Operational Interpretation of Weight-Based Resource Quantifiers in Convex Quantum Resource Theories

Area of Science:

• Quantum Information Theory
• Quantum Resource Theories
• Quantum Measurement Theory

Background:

• Convex quantum resource theories provide a framework for quantifying quantum resources.
• Existing quantifiers may lack operational interpretations for arbitrary resources.
• The resource theory of entanglement has a long-standing quantifier without a clear operational meaning.

Purpose of the Study:

• Introduce a universal resource quantifier, the weight of resource, for convex quantum resource theories.
• Establish an operational interpretation for this quantifier in the context of resource exclusion tasks.
• Connect measurement resource quantifiers to information-theoretic quantities for quantum channels.

Main Methods:

• Definition of the weight of resource for states and measurements.
• Analysis of the operational task of excluding subchannels (states).
• Introduction of exclusion-type information-theoretic quantities for quantum channels.

Main Results:

• The weight of resource quantifies the advantage of resourceful states/measurements over free ones in exclusion tasks.
• A connection is established between the weight of resource of a measurement and exclusion-type information of quantum-to-classical channels.
• The introduced framework provides an operational interpretation for the 21-year-old Lewenstein-Sanpera decomposition in entanglement theory.

Conclusions:

• The weight of resource offers a unified and operationally meaningful way to quantify resources in various quantum theories.
• This work bridges the gap between abstract resource quantification and concrete operational tasks.
• The findings provide new insights into entanglement theory and quantum channel characterization.