Operational Resource Theory of Coherence.

Area of Science:

• Quantum Information Science
• Quantum Thermodynamics
• Foundations of Quantum Mechanics

Background:

• Coherence is a fundamental resource in quantum mechanics, essential for quantum computation and information processing.
• Understanding the quantification and manipulation of coherence under realistic conditions (incoherent operations) is crucial for developing quantum technologies.

Purpose of the Study:

• To establish an operational theory for quantifying quantum coherence.
• To introduce and define 'coherence distillation' and 'coherence cost' as fundamental measures.
• To provide an operational interpretation for the relative entropy of coherence.

Main Methods:

• Focusing on the optimal rates of tasks involving quantum state processing under incoherent operations.
• Introducing and analyzing the concepts of coherence distillation and coherence cost.
• Deriving single-letter formulas for these quantities in the asymptotic limit of many state copies.

Main Results:

• The distillable coherence is shown to be equal to the relative entropy of coherence.
• The coherence cost is determined by the coherence of formation, an optimization over convex decompositions.
• Demonstrated that no 'bound coherent states' exist, where coherence is consumed without possibility of recovery.
• Established a criterion for characterizing all reversible states in coherence theory, showing it is generically irreversible.

Conclusions:

• The relative entropy of coherence and coherence of formation are operationally meaningful quantities.
• Coherence theory under incoherent operations is predominantly irreversible.
• These findings provide a robust framework for understanding and utilizing coherence as a resource in quantum information processing.