Graph states of prime-power dimension from generalized CNOT quantum circuit

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Entanglement

Background:

• Multipartite graph states are crucial for quantum information processing.
• Classifying and understanding these states is essential for developing quantum technologies.
• Previous methods for constructing and classifying graph states were complex.

Purpose of the Study:

• To construct multipartite graph states with dimensions as powers of prime numbers.
• To develop a standard form for graph states simplifying their classification.
• To identify and characterize multipartite maximally entangled states.

Main Methods:

• Construction of graph states using finite fields.
• Application of generalized controlled-NOT quantum circuits on two qudits.
• Development of a standard form for graph states invariant under local unitary transformations and particle permutations.

Main Results:

• A simplified classification of graph states, demonstrated up to five qudits.
• Identification of specific graph states as multipartite maximally entangled states.
• Proof of the existence of 4-partite maximally entangled states for specific prime power dimensions.

Conclusions:

• The proposed standard form significantly simplifies the study and classification of multipartite graph states.
• The findings contribute to the understanding of multipartite entanglement and its potential applications.
• The existence of multipartite maximally entangled states is confirmed for certain dimensions, advancing quantum network research.