Qiushi Liu

We present a systematic framework addressing the challenge of identifying optimal sequential strategies for noisy quantum metrology under resource constraints, with a focus on restricted ancillae. While achieving the optimal metrological precision generally requires quantum error correction, we derive rigorous sufficient conditions for attaining the Heisenberg limit using ancilla-free sequential strategies, either without control or with identical unitary controls, based on a spectral analysis of the quantum channel. Complementing this asymptotic analysis, we introduce an efficient tensor network algorithm for optimizing ancilla-constrained metrological strategies in the finite-query regime, adaptable to a wide variety of noise models and experimental control capabilities.

One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this work, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration. With our framework, we show there exists a strict hierarchy of the precision limits for different families of strategies.