Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Gong, Zihao, Guha, Saikat
Institution: University of Maryland, College Park
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Office of Naval Research
Award: G1829052184
OpenAlex ID: W7223007589