2011/01/31 by Marco G. Genoni, Paolo Giorda, Matteo G. A. Paris
Computer Science · Mathematics · Physics and Astronomy · #Covariance #Eigenvalues and eigenvectors #Gaussian #Gaussian function #Gaussian random field #Mathematical analysis #Mathematics #Non-Gaussianity #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum state #Statistical physics #Statistics #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1088/1751-8113/44/15/152001
published as J. Phys. A 44, 152001 (2011) · 7 pages, 1 figure, revised version
arxiv created 2011/03/01 · openalex publication_date 2011/03/16 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We address the non-Gaussianity (nG) of states obtained by weakly perturbing a Gaussian state and investigate the relationships with quantum estimation. For classical perturbations, i.e. perturbations to eigenvalues, we found that the nG of the perturbed state may be written as the quantum Fisher information (QFI) distance minus a term depending on the infinitesimal energy change, i.e. it provides a lower bound to statistical distinguishability. Upon moving on isoenergetic surfaces in a neighbourhood of a Gaussian state, nG thus coincides with a proper distance in the Hilbert space and exactly quantifies the statistical distinguishability of the perturbations. On the other hand, for perturbations leaving the covariance matrix unperturbed, we show that nG provides an upper bound to the QFI. Our results show that the geometry of non-Gaussian states in the neighbourhood of a Gaussian state is definitely not trivial and cannot be subsumed by a differential structure. Nevertheless, the analysis of perturbations to a Gaussian state reveals that nG may be a resource for quantum estimation. The nG of specific families of perturbed Gaussian states is analysed in some detail with the aim of finding the maximally non-Gaussian state obtainable from a given Gaussian one.