The Most Informative Cramér--Rao Bound for Quantum Two-Parameter Estimation with Pure State Probes

• URL: http://arxiv.org/abs/2511.14950v1
• Date: Tue, 18 Nov 2025 22:15:14 GMT
• Title: The Most Informative Cramér--Rao Bound for Quantum Two-Parameter Estimation with Pure State Probes
• Authors: Simon K. Yung, C. M. Yung, Lorcán O. Conlon, Syed M. Assad,
• Abstract summary: We present a new expression for the achievable bound for two- parameter estimation with pure states.<n>We also determine the optimal measurements.<n>To demonstrate the utility of our result, we determine the precision limit for estimating displacements using grid states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Optimal measurements for quantum multiparameter estimation are complicated by the uncertainty principle. Generally, there is a trade-off between the precision with which different parameters can be simultaneously estimated. The task of determining the minimum achievable estimation error is a central task of multiparameter quantum metrology. For estimating parameters encoded in pure quantum states, the ultimate limit is known, but is given by the solution of a non-trivial minimisation problem. We present a new expression for the achievable bound for two-parameter estimation with pure states that is considerably simpler. We also determine the optimal measurements, completing the problem of two-parameter estimation with pure state probes. To demonstrate the utility of our result, we determine the precision limit for estimating displacements using grid states.

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