Irreducible multiparty correlations in quantum states without maximal rank

Area of Science:

• Quantum Information Science
• Quantum Correlation Analysis

Background:

• Multipartite quantum states exhibit complex correlations.
• Classifying these correlations is crucial for understanding quantum systems.
• Existing methods struggle with non-maximal rank states.

Purpose of the Study:

• To classify n-partite quantum state correlations into irreducible k-party correlations.
• To define a measure for the degree of irreducible k-party correlation.
• To develop a method for calculating these correlations in challenging quantum states.

Main Methods:

• Classification of correlations into irreducible k-party components (2 <= k <= n).
• Definition of a correlation measure using the principle of maximal entropy.
• Application of a continuity approach to overcome calculation difficulties.

Main Results:

• Irreducible k-party correlations are defined as those present in k parties but not in k-1 parties.
• A novel measure for the degree of irreducible k-party correlation is established.
• The degrees of irreducible multiparty correlations are successfully obtained for n-qubit stabilizer and generalized GHZ states.

Conclusions:

• The study provides a framework for classifying and quantifying multipartite quantum correlations.
• The developed measure and methods enable analysis of complex quantum states.
• The findings reveal the distribution of multiparty correlations in specific quantum systems.