TL;DR
This paper presents a new approach to quantum metrology bounds for mixed states using purification, enabling better estimation precision through novel bounds and measurement strategies.
Contribution
It introduces formulations of the QCRB and HCRB via purification, linking mixed states to their purifications, and proposes methods to asymptotically attain these bounds.
Findings
Bound values for mixed states are connected to their purifications.
A new method achieves asymptotic attainment of bounds using random purification channels.
The approach improves estimation precision in multi-parameter quantum metrology.
Abstract
We introduce new formulations of the quantum Cram\'{e}r-Rao bound (QCRB) and the Holevo Cram\'{e}r-Rao bound (HCRB) in multi-parameter quantum metrology via purification, where we show their values for any mixed state are connected to that for its purification with nuisance parameters introduced on the environmental system. Using this technique, we develop a new 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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