Non-commutativity as a Universal Characterization for Enhanced Quantum Metrology

• URL: http://arxiv.org/abs/2511.22280v1
• Date: Thu, 27 Nov 2025 10:03:09 GMT
• Title: Non-commutativity as a Universal Characterization for Enhanced Quantum Metrology
• Authors: Ningxin Kong, Haojie Wang, Mingsheng Tian, Yilun Xu, Geng Chen, Yu Xiang, Qiongyi He,
• Abstract summary: We introduce the nilpotency index $mathcalK$, which quantifies the depth of non-commutativity between operators during the encoding process.<n>We show that a finite $mathcalK$ yields an enhanced scaling of root-mean-square error as $N- (1+mathcalK)$.<n>Remarkably, in the limit $mathcalK to infty$, exponential precision scaling $N-1e-N$ is achievable.
• Score: 14.709867911704924
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A central challenge in quantum metrology is to effectively harness quantum resources to surpass classical precision bounds. Although recent studies suggest that the indefinite causal order may enable sensitivities to attain the super-Heisenberg scaling, the physical origins of such enhancements remain elusive. Here, we introduce the nilpotency index $\mathcal{K}$, which quantifies the depth of non-commutativity between operators during the encoding process, can act as a fundamental parameter governing quantum-enhanced sensing. We show that a finite $\mathcal{K}$ yields an enhanced scaling of root-mean-square error as $N^{-(1+\mathcal{K})}$. Meanwhile, the requirement for indefinite causal order arises only when the nested commutators become constant. Remarkably, in the limit $\mathcal{K} \to \infty$, exponential precision scaling $N^{-1}e^{-N}$ is achievable. We propose experimentally feasible protocols implementing these mechanisms, providing a systematic pathway towards practical quantum-enhanced metrology.

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