Fundamental limits of metrology at thermal equilibrium
- URL: http://arxiv.org/abs/2402.06582v1
- Date: Fri, 9 Feb 2024 18:01:45 GMT
- Title: Fundamental limits of metrology at thermal equilibrium
- Authors: Paolo Abiuso, Pavel Sekatski, John Calsamiglia, Mart\'i
Perarnau-Llobet
- Abstract summary: We consider the estimation of an unknown parameter $theta$ through a quantum probe at thermal equilibrium.
We find the maximal Quantum Fisher Information attainable via arbitrary $HC$, which provides a fundamental bound on the measurement precision.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider the estimation of an unknown parameter $\theta$ through a quantum
probe at thermal equilibrium. The probe is assumed to be in a Gibbs state
according to its Hamiltonian $H_\theta$, which is divided in a
parameter-encoding term $H^P_\theta$ and an additional, parameter-independent,
control $H^C$. Given a fixed encoding, we find the maximal Quantum Fisher
Information attainable via arbitrary $H^C$, which provides a fundamental bound
on the measurement precision. Our bounds show that: (i) assuming full control
of $H^C$, quantum non-commutativity does not offer any fundamental advantage in
the estimation of $\theta$; (ii) an exponential quantum advantage arises at low
temperatures if $H^C$ is constrained to have a spectral gap; (iii) in the case
of locally-encoded parameters, the optimal sensitivity presents a
Heisenberg-like $N^2$-scaling in terms of the number of particles of the probe,
which can be reached with local measurements. We apply our results to
paradigmatic spin chain models, showing that these fundamental limits can be
approached using local two-body interactions. Our results set the fundamental
limits and optimal control for metrology with thermal and ground state probes,
including probes at the verge of criticality.
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