Estimation of Hamiltonian parameters from thermal states
- URL: http://arxiv.org/abs/2401.10343v1
- Date: Thu, 18 Jan 2024 19:15:36 GMT
- Title: Estimation of Hamiltonian parameters from thermal states
- Authors: Luis Pedro Garc\'ia-Pintos, Kishor Bharti, Jacob Bringewatt, Hossein
Dehghani, Adam Ehrenberg, Nicole Yunger Halpern, Alexey V. Gorshkov
- Abstract summary: We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature.
We show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than $1/sqrtn$, beating the standard quantum limit.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We upper- and lower-bound the optimal precision with which one can estimate
an unknown Hamiltonian parameter via measurements of Gibbs thermal states with
a known temperature. The bounds depend on the uncertainty in the Hamiltonian
term that contains the parameter and on the term's degree of noncommutativity
with the full Hamiltonian: higher uncertainty and commuting operators lead to
better precision. We apply the bounds to show that there exist entangled
thermal states such that the parameter can be estimated with an error that
decreases faster than $1/\sqrt{n}$, beating the standard quantum limit. This
result governs Hamiltonians where an unknown scalar parameter (e.g. a component
of a magnetic field) is coupled locally and identically to $n$ qubit sensors.
In the high-temperature regime, our bounds allow for pinpointing the optimal
estimation error, up to a constant prefactor. Our bounds generalize to joint
estimations of multiple parameters. In this setting, we recover the
high-temperature sample scaling derived previously via techniques based on
quantum state discrimination and coding theory. In an application, we show that
noncommuting conserved quantities hinder the estimation of chemical potentials.
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