All Quantum Resources Provide an Advantage in Exclusion Tasks.

Area of Science:

• Quantum Information Science
• Quantum Resource Theories

Background:

• A fundamental aspect of quantum resource theories is the need for a robust measure.
• This measure should possess essential theoretical properties and a clear operational interpretation.

Purpose of the Study:

• To demonstrate that the convex weight, a natural measure of quantum resource cost, satisfies all desired properties.
• To establish the operational meaning of the convex weight in terms of quantum exclusion tasks.

Main Methods:

• General theoretical framework for convex weight.
• Application to specific quantum devices: state assemblages, measurement sets, and transformation sets.
• Analytical characterization of convex components and weights.

Main Results:

• The convex weight possesses all fundamental properties required of a quantum resource measure.
• The convex weight directly corresponds to the relative advantage in exclusion (antidistinguishability) tasks.
• A complete characterization of convex components and weights for various quantum devices is provided.

Conclusions:

• The convex weight is a well-behaved and operationally meaningful measure in quantum resource theories.
• This work provides a complete analytical framework for understanding and bounding the convex weight.