Attainable Boundaries versus Operational Equivalence: Dual Benchmarks for the Hierarchical Assessment of Quantum Resources

Abstract:While conventional quantum resource theories quantify utility relative to an idealized set of free states, practical implementations are confined to a specific supply environment---a framework encompassing all states realizable or preparable via current experimental apparatus and design choices, not limited to free states. This work proposes a novel framework for evaluating the relative utility of arbitrary quantum states against the resource set made accessible by these current selections. We specifically focus our investigation on two canonical representations: the set of states reachable via free operations as the attainable boundary imposed by current experimental constraints, and the set defined through numerical optimization as the criterion for operational equivalence. Our framework establishes two core evaluation methodologies. First, we provide a strategy-dependent benchmark by assessing a state's performance relative to the reference set under its individually optimized strategy, thereby quantifying achievable performance. Second, we derive a computable lower bound on this superiority by considering optimal strategies for each state individually, enabling the quantification of strategy-independent relative performance independent of specific experimental setups. Beyond relative efficiency metrics, we demonstrate the practical utility of this approach for resource management scenarios, including the selective extraction of states advantageous for storage and distribution, and the concentration of residual resources. Using quantum entanglement as a paradigmatic example, we prove that distillable entanglement can be fully recovered via extraction and concentration when the reference set is restricted to pure states, thereby demonstrating the practical relevance of our framework.

arXiv:2610.11094 [quant-ph]

(or arXiv:2610.11094v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.11094 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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