Entropic Tests of Multipartite Nonlocality and State-Independent Contextuality

Area of Science:

• Quantum Information Theory
• Quantum Foundations
• Quantum Correlations

Background:

• Existing methods for studying quantum correlations, such as those based on correlation functions, have limitations in fully capturing nonclassical correlations.
• Information-theoretic approaches offer a powerful framework for quantifying and understanding quantum phenomena.

Purpose of the Study:

• To introduce a multipartite extension of Zurek's information-theoretic distance.
• To develop a novel tool for analyzing quantum correlations from an information-theoretic viewpoint.
• To derive new entropic tests for multipartite nonlocality and state-independent contextuality.

Main Methods:

• Extending an existing information-theoretic distance to a multipartite setting.
• Developing entropic tests for quantum nonlocality in systems of three and an arbitrary even number of qubits.
• Formulating a test for state-independent contextuality.
• Re-deriving known inequalities (tripartite Mermin, Cabello's state-independent noncontextuality) using the new framework.

Main Results:

• A new information-theoretic tool for studying quantum correlations has been developed.
• Entropic tests for multipartite nonlocality (three qubits, arbitrary even qubits) and state-independent contextuality are derived.
• The framework successfully re-derives established inequalities, validating its approach.

Conclusions:

• The information-theoretic distance approach offers a more general framework for nonclassical correlations compared to traditional methods.
• This work provides new tools for investigating multipartite nonlocality and state-independent contextuality.
• The findings suggest a unified information-theoretic perspective on diverse quantum phenomena.