Information--control limits for record-indistinguishable reset of a monitored qubit
Abstract
A qubit that is continuously monitored from the moment it is prepared in its excited state writes evidence of that preparation into its measurement record. We ask how much control is needed to reset such a qubit to its ground state while keeping its complete record statistically close to the record of an undriven ground-state qubit. The qubit is measured in σz at rate Γm with efficiency η and has no relaxation. For feedback that acts causally on the record, distinguishability is the Kullback--Leibler divergence D of the controlled record law from the reference law, and the control cost is the quadratic effort J, the integrated squared Rabi frequency. We prove that every open-loop drive leaves D infinite and that every admissible control obeys DJ≥ΓmU(η,D/κ0), where U is given by a one-parameter family of integrals and κ0=1−ln2. Our main result is the exact high-effort constant limε↓0inf{DJ/Γm: D≤ε}=K(η), where K(η)=[∫0π√(2η(1+cosθ)2+(1−η)sin2θ) dθ]2; an explicit sequence of two-phase feedback policies attains it. The first term of the integrand is the population evidence that the record receives while the qubit is rotated toward the ground state. The second is the price of the impurity created when the unrecorded part of the measurement dephases the coherence that the rotation needs; the record receives this evidence later, when the measurement repurifies the qubit. The global constant c(η)=inf DJ/Γm satisfies K/2≤ F2≤ c≤ K, where F2 is again given by an integral; c is known exactly at η=1 and in the limit η→0. With any nonzero relaxation rate the unconstrained infimum of DJ vanishes, so c(η) is specific to the relaxation-free model.
Related
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BibTeX
@misc{bugu2026informationcontrol,
title = {{Information--control limits for record-indistinguishable reset of a monitored qubit}},
author = {Sinan Bugu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.11393},
eprint = {2611.11393},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.11393},
}
RIS
TY - UNPB
TI - Information--control limits for record-indistinguishable reset of a monitored qubit
AU - Sinan Bugu
PY - 2026
DA - 2026/11/08
PB - arXiv
DO - 10.48550/arxiv.2611.11393
UR - https://arxiv.org/abs/2611.11393
AB - A qubit that is continuously monitored from the moment it is prepared in its excited state writes evidence of that preparation into its measurement record. We ask how much control is needed to reset such a qubit to its ground state while keeping its complete record statistically close to the record of an undriven ground-state qubit. The qubit is measured in σ_z at rate Γ_m with efficiency η and has no relaxation. For feedback that acts causally on the record, distinguishability is the Kullback--Leibler divergence D of the controlled record law from the reference law, and the control cost is the quadratic effort J, the integrated squared Rabi frequency. We prove that every open-loop drive leaves D infinite and that every admissible control obeys DJ≥Γ_mU(η,D/κ_0), where U is given by a one-parameter family of integrals and κ_0=1−ln2. Our main result is the exact high-effort constant lim_ε↓0inf{DJ/Γ_m: D≤ε}=K(η), where K(η)=[∫_0^π√(2η(1+cosθ)^2+(1−η)sin^2θ) dθ]^2; an explicit sequence of two-phase feedback policies attains it. The first term of the integrand is the population evidence that the record receives while the qubit is rotated toward the ground state. The second is the price of the impurity created when the unrecorded part of the measurement dephases the coherence that the rotation needs; the record receives this evidence later, when the measurement repurifies the qubit. The global constant c(η)=inf DJ/Γ_m satisfies K/2≤ F_2≤ c≤ K, where F_2 is again given by an integral; c is known exactly at η=1 and in the limit η→0. With any nonzero relaxation rate the unconstrained infimum of DJ vanishes, so c(η) is specific to the relaxation-free model.
ER -