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Description
We present a local framework for quantum parameter estimation in linear optical systems, where the unknown parameter is encoded through deformations of an experimentally accessible mode basis. The resulting quantum Fisher information decomposes into two distinct contributions: a coherent contribution, generated by parameter-induced dynamics within the accessible modes and capable of Heisenberg scaling, and a geometric leakage contribution, arising from coupling to inaccessible modes and limited to standard quantum scaling. This decomposition is obtained via a purification together with a minimization over Kraus representations at the working point. It depends only on the accessible mode functions, their covariance matrix, and the projector onto the accessible system subspace. We further provide a general method for constructing optimal input states that achieve Heisenberg scaling using the eigenbasis of the system generator. We apply the formalism to two-point-source imaging with a general complex point-spread function. For two-mode systems, we show that the system generator generally contains both a number term and an SU(2) mode-mixing term, both distinct from the leakage contribution. This separation identifies mode deformations that generate coherent quantum sensitivity with Heisenberg scaling, as opposed to deformations that produce only leakage into inaccessible modes and therefore exhibit standard quantum scaling. For a Gaussian point-spread function with linear and cubic phase, we find a quantum advantage in the absence of photon loss to additional environmental modes.