Reduced and projected two-particle entanglement at finite temperatures

Area of Science:

• Quantum physics
• Mesoscopic conductors
• Entanglement theory

Background:

• Two-particle entanglement is crucial for quantum information processing.
• Detecting entanglement in mesoscopic systems at finite temperatures presents significant challenges.
• Existing theories often assume ideal conditions, neglecting thermal effects.

Purpose of the Study:

• To develop a theoretical framework for entanglement production and detection in mesoscopic conductors at finite temperatures.
• To differentiate between projected and reduced density matrix entanglement.
• To apply the theory to a specific experimental setup and analyze its findings.

Main Methods:

• Formulating a theory for two-particle entanglement in mesoscopic conductors.
• Analyzing the projected density matrix and reduced density matrix entanglement.
• Comparing theoretical predictions with experimental results from a fermionic Hanbury Brown Twiss interferometer.

Main Results:

• The entanglement of the projected density matrix differs from that of the reduced density matrix.
• Reduced entanglement serves as a witness for projected entanglement under general conditions.
• Despite significant entanglement production in the Neder et al. experiment, the detectable entanglement was found to be close to zero.

Conclusions:

• The theoretical framework provides a new perspective on entanglement detection in realistic experimental settings.
• Finite temperature effects and measurement techniques significantly impact the detectability of entanglement.
• Further research is needed to bridge the gap between theoretical entanglement production and experimental detection in mesoscopic systems.