Operational Advantage of Quantum Resources in Subchannel Discrimination (1809.01672v3)

Abstract: One of the central problems in the study of quantum resource theories is to provide a given resource with an operational meaning, characterizing physical tasks in which the resource can give an explicit advantage over all resourceless states. We show that this can always be accomplished for all convex resource theories. We establish in particular that any resource state enables an advantage in a channel discrimination task, allowing for a strictly greater success probability than any state without the given resource. Furthermore, we find that the generalized robustness measure serves as an exact quantifier for the maximal advantage enabled by the given resource state in a class of subchannel discrimination problems, providing a universal operational interpretation to this fundamental resource quantifier. We also consider a wider range of subchannel discrimination tasks and show that the generalized robustness still serves as the operational advantage quantifier for several well-known theories such as entanglement, coherence, and magic.

Operational Advantage of Quantum Resources in Subchannel Discrimination

The paper "Operational Advantage of Quantum Resources in Subchannel Discrimination" addresses a significant question in quantum resource theories: providing operational meaning to quantum resources. This work explores the capability of quantum resource states to offer advantages in discrimination tasks compared to resourceless states, focusing on convex resource theories.

The authors establish that every resource state in any convex quantum resource theory can be used to achieve greater success in subchannel discrimination tasks than any free states. This finding emphasizes the utility of quantum resources beyond theoretical interest and ensures practical relevance. Particularly, they highlight the generalized robustness measure as a universal quantifier for this advantage, granting operational significance to a previously geometrically focused resource metric.

The paper comprises several important components:

1. Channel Discrimination Utility: The authors extend known results from specific theories like entanglement to all convex resource theories. They prove that every resource state manifests an advantage in channel discrimination tasks, providing a broader operational characterization across different resource theories.
2. Generalized Robustness Measure: The generalized robustness measure is posited as a key quantifier of the operational success in subchannel discrimination. The paper proves its adequacy as a measure of maximal advantage in various discrimination problems, undeniably linking resource quantification with practical quantum information tasks.
3. Measurements and Flexibility: While robust success quantification can be influenced by measurement flexibility, the authors show that underlying quantum resources maintain their operational advantage even when measurement protocols vary within the field of free measurements. Notably, they explore scenarios where the generalized robustness remains consistent across separability, coherence, and magic even when measurements are restricted to free or rank-one measurements.
4. Theory and Practical Implications: By establishing the operational significance of quantum resources in subchannel discrimination, the research encourages a refined understanding of resource theories' role in quantum technologies like quantum communication and computation. It also opens avenues for operational tasks, such as resource certification, where these quantum resources can be effectively discerned and exploited for their advantages in practical settings.

This paper provides a rigorous extension of quantum resource theories into operational tasks, supporting the idea that quantum resources have innate advantages beyond their theoretical foundations. Future research can build upon these results, exploring further implications for non-convex resource theories and expanding the operational frontier of quantum resources into broader technological implementations.