Quantifying coherence

Area of Science:

• Quantum Information Theory
• Quantum Physics

Background:

• Coherence is a fundamental property in quantum mechanics.
• Quantifying coherence is crucial for understanding and utilizing quantum phenomena.
• Existing methods for coherence quantification lack a rigorous, resource-based framework.

Purpose of the Study:

• To introduce a rigorous theoretical framework for quantifying coherence.
• To identify intuitive and computable measures of coherence.
• To establish defining conditions for valid coherence measures.

Main Methods:

• Adopting the perspective of coherence as a physical resource.
• Deriving defining conditions that coherence measures must satisfy.
• Analyzing various functionals to determine their validity as coherence measures.

Main Results:

• A rigorous framework for coherence quantification has been established.
• Intuitive and easily computable measures of coherence have been identified.
• Classes of functionals satisfying the defining conditions were identified, distinguishing them from non-coherence quantities.

Conclusions:

• The developed framework provides a solid foundation for coherence quantification.
• Further research is needed to fully develop the theory of coherence as a resource.
• The identified measures offer practical tools for quantum information processing.