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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.16978 |
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| _version_ | 1866911690991337472 |
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| author | Gandar, Edward Rubio, Jesús |
| author_facet | Gandar, Edward Rubio, Jesús |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16978 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Closed-form Bayesian quantum estimation of Gaussian states Gandar, Edward Rubio, Jesús Quantum Physics 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. |
| title | Closed-form Bayesian quantum estimation of Gaussian states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.16978 |