Operational Characterizations and Resource Structure of the Interactive Weight of Quantum Instruments
Abstract
Quantifying the interactivity of quantum instruments is fundamental to understanding their resource structure and operational capabilities. Here, we introduce the interactive weight of quantum instruments as a resource quantifier that measures the minimum fraction of an instrument that cannot be explained by non-interactive components. Through quantum-information tasks including quantum-state recovery, positive linear loss games, and environment-assisted input-blind extraction, we establish quantitative bounds on the interactive weight of quantum instruments and exact operational characterizations of its complementary quantity, the maximal non-interactive content. In particular, we extend environment-assisted input-blind extraction to the setting of restricted environmental access and develop a corresponding framework. Within the allowed-operations framework introduced by Hsieh et al., we establish fundamental resource-theoretic properties of the interactive weight of quantum instruments, including faithfulness, convexity, and monotonicity under deterministic allowed operations. Furthermore, we prove that the maximal non-interactive content satisfies exact multiplicativity under independent parallel composition, yielding necessary constraints on multicopy resource conversion and establishing the finite-copy maximal-weight distillation no-go result under deterministic allowed operations. These results establish a unified theoretical framework for the interactive weight of quantum instruments from the perspectives of resource quantification, operational interpretation, and resource conversion, providing systematic theoretical tools for the quantitative comparison and conversion of interactive quantum instruments.
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BibTeX
@misc{he2026operational,
title = {{Operational Characterizations and Resource Structure of the Interactive Weight of Quantum Instruments}},
author = {Yongxi He and Xin Hong and Yu Luo and Xiangzhen Zhou and Shenggang Ying},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07371},
eprint = {2611.07371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07371},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Operational Characterizations and Resource Structure of the Interactive Weight of Quantum Instruments
AU - Yongxi He
AU - Xin Hong
AU - Yu Luo
AU - Xiangzhen Zhou
AU - Shenggang Ying
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07371
UR - https://arxiv.org/abs/2611.07371
AB - Quantifying the interactivity of quantum instruments is fundamental to understanding their resource structure and operational capabilities. Here, we introduce the interactive weight of quantum instruments as a resource quantifier that measures the minimum fraction of an instrument that cannot be explained by non-interactive components. Through quantum-information tasks including quantum-state recovery, positive linear loss games, and environment-assisted input-blind extraction, we establish quantitative bounds on the interactive weight of quantum instruments and exact operational characterizations of its complementary quantity, the maximal non-interactive content. In particular, we extend environment-assisted input-blind extraction to the setting of restricted environmental access and develop a corresponding framework. Within the allowed-operations framework introduced by Hsieh et al., we establish fundamental resource-theoretic properties of the interactive weight of quantum instruments, including faithfulness, convexity, and monotonicity under deterministic allowed operations. Furthermore, we prove that the maximal non-interactive content satisfies exact multiplicativity under independent parallel composition, yielding necessary constraints on multicopy resource conversion and establishing the finite-copy maximal-weight distillation no-go result under deterministic allowed operations. These results establish a unified theoretical framework for the interactive weight of quantum instruments from the perspectives of resource quantification, operational interpretation, and resource conversion, providing systematic theoretical tools for the quantitative comparison and conversion of interactive quantum instruments.
ER -