Perturbation theory for quantum information quantities of Gaussian states
Abstract
Many quantum-information tasks can benefit from Gaussian quantum resources, while their fundamental performance limits are characterized by quantum information quantities. However, a unified perturbation theory for these quantities directly within the Gaussian-state formalism has been lacking. We develop such a theory for the von Neumann entropy, quantum relative entropy, quantum Chernoff quantity, and quantum fidelity, using perturbations of the moments of a reference Gaussian state. Using general Fréchet-derivative identities, we derive compact second-order expressions for reference-state covariance matrices whose symplectic eigenvalues are all greater than 1/2. We also show that the perturbative quantum Chernoff quantity is maximized at its symmetric point, yielding the quantum Chernoff exponent (QCE). We further show that symplectic eigenvalues equal to 1/2 can lead to slower asymptotic vanishing, potentially improving the corresponding fundamental performance limits. For reference-state covariance matrices containing symplectic eigenvalues both equal to and greater than 1/2, we identify sufficient conditions under which the former determine the leading covariance-matrix contributions, allowing the remaining modes to be traced out without changing the leading-order asymptotic scaling or the coefficient. Applying the framework to quantum illumination and incoherent-light sub-Rayleigh object discrimination, we recover known asymptotic QCEs directly within the Gaussian-state formalism. In the latter problem, the slower asymptotic vanishing explains the known quadratic scaling of the QCE with the source separation.
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BibTeX
@misc{gong2026perturbation,
title = {{Perturbation theory for quantum information quantities of Gaussian states}},
author = {Zihao Gong and Saikat Guha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25792},
eprint = {2610.25792},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25792},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Perturbation theory for quantum information quantities of Gaussian states
AU - Zihao Gong
AU - Saikat Guha
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25792
UR - https://arxiv.org/abs/2610.25792
AB - Many quantum-information tasks can benefit from Gaussian quantum resources, while their fundamental performance limits are characterized by quantum information quantities. However, a unified perturbation theory for these quantities directly within the Gaussian-state formalism has been lacking. We develop such a theory for the von Neumann entropy, quantum relative entropy, quantum Chernoff quantity, and quantum fidelity, using perturbations of the moments of a reference Gaussian state. Using general Fréchet-derivative identities, we derive compact second-order expressions for reference-state covariance matrices whose symplectic eigenvalues are all greater than 1/2. We also show that the perturbative quantum Chernoff quantity is maximized at its symmetric point, yielding the quantum Chernoff exponent (QCE). We further show that symplectic eigenvalues equal to 1/2 can lead to slower asymptotic vanishing, potentially improving the corresponding fundamental performance limits. For reference-state covariance matrices containing symplectic eigenvalues both equal to and greater than 1/2, we identify sufficient conditions under which the former determine the leading covariance-matrix contributions, allowing the remaining modes to be traced out without changing the leading-order asymptotic scaling or the coefficient. Applying the framework to quantum illumination and incoherent-light sub-Rayleigh object discrimination, we recover known asymptotic QCEs directly within the Gaussian-state formalism. In the latter problem, the slower asymptotic vanishing explains the known quadratic scaling of the QCE with the source separation.
ER -