Abstract
We derive the lower bounds for a non-Gaussianity measure based on quantum relative entropy (QRE). Our approach draws on the observation that the QRE-based non-Gaussianity measure of a single-mode quantum state is lower bounded by a function of the negentropies for quadrature distributions with maximum and minimum variances. We demonstrate that the lower bound can outperform the previously proposed bound by the negentropy of a quadrature distribution. Furthermore, we extend our method to establish lower bounds for the QRE-based non-Gaussianity measure of a multimode quantum state that can be measured by homodyne detection, with or without leveraging a Gaussian unitary operation. Finally, we explore how our lower bound finds application in non-Gaussian entanglement detection.
Highlights
We show that the sum of the negentropies for two quadrature distributions with the maximum and minimum variances provides a lower bound for the quantum relative entropy (QRE)-based non-Gaussianity measure of a single-mode quantum state
We derived observable lower bounds for a non-Gaussianity measure based on QRE
We first established a lower bound for a single-mode quantum state as a function of the negentropies of quadrature distributions with the maximum and minimum variances, and we showed that it could perform better than the previously proposed bound in [46]
Summary
For the case of QRE-based non-Gaussianity measure, observable lower bounds have been developed to address this issue by using the information of the covariance matrix in conjunction with the photon number distribution [69] and the negentropy of a quadrature distribution [46]. The former, i.e., the lower bound in [69], works better than the latter, i.e., the lower bound in [46], especially for quantum states with rotational symmetry in phase space but demands two measurement setups, i.e., homodyne detection and photon-number-resolving detection, in general. We propose a method to detect non-Gaussian entangled states beyond the Gaussian positive partial transposition (PPT) entanglement criteria with our lower bound
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