# Every quantum helps: Operational advantage of quantum resources beyond convexity

### APA

Kuroiwa, K. (2024). Every quantum helps: Operational advantage of quantum resources beyond convexity. Perimeter Institute. https://pirsa.org/24010072

### MLA

Kuroiwa, Kohdai. Every quantum helps: Operational advantage of quantum resources beyond convexity. Perimeter Institute, Jan. 10, 2024, https://pirsa.org/24010072

### BibTex

@misc{ pirsa_PIRSA:24010072, doi = {10.48660/24010072}, url = {https://pirsa.org/24010072}, author = {Kuroiwa, Kohdai}, keywords = {Quantum Information}, language = {en}, title = {Every quantum helps: Operational advantage of quantum resources beyond convexity}, publisher = {Perimeter Institute}, year = {2024}, month = {jan}, note = {PIRSA:24010072 see, \url{https://pirsa.org}} }

Kohdai Kuroiwa Perimeter Institute for Theoretical Physics

## Abstract

As quantum technologies are expected to provide us with unprecedented benefits, identifying what quantum-mechanical properties are useful is a pivotal question. Quantum resource theories provide a unified framework to analyze such quantum properties, which has been successful in the understanding of fundamental properties such as entanglement and coherence. While these are examples of convex resources, for which quantum advantages can always be identified, many physical resources are described by a non-convex set of free states and their interpretation has so far remained elusive. In this work, we address the fundamental question of the usefulness of quantum resources without convexity assumption, by providing two operational interpretations of the generalized robustness resource measure in general resource theories. On the one hand, we characterize the generalized robustness in terms of a non-linear resource witness and reveal that any state is more advantageous than a free one in some multi-copy channel discrimination task. On the other hand, we consider a scenario where a theory is characterized by multiple constraints and show that the generalized robustness coincides with the worst-case advantage in a single-copy channel discrimination setting. We further extend these results to the weight resource measure and QRTs for quantum channels and quantum instruments. Based on these characterizations, we conclude that every quantum resource state shows a qualitative and quantitative advantage in discrimination problems in a general resource theory even without any assumption on the structure of the free sets. This talk is based on arXiv:2310.09154 and arXiv:2310.09321.

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