The von Neumann Entropy for Mixed States

Area of Science:

• Quantum Information Theory
• Statistical Mechanics
• Atomic Physics

Background:

• The Araki-Lieb inequality is crucial for calculating subsystem entropy in pure initial states.
• Calculating entropy for subsystems initially in mixed states remains a challenge.
• Existing methods struggle when dealing with mixed initial states in quantum systems.

Purpose of the Study:

• To develop a method for calculating quantum entropy when one subsystem is initially in a mixed state.
• To extend the applicability of the Araki-Lieb inequality.
• To determine the von Neumann entropy for large quantum systems in specific interaction scenarios.

Main Methods:

• Application of the Araki-Lieb inequality to a system with a mixed initial state.
• Analysis of a two-level atom interacting with a quantized field.
• Derivation of the von Neumann entropy for the larger subsystem.

Main Results:

• Demonstrated a novel method to calculate quantum entropy for mixed initial states.
• Successfully applied the Araki-Lieb inequality in a scenario previously considered intractable.
• Obtained the von Neumann entropy for an infinite system in the context of atom-field interaction.

Conclusions:

• The Araki-Lieb inequality can be effectively used to calculate von Neumann entropy even when subsystems start in mixed states.
• This work provides a new pathway for entropy calculations in complex quantum systems.
• The findings have implications for understanding quantum information in diverse physical settings.