Non-Gaussianity and entropy-bounded uncertainty relations: Application to detection of non-Gaussian entangled states

Kyunghyun Baek, Hyunchul Nha

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4 Citations (Scopus)


We suggest an improved version of the Robertson-Schrödinger uncertainty relation for canonically conjugate variables by taking into account a pair of characteristics of states: non-Gaussianity and mixedness quantified by using fidelity and entropy, respectively. This relation is saturated by both Gaussian and Fock states and provides a strictly improved bound for any non-Gaussian states or mixed states. For the case of Gaussian states, it is reduced to the entropy-bounded uncertainty relation derived by Dodonov. Furthermore, we consider readily computable measures of both characteristics and find a weaker but more readily accessible bound. With its generalization to the case of two-mode states, we show applicability of the relation to detect entanglement of non-Gaussian states.

Original languageEnglish
Article number042314
JournalPhysical Review A
Issue number4
Publication statusPublished - 10 Oct 2018


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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