Attainable Boundaries versus Operational Equivalence: Dual Benchmarks for the Hierarchical Assessment of Quantum Resources
Abstract
Conventional resource theories quantify utility against an idealized free set ℱ. In practice, however, realizable states are confined to a specific supply environment ℰ shaped by experimental and noise constraints. We propose a framework that evaluates the relative utility of arbitrary states with respect to ℰ, using two reference representations: the set of states reachable by free operations (defining the attainable boundary) and the set obtained via numerical optimization (defining operational equivalence). Two complementary methodologies are established. First, by assessing each state under its individually optimized strategy, we provide a strategy-dependent benchmark that quantifies achievable performance. Second, by deriving the optimal strategy for each state separately, we obtain a computable lower bound, yielding a strategy-independent measure of relative superiority that is independent of specific setups. To realize these methodologies numerically, we introduce relative measures based on the generalized robustness and the relative entropy. We then establish, theoretically, a quantitative hierarchical relation between the strategy-dependent benchmark and the strategy-independent lower bound. In a thermodynamic setting, the minimum work cost for synthesizing a target state is lower-bounded by the free-energy difference, which reflects only absolute utility. Applying our framework, we identify this bound as a strategy-independent quantification. Through two scenarios based respectively on information-theoretic distance and thermodynamic distance, we derive upper bounds on the minimum work cost for recovering entanglement in a noisy environment. We show that, at moderate and low temperatures in the low-noise regime, the thermodynamic-distance-based upper bound is tighter than the information-theoretic one.
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BibTeX
@misc{kim2026attainable,
title = {{Attainable Boundaries versus Operational Equivalence: Dual Benchmarks for the Hierarchical Assessment of Quantum Resources}},
author = {Sunho Kim and Chunhe Xiong and Junde Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11094},
eprint = {2610.11094},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11094},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Attainable Boundaries versus Operational Equivalence: Dual Benchmarks for the Hierarchical Assessment of Quantum Resources
AU - Sunho Kim
AU - Chunhe Xiong
AU - Junde Wu
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.11094
UR - https://arxiv.org/abs/2610.11094
AB - Conventional resource theories quantify utility against an idealized free set ℱ. In practice, however, realizable states are confined to a specific supply environment ℰ shaped by experimental and noise constraints. We propose a framework that evaluates the relative utility of arbitrary states with respect to ℰ, using two reference representations: the set of states reachable by free operations (defining the attainable boundary) and the set obtained via numerical optimization (defining operational equivalence). Two complementary methodologies are established. First, by assessing each state under its individually optimized strategy, we provide a strategy-dependent benchmark that quantifies achievable performance. Second, by deriving the optimal strategy for each state separately, we obtain a computable lower bound, yielding a strategy-independent measure of relative superiority that is independent of specific setups. To realize these methodologies numerically, we introduce relative measures based on the generalized robustness and the relative entropy. We then establish, theoretically, a quantitative hierarchical relation between the strategy-dependent benchmark and the strategy-independent lower bound. In a thermodynamic setting, the minimum work cost for synthesizing a target state is lower-bounded by the free-energy difference, which reflects only absolute utility. Applying our framework, we identify this bound as a strategy-independent quantification. Through two scenarios based respectively on information-theoretic distance and thermodynamic distance, we derive upper bounds on the minimum work cost for recovering entanglement in a noisy environment. We show that, at moderate and low temperatures in the low-noise regime, the thermodynamic-distance-based upper bound is tighter than the information-theoretic one.
ER -