- Accepted Paper
Optimizing photon-number distributions of Gaussian states in the presence of loss
Phys. Rev. A - Accepted 13 November, 2026
DOI: https://doi.org/10.1103/b1f9-33jl
Phys. Rev. A - Accepted 13 November, 2026
DOI: https://doi.org/10.1103/b1f9-33jl
We analyze the impact of photon loss on the photon-number statistics of Gaussian states. Specifically, we propose and carefully evaluate several methods to mitigate deviations in the photon-number distributions of lossy (displaced) squeezed vacuum states from those of their lossless counterparts. These methods rely on appropriately redefining the parameters of Gaussian states when the loss budget is known in order to recover, as closely as possible, the desired photon-number distribution associated with each target state. While it is intrinsically hard to directly optimize the photon-number distribution of high-dimensional, correlated multimode Gaussian states, the proposed methods are instead based on optimizing specific key properties such as fidelity, phase-space functions, low-order moments of the underlying photon-number statistics, or overlap with the vacuum state. In particular, our results show that optimizing the fidelity between a pure Gaussian target state and a modified Gaussian state that has passed through a loss channel does typically not result in closeness of the corresponding photon-number distributions. Furthermore, we prove that vacuum-overlap correction minimizes the deviation in the photon-number distribution over broad parameter ranges for single-mode squeezed vacuum. For displaced and multimode instances, including systems with up to seven modes, our numerical results indicate that vacuum matching provides an effective and efficiently computable heuristic, although its near-optimality cannot be certified once the full photon-number distribution becomes classically inaccessible. As photon loss is a key limitation in photonic quantum simulations, with Gaussian boson sampling providing an important motivation and application context, our results provide insights into their performance and limitations in lossy environments and offer guidelines for mitigating these imperfections.
If the author has provided any supplemental materials with this article they will be available upon publication of the version of record.