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Classifying N-qubit entanglement via Bell's inequalities
Sixia Yu1, Zeng-Bing Chen, Jian-Wei Pan
1Department of Modern Physics, University of Science and Technology of China, Hefei 230027, People's Republic of China.
Physical Review Letters
|March 14, 2003
Summary
Entangled states of N qubits are classified into N-1 classes based on their entanglement index. A higher entanglement index indicates greater entanglement and larger violations of Bell
Area of Science:
- Quantum Information Science
- Quantum Entanglement Theory
Background:
- Quantum states of N qubits exhibit varying degrees of entanglement.
- Entanglement is a key resource in quantum information processing.
Purpose of the Study:
- To classify all possible states of N qubits into distinct entanglement classes.
- To introduce a quantitative measure, the entanglement index, for characterizing these classes.
Main Methods:
- Classification of N-qubit states based on entanglement properties.
- Definition of an entanglement index dependent on the partition of N.
Main Results:
- Identified N-1 distinct entanglement classes for N qubits, ranging from 2-entangled to N-entangled (fully entangled) states.
- Established that the entanglement index quantifies the degree of entanglement and separability.
- Demonstrated a correlation between a higher entanglement index and a larger maximal violation of Bell's inequality.
Conclusions:
- A comprehensive classification scheme for N-qubit entangled states is proposed.
- The entanglement index provides a valuable tool for quantifying and comparing entanglement across different states.
- This framework enhances our understanding of quantum correlations and their potential for Bell's inequality violations.