Asymptotic irrelevance of entanglement in quantum metrology
Year: 2015
Type: preprint
Abstract: Quantum systems allow one to sense physical parameters beyond the reach of classical statistics---with resolutions greater than $1/N$, where $N$ is the number of constituent particles independently probing the parameter. In principle, the Heisenberg Limit $1/N^{2}$ may even be reached, which requires both the relative size of the largest entangled block and the geometric measure of entanglement to be non-vanishing as $N\!\to\!\infty$. Yet, we demonstrate that in the asymptotic $N$ limit any precision scaling arbitrarily close to the Heisenberg Limit ($1/N^{2-\varepsilon}$ with any $\varepsilon\!>\!0$) may be attained, even though the system gradually becomes noisier and separable, and both the above entanglement quantifiers asymptotically vanish. Our results thus show that quantum systems achieve nearly optimal resolution scaling despite arbitrarily small amount of entanglement present. In deriving these results, we also establish a continuity relation for the Quantum Fisher Information of independent interest.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W798779255