant implications are considered in this work.

A generalization of the Entropy Power Inequality to Bosonic Quantum Systems