Optimality and Noise-Resilience of Critical Quantum Sensing
arxiv(2024)
Abstract
We compare critical quantum sensing to passive quantum strategies to perform
frequency estimation, in the case of single-mode quadratic Hamiltonians. We
show that, while in the unitary case both strategies achieve precision scaling
quadratic with the number of photons, in the presence of dissipation this is
true only for critical strategies. We also establish that working at the
exceptional point or beyond threshold provides sub-optimal performance. This
critical enhancement is due to the emergence of a transient regime in the open
critical dynamics, and is invariant to temperature changes. When considering
both time and system size as resources, for both strategies the precision
scales linearly with the product of the total time and the number of photons,
in accordance with fundamental bounds. However, we show that critical protocols
outperform optimal passive strategies if preparation and measurement times are
not negligible.
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