Reduced dynamical maps in the presence of initial correlations

Area of Science:

• Quantum Physics
• Quantum Information Theory
• Open Quantum Systems

Background:

• Initial system-environment correlations are crucial in open quantum systems.
• Existing frameworks often struggle with these correlations, limiting their applicability.
• Understanding these correlations is key to accurately modeling quantum dynamics.

Purpose of the Study:

• To develop a novel framework for constructing completely positive dynamical evolutions.
• To incorporate system-environment initial correlations into quantum dynamics.
• To explore the implications of these correlations for quantum information processing.

Main Methods:

• Utilizing the commutativity of the compatibility domain derived from marginal states.
• Applying fundamental properties of completely positive maps.
• Analyzing correlated states with finite quantum discord (excluding entangled states).

Main Results:

• A new framework for constructing completely positive dynamical evolutions in the presence of initial correlations.
• Demonstration that the framework accommodates states with finite quantum discord.
• Explicit illustration of the non-uniqueness of completely positive extensions beyond the compatibility domain.

Conclusions:

• The proposed framework offers a robust method for studying open quantum systems with initial correlations.
• The findings highlight the importance of considering initial correlations for accurate quantum dynamics.
• The study provides critical insights into the application of these maps in open quantum systems.