System-bath entanglement theorem with Gaussian environments.

Area of Science:

• Quantum mechanics
• Quantum information theory
• Condensed matter physics

Background:

• Quantum systems are often influenced by their environment (bath).
• Understanding system-bath interactions is crucial for quantum dynamics.
• Quantifying entanglement between system and bath is challenging.

Purpose of the Study:

• To establish a general theorem for system-bath entanglement in Gaussian environments.
• To connect entangled response functions of composite systems to local ones.
• To enable evaluation of system-bath entanglement within existing quantum dissipation theories.

Main Methods:

• Development of the "system-bath entanglement theorem."
• Validation using the exact dissipaton-equation-of-motion approach.
• Numerical demonstrations on spin-boson systems with Fano interference spectroscopies.

Main Results:

• The system-bath entanglement theorem is established for arbitrary systems and Gaussian baths.
• The theorem relates composite entangled response functions to local system response functions.
• The theorem's validity is confirmed through direct evaluation and numerical examples.

Conclusions:

• The established theorem provides a powerful tool for analyzing system-bath entanglement.
• This work extends the applicability of quantum dissipation theories to entanglement properties.
• The findings facilitate deeper understanding of quantum correlations in complex systems.