Assisted Distillation of Quantum Coherence.

Area of Science:

• Quantum Information Science
• Quantum Thermodynamics
• Quantum Foundations

Background:

• Coherence is a key resource in quantum mechanics, essential for quantum computation and information processing.
• Assisted processes, involving collaboration between multiple systems or parties, are crucial for enhancing quantum tasks.
• Understanding the limits of coherence generation and manipulation is vital for advancing quantum technologies.

Purpose of the Study:

• To introduce and analyze the novel task of assisted coherence distillation.
• To define and characterize 'coherence of assistance' as a fundamental quantity in this process.
• To explore the connection between coherence distillation, von Neumann entropy, and multipartite quantum systems.

Main Methods:

• Development of the theoretical framework for assisted coherence distillation.
• Introduction of local quantum-incoherent operations and classical communication (LQICC) as the operational paradigm.
• Mathematical characterization of the asymptotic rate of distillation for pure states.

Main Results:

• The asymptotic rate of assisted coherence distillation for pure states is proven to be equal to the coherence of assistance.
• Properties of coherence of assistance are derived, analogous to entanglement of assistance.
• A novel interpretation of von Neumann entropy is proposed: it quantifies the maximum achievable gain in quantum coherence through assistance.

Conclusions:

• Assisted coherence distillation provides a new perspective on quantifying and generating quantum coherence.
• The concept of coherence of assistance offers a valuable tool for understanding quantum correlations.
• The findings have implications for quantum information processing, quantum thermodynamics, and the fundamental understanding of quantum entropy.