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A generalization of the entropy power inequality to bosonic quantum systems

Nature Photonics volume 8, pages 958–964 (2014)Cite this article

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Abstract

In most communication schemes, information is transmitted via travelling modes of electromagnetic radiation. These modes are unavoidably subject to environmental noise along any physical transmission medium, and the quality of the communication channel strongly depends on the minimum noise achievable at the output. For classical signals, such noise can be rigorously quantified in terms of the associated Shannon entropy and it is subject to a fundamental lower bound called the entropy power inequality. However, electromagnetic fields are quantum mechanical systems, so the quantum nature of the information carrier cannot be neglected—especially in low-intensity signals—and many important results derived within classical information theory require non-trivial extensions to the quantum regime. Here, we prove one possible generalization of the entropy power inequality to quantum bosonic systems. The impact of this inequality in quantum information theory is potentially large and some relevant implications are considered in this work.

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Figure 1: Graphical representation of coherent mixing of two inputs A and B.
Figure 2: Entropy power versus photon number inequality.
Figure 3: Capacity region (expressed in nats per channel uses) for a broadcasting channel12,13.

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Acknowledgements

The authors thank L. Ambrosio, S. Di Marino and A.S. Holevo for comments and discussions. A.M. acknowledges support from the Progetto Giovani Ricercatori 2013 of Scuola Normale Superiore. This work is partially supported by the EU Collaborative Project TherMiQ (grant agreement 618074).

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Authors and Affiliations

  1. NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Pisa, I-56127, Italy

    G. De Palma, A. Mari & V. Giovannetti

  2. INFN, Largo B. Pontecorvo, 3, 56127, Pisa, Italy

    G. De Palma

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  1. G. De Palma
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  2. A. Mari
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  3. V. Giovannetti
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All authors contributed equally to the research work and writing of the manuscript.

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Correspondence to V. Giovannetti.

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De Palma, G., Mari, A. & Giovannetti, V. A generalization of the entropy power inequality to bosonic quantum systems. Nature Photon 8, 958–964 (2014). https://doi.org/10.1038/nphoton.2014.252

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