The Structure of Higher-Order Quantum Resources with an Application to Coherence
Abstract
We develop a general framework for higher-order quantum resources that treats the resourcefulness of quantum states, channels, and supermaps (also called processes) in a unified manner. By generalizing well-established concepts from resource theories of states and channels, we introduce and study supermap resource monotones and supermap distillation and dilution. As free supermaps, we consider free networks (supermaps that can be implemented with free channels), compatible supermaps (sets of supermaps closed under arbitrary composition), and maximally free superchannels. Specializing to approximate channel-to-channel conversions, we show that under mild assumptions, the conversion error with respect to the diamond distance and the worst-case infidelity coincide. We then apply the general framework to resource theories of dynamical coherence, where we establish the existence of largest sets of compatible supermaps. By characterizing these sets with semidefinite constraints, we show that they are strictly larger than the corresponding free networks but do not contain all maximally free superchannels. We finish by investigating the operational differences of these sets in one-shot channel distillation and dilution, providing solutions for both tasks in the parallel setting and for dilution in the adaptive setting.
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BibTeX
@misc{ahnefeld2026structure,
title = {{The Structure of Higher-Order Quantum Resources with an Application to Coherence}},
author = {Felix Ahnefeld and Thomas Theurer and Martin B. Plenio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40186},
eprint = {2609.40186},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40186},
}
RIS
TY - UNPB
TI - The Structure of Higher-Order Quantum Resources with an Application to Coherence
AU - Felix Ahnefeld
AU - Thomas Theurer
AU - Martin B. Plenio
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40186
UR - https://arxiv.org/abs/2609.40186
AB - We develop a general framework for higher-order quantum resources that treats the resourcefulness of quantum states, channels, and supermaps (also called processes) in a unified manner. By generalizing well-established concepts from resource theories of states and channels, we introduce and study supermap resource monotones and supermap distillation and dilution. As free supermaps, we consider free networks (supermaps that can be implemented with free channels), compatible supermaps (sets of supermaps closed under arbitrary composition), and maximally free superchannels. Specializing to approximate channel-to-channel conversions, we show that under mild assumptions, the conversion error with respect to the diamond distance and the worst-case infidelity coincide. We then apply the general framework to resource theories of dynamical coherence, where we establish the existence of largest sets of compatible supermaps. By characterizing these sets with semidefinite constraints, we show that they are strictly larger than the corresponding free networks but do not contain all maximally free superchannels. We finish by investigating the operational differences of these sets in one-shot channel distillation and dilution, providing solutions for both tasks in the parallel setting and for dilution in the adaptive setting.
ER -