We knows that quantum information allows us to estimate certain unknown parameters to precisions beyond classical limits. The archetypal example, being the use of the NOON state – a superposition of N photons in either Mode A or Mode B – for phase estimation. Unfortunately, this same state is very fragile – if you accidentally lose a single one of these N photons, it becomes essentially useless.

Is this a generic trait for quantum metrology? This manuscript establishes such a trade-off. We related the performance of a probe state at estimating a parameter – as quantified by the quantum Fisher information– to the amount of purity this parameter undergoes statistical fluctuation.

- Fragile states are better for quantum metrology

*Kavan Modi, Lucas C. Céleri, Jayne Thompson, Mile Gu*