Multiparameter function estimation for general Hamiltonians

• URL: http://arxiv.org/abs/2605.04136v1
• Date: Tue, 05 May 2026 18:00:00 GMT
• Title: Multiparameter function estimation for general Hamiltonians
• Abstract summary: We derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian.<n>Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the corresponding bound for estimating a function of multiple parameters-each coupled to distinct and possibly non-commuting generators-remains unknown in general. Here, we derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian that attains this bound. We show that, although the task is fundamentally a multiparameter problem, our tight bound reduces to an optimized single-parameter quantum Cramér-Rao bound, even for arbitrary generator sets. Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems.

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