Performance comparison of Gilbert's algorithm and machine learning in classifying Bell-diagonal two-qutrit...

Area of Science:

• Quantum Information Theory
• Quantum Mechanics
• Quantum Computing

Background:

• Classifying quantum states as entangled or separable is a fundamental yet challenging task in quantum information theory.
• Two-qutrit Bell-diagonal states, mixtures of nine mutually orthogonal maximally entangled states, present a particularly nontrivial case.

Purpose of the Study:

• To revise and clarify the classification of two-qutrit Bell-diagonal states.
• To apply entanglement cartography to determine the entanglement status of previously unclassified states.

Main Methods:

• Application of Gilbert's algorithm to analyze quantum states.
• Utilizing entanglement cartography for state classification.
• Revision of prior results concerning two-qutrit Bell-diagonal states.

Main Results:

• Most states previously classified as unknown are determined to be separable.
• Identified states exhibit negligible entanglement, rendering them practically irrelevant.
• The applied technique offers a robust method for analyzing quantum state entanglement.

Conclusions:

• The study successfully clarifies the entanglement status of a significant class of quantum states.
• The developed methodology, using Gilbert's algorithm and entanglement cartography, is effective for complex quantum state analysis.
• This approach has broad applicability for classifying entanglement in more general quantum systems.