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Every Quantum Helps: Operational Advantage of Quantum Resources beyond Convexity
Kohdai Kuroiwa1,2, Ryuji Takagi3, Gerardo Adesso4
1Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, Ontario N2L 3G1, Canada.
Physical Review Letters
|April 29, 2024
Summary
This study explores quantum resource theories, focusing on non-convex resources. It shows that all quantum resource states offer advantages in channel discrimination tasks, even without convexity assumptions.
Area of Science:
- Quantum Information Science
- Quantum Computing Theory
Background:
- Quantum resource theories provide a framework for understanding quantum properties like entanglement and coherence.
- Many physical resources are non-convex, making their interpretation and usefulness challenging.
Purpose of the Study:
- To provide operational interpretations for generalized robustness in quantum resource theories without convexity assumptions.
- To demonstrate the inherent usefulness of quantum resource states in general resource theories.
Main Methods:
- Characterizing generalized robustness using a nonlinear resource witness.
- Analyzing a scenario with multiple constraints in quantum resource theories.
Main Results:
- Any quantum state demonstrates an advantage over a free state in multicopy channel discrimination.
- Generalized robustness equals the worst-case advantage in single-copy channel discrimination under multiple constraints.
Conclusions:
- Every quantum resource state offers a qualitative and quantitative advantage in discrimination tasks.
- This holds true in general resource theories, irrespective of the free states' structure.
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