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Standard federated learning (FL) algorithms typically require multiple rounds of communication between the server and the clients, which has several drawbacks, including requiring constant network connectivity, repeated investment of computational resources, and susceptibility to privacy attacks. One-Shot FL is a new paradigm that aims to address this challenge by enabling the server to train a global model in a single round of communication. In this work, we present FedFisher, a novel algorithm for one-shot FL that makes use of Fisher information matrices computed on local client models, motivated by a Bayesian perspective of FL. First, we theoretically analyze FedFisher for two-layer over-parameterized ReLU neural networks and show that the error of our one-shot FedFisher global model becomes vanishingly small as the width of the neural networks and amount of local training at clients increases. Next, we propose practical variants of FedFisher using the diagonal Fisher and K-FAC approximation for the full Fisher and highlight their communication and compute efficiency for FL. Finally, we conduct extensive experiments on various datasets, which show that these variants of FedFisher consistently improve over competing baselines.