Data di Pubblicazione:
2011
Citazione:
Geometry of perturbed Gaussian states and quantum estimation / M. G. Genoni, P. Giorda, M. Paris. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 44:15(2011), pp. 152001.152001.1-152001.152001.7. [10.1088/1751-8113/44/15/152001]
Abstract:
We address the nonGaussianity (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 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 nonGaussian 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 analyzed in some details with the aim of finding the maximally non Gaussian state obtainable from a given Gaussian one.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
M.G. Genoni, P. Giorda, M. Paris
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