Metrology of weak quantum perturbations

Fuente: arXiv
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Main Authors: Mohammdi, Sidali, Bina, Matteo, Gharbi, Abdelhakim, Paris, Matteo G. A.
Format: Preprint
Published: 2023
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_version_ 1866916615094796288
author Mohammdi, Sidali
Bina, Matteo
Gharbi, Abdelhakim
Paris, Matteo G. A.
author_facet Mohammdi, Sidali
Bina, Matteo
Gharbi, Abdelhakim
Paris, Matteo G. A.
contents We consider quantum systems with a Hamiltonian containing a weak perturbation i.e. $\boldsymbol{H=H_0} + \boldsymbolλ \cdot \boldsymbol{\tilde{H}}$, $\boldsymbolλ= \{λ_1, λ_2,...\}$, $\boldsymbol{\tilde{H}}$ $= \{H_1, H_2,...\}$, $\left|\boldsymbolλ\right| \ll 1$, and address situations where $\boldsymbol{\tilde{H}}$ is known but the values of the couplings $\boldsymbolλ$ are unknown, and should be determined by performing measurements on the system. We consider two scenarios: in the first one we assume that measurements are performed on a given stationary state of the system, e.g., the ground state, whereas in the second one an initial state is prepared and then measured after evolution. In both cases, we look for the optimal measurements to estimate the couplings and evaluate the ultimate limits to precision. In particular, we derive general results for one and two couplings, and analyze in details some specific qubit models. Our results indicates that dynamical estimation schemes may provide enhanced precision upon a suitable choice of the initial preparation and the interaction time.
format Preprint
id arxiv_https___arxiv_org_abs_2310_03820
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Metrology of weak quantum perturbations
Mohammdi, Sidali
Bina, Matteo
Gharbi, Abdelhakim
Paris, Matteo G. A.
Quantum Physics
We consider quantum systems with a Hamiltonian containing a weak perturbation i.e. $\boldsymbol{H=H_0} + \boldsymbolλ \cdot \boldsymbol{\tilde{H}}$, $\boldsymbolλ= \{λ_1, λ_2,...\}$, $\boldsymbol{\tilde{H}}$ $= \{H_1, H_2,...\}$, $\left|\boldsymbolλ\right| \ll 1$, and address situations where $\boldsymbol{\tilde{H}}$ is known but the values of the couplings $\boldsymbolλ$ are unknown, and should be determined by performing measurements on the system. We consider two scenarios: in the first one we assume that measurements are performed on a given stationary state of the system, e.g., the ground state, whereas in the second one an initial state is prepared and then measured after evolution. In both cases, we look for the optimal measurements to estimate the couplings and evaluate the ultimate limits to precision. In particular, we derive general results for one and two couplings, and analyze in details some specific qubit models. Our results indicates that dynamical estimation schemes may provide enhanced precision upon a suitable choice of the initial preparation and the interaction time.
title Metrology of weak quantum perturbations
topic Quantum Physics
url https://arxiv.org/abs/2310.03820