Operational Quantification of Continuous-Variable Quantum Resources.

Area of Science:

• Quantum Information Science
• Quantum Optics
• Quantum Information Theory

Background:

• Quantum states possess diverse resources crucial for practical applications.
• Existing methods for quantifying quantum resources are often limited to finite dimensions or lack operational connections.
• There is a need for universally applicable methods to measure and compare different types of quantum resources.

Purpose of the Study:

• To develop a general method for quantifying resources in continuous-variable quantum systems.
• To establish an operationally meaningful and well-behaved resource quantifier.
• To demonstrate the applicability of the proposed method to various physically relevant quantum resources.

Main Methods:

• Introduction of a general quantification method based on the robustness measure for continuous-variable quantum systems.
• Demonstration of the operational interpretation of the robustness measure in channel discrimination tasks.
• Analysis of the properties of the robustness measure as a bona fide resource quantifier within convex resource theories.

Main Results:

• The robustness measure is applicable to diverse resources including optical nonclassicality, entanglement, genuine non-Gaussianity, and coherence.
• The measure has a direct operational interpretation as the advantage in channel discrimination tasks.
• The robustness is a well-behaved resource quantifier, unlike the standard robustness, and is directly observable via a single witness operator.

Conclusions:

• The developed robustness measure provides a universally applicable and operationally relevant tool for quantifying resources in continuous-variable quantum systems.
• The measure is shown to be a bona fide resource quantifier and directly observable, facilitating practical applications.
• The exact computability of the robustness is demonstrated for several classes of quantum states.