Set Coherence: Basis-Independent Quantification of Quantum Coherence

Area of Science:

• Quantum Information Science
• Quantum Foundations

Background:

• Quantum state coherence is typically defined with respect to a preferred basis, introducing arbitrariness.
• This basis dependence limits the characterization of coherence in multipartite or collective quantum systems.

Purpose of the Study:

• Introduce and quantify 'set coherence' as a basis-independent measure for the coherence of quantum state sets.
• Develop operational measures for set coherence applicable to both quantum states and measurements.
• Connect set coherence to existing resource theories in quantum information.

Main Methods:

• Definition of set coherence as a basis-independent property of quantum state ensembles.
• Construction of quantitative measures for set coherence.
• Establishing operational meaning through quantum discrimination games.
• Relating set coherence to resource-theoretic frameworks.

Main Results:

• Set coherence provides a robust, basis-independent characterization of collective quantum coherence.
• The developed measures quantify the advantage of using coherent sets of quantum states or measurements.
• These measures align with established resource-theoretic approaches, offering a unified perspective.

Conclusions:

• Set coherence offers a novel and fundamental way to understand and quantify quantum coherence in a basis-independent manner.
• The operational measures provide practical tools for identifying and utilizing quantum resources.
• This work bridges different approaches to quantum resources, enhancing the understanding of quantum advantage.