Closed-form Bayesian quantum estimation of Gaussian states

• URL: http://arxiv.org/abs/2605.16978v1
• Date: Sat, 16 May 2026 12:56:59 GMT
• Title: Closed-form Bayesian quantum estimation of Gaussian states
• Abstract summary: We introduce a variational framework reducing the optimisation over measurements and estimators to a finite-dimensional linear problem.<n>We show that the framework yields experimentally feasible strategies based on Gaussian operations and quadrature measurements.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and largely numerical due to the complexity of the underlying parameter integrals. Here, we introduce a variational framework reducing the optimisation over measurements and estimators to a finite-dimensional linear problem and admitting closed-form solutions. This is achieved by restricting the analysis to operators polynomial in the canonical quadratures, leading to solutions with a geometric interpretation as orthogonal projections of the global optimum. We further derive a necessary and sufficient condition for global optimality. Through single-shot examples, we show that the framework yields experimentally feasible strategies based on Gaussian operations and quadrature measurements that are either optimal or near-optimal, and that replacing the induced estimator with the posterior mean further improves performance towards the global optimum.

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