What is a Gaussian channel, and when is it physically implementable using a multiport interferometer?

Area of Science:

• Quantum Information Science
• Continuous-Variable Quantum Systems
• Quantum Communication

Background:

• Quantum Gaussian channels are essential models for quantum communication and information processing.
• Existing literature presents multiple, sometimes conflicting, definitions of these channels.
• Physical implementation of quantum channels is crucial for developing quantum technologies.

Purpose of the Study:

• To provide a unified framework for understanding quantum Gaussian channels.
• To investigate the physical realization of quantum Gaussian channels using linear optics.
• To address foundational questions and clarify misunderstandings in the field.

Main Methods:

• Formal proof of equivalence between different definitions of quantum Gaussian channels.
• Analysis of linear optical multiport interferometers for channel implementation.
• Characterization of Gaussian channels using ampliations and specific matrix pairs.

Main Results:

• A rigorous, unified framework for quantum Gaussian channels is established.
• New characterizations of Gaussian channels based on ampliations are introduced.
• Conditions for the physical implementability of Gaussian channels via linear optics are precisely defined.

Conclusions:

• The study clarifies foundational aspects of quantum Gaussian channels.
• It offers a pathway for the physical realization of these channels using linear optics.
• This work resolves ambiguities and advances the understanding of quantum information processing.