Improving the estimation of spin-bath parameters via initial correlations and a two-qubit probe
Abstract
We study how a second qubit can improve the estimation of spin-environment parameters when only one of the two qubits is measured. Both qubits are coupled to a common spin bath through the exactly solvable central-spin model, in which populations and coherences both evolve. Because the bath operator coupled to the qubits commutes with the bath Hamiltonian, the environment induces no effective interaction between the qubits. Without initial correlations or direct inter-qubit coupling, the two-qubit probe therefore performs exactly like a single qubit. When initial system-environment correlations are included, preparing the second qubit reshapes the environment statistics in a parameter-dependent way, and the measured qubit reads out this imprint. This improves the quantum Fisher information (QFI) for the coupling strength by factors of 3-4 relative to a correlated single-qubit probe, and by more than an order of magnitude relative to an uncorrelated one. For temperature estimation, the improvement reaches a factor of about 8. A direct Ising coupling does not help by itself, but the advantage persists in its presence. We also derive the classical Fisher information for arbitrary projective measurements and identify the measurement that saturates the QFI, which in general lies out of the equatorial plane of the Bloch sphere.
Related
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BibTeX
@misc{khan2026improving,
title = {{Improving the estimation of spin-bath parameters via initial correlations and a two-qubit probe}},
author = {Anila Khan and Huzaifa Amjad and Rizwan Abbas and Ali Raza Mirza},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23582},
eprint = {2610.23582},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23582},
}
RIS
TY - UNPB
TI - Improving the estimation of spin-bath parameters via initial correlations and a two-qubit probe
AU - Anila Khan
AU - Huzaifa Amjad
AU - Rizwan Abbas
AU - Ali Raza Mirza
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23582
UR - https://arxiv.org/abs/2610.23582
AB - We study how a second qubit can improve the estimation of spin-environment parameters when only one of the two qubits is measured. Both qubits are coupled to a common spin bath through the exactly solvable central-spin model, in which populations and coherences both evolve. Because the bath operator coupled to the qubits commutes with the bath Hamiltonian, the environment induces no effective interaction between the qubits. Without initial correlations or direct inter-qubit coupling, the two-qubit probe therefore performs exactly like a single qubit. When initial system-environment correlations are included, preparing the second qubit reshapes the environment statistics in a parameter-dependent way, and the measured qubit reads out this imprint. This improves the quantum Fisher information (QFI) for the coupling strength by factors of 3-4 relative to a correlated single-qubit probe, and by more than an order of magnitude relative to an uncorrelated one. For temperature estimation, the improvement reaches a factor of about 8. A direct Ising coupling does not help by itself, but the advantage persists in its presence. We also derive the classical Fisher information for arbitrary projective measurements and identify the measurement that saturates the QFI, which in general lies out of the equatorial plane of the Bloch sphere.
ER -