Currencies in Resource Theories.

Area of Science:

• Quantum Information Science
• Thermodynamics
• Resource Theory

Background:

• Quantifying physical resources like entangled states or heat baths is challenging due to idealizations in current resource theories.
• Existing methods often assume perfect state knowledge or independent resource copies, limiting practical applications.

Purpose of the Study:

• To introduce a general theoretical tool called "currencies" for quantifying realistic physical resources.
• To develop a framework applicable to experimental settings with imperfect control and partial state information.

Main Methods:

• Developed the concept of "currencies" as a subset of resources used to quantify others.
• Established necessary and sufficient conditions for resource conversion based on weak theoretical assumptions.
• Generalized axiomatic approaches to thermodynamic entropy and work.

Main Results:

• Introduced a general tool for quantifying realistic physical resources under imperfect conditions.
• Demonstrated that weak assumptions yield useful currencies for resource conversion.
• Derived operational single-shot entropies for arbitrary resource descriptions by applying the framework to unital maps.

Conclusions:

• The developed "currency" framework offers a robust method for resource quantification in realistic scenarios.
• This approach generalizes existing resource theories and provides new insights into thermodynamic entropy and work.
• Enables practical quantification of quantum states and other physical resources in experimental contexts.