Distilling Gaussian states with Gaussian operations is impossible.

Area of Science:

• Quantum Information Science
• Quantum Optics
• Quantum Communication

Background:

• Entanglement distillation is crucial for quantum communication, enabling error correction and state purification.
• Finite-dimensional quantum states can be distilled using iterative protocols with local operations and classical communication.
• Gaussian quantum states are fundamental in continuous-variable quantum information processing.

Purpose of the Study:

• To investigate the possibility of distilling Gaussian quantum states using specific local operations and detection methods.
• To determine if entanglement distillation protocols successful for finite-dimensional systems can be applied to Gaussian states.
• To explore the limitations and implications for distributing Gaussian quantum states over long distances.

Main Methods:

• Analysis of distillation protocols for Gaussian quantum states.
• Consideration of local unitary operations preserving Gaussianity.
• Inclusion of homodyne detection, classical communication, and postprocessing.
• Comparison with distillation protocols for finite-dimensional systems.

Main Results:

• Demonstration that no distillation protocol exists for Gaussian quantum states under the specified conditions.
• Highlighting the contrast with successful distillation methods for finite-dimensional quantum states.
• Identification of limitations imposed by Gaussianity preservation and homodyne detection.

Conclusions:

• The absence of a distillation protocol for Gaussian states has significant ramifications for quantum communication networks.
• The findings necessitate alternative strategies for distributing high-fidelity Gaussian states over large distances.
• The study clarifies the boundaries of applying entanglement distillation techniques across different quantum state types.