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arXiv · 2605.03975

Quantum metrology of mixed states via purification

Sisi Zhou
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Abstract

Multiparameter quantum metrology is ubiquitous in physics, yet it remains fundamentally challenging. As reflected by the uncertainty principle, distinct unknown parameters generally cannot be estimated simultaneously at their individual ultimate precision limits. The quantum Cram\'{e}r--Rao bound (QCRB) and the Holevo Cram\'{e}r--Rao bound (HCRB) represent the ultimate precision bounds in multiparameter quantum metrology. Here we introduce new formulations of these bounds based on quantum state purification. We show that, for any mixed state, their values are directly related to those of its purification, provided that nuisance parameters are introduced on the environmental system. Leveraging this connection, we develop a remarkably simple method for asymptotically attaining either the HCRB or twice the QCRB for arbitrary mixed states, using random purification channels and individual measurements.

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Sisi Zhou. 2026-05-05. Quantum metrology of mixed states via purification. https://arxiv.org/abs/2605.03975

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