Device-independent tests of classical and quantum dimensions

Area of Science:

• Quantum information science
• Classical and quantum system analysis

Background:

• Determining the dimensionality of physical systems is crucial for understanding their complexity.
• Existing methods for dimension testing often rely on specific system assumptions or are limited in scope.

Purpose of the Study:

• To develop a general formalism for testing the dimensionality of classical and quantum systems in a black-box scenario.
• To derive lower bounds on the classical dimension required for reproducing measurement data.
• To generalize quantum dimension witnesses for arbitrary quantum systems.

Main Methods:

• Development of a general theoretical framework for dimension testing.
• Derivation of mathematical bounds on classical and quantum dimensions.
• Construction of classical and quantum dimension witnesses.

Main Results:

• A unified formalism for black-box dimension testing is established.
• Lower bounds on classical dimensions are derived from measurement data.
• Generalized quantum dimension witnesses are introduced, providing lower bounds on Hilbert space dimensions.

Conclusions:

• The developed formalism offers a robust approach to characterizing system dimensionality.
• The findings enable the determination of minimal classical or quantum resources needed to explain experimental observations.
• This work provides practical tools for dimension witnessing in diverse physical systems.