We study the relation between quantum entanglement and electron correlation in quantum chemistry calculations. We prove that the Hartree-Fock (HF) wave function does not violate Bell's inequality, thus is not entangled while the configuration interaction (CI) wave function is entangled since it violates Bell's inequality. Entanglement is related to electron correlation and might be used as an alternative measure of the electron correlation in quantum chemistry calculations. As an example we show the calculations of entanglement for the H $_2$ molecule and how it is related to electron correlation of the system, which is the difference between the exact and the HF energies.We study the relation between quantum entanglement and electron correlation in quantum chemistry calculations. We prove that the Hartree-Fock (HF) wave function does not violate Bell's inequality, thus is not entangled while the configuration interaction (CI) wave function is entangled since it violates Bell's inequality. Entanglement is related to electron correlation and might be used as an alternative measure of the electron correlation in quantum chemistry calculations. As an example we show the calculations of entanglement for the H$_2$ molecule and how it is related to electron correlation of the system, which is the difference between the exact and the HF energies.

arXiv:quant-ph/0701081Bulletin of the American Physical SocietyJan 13, 20070 citations

Violation $\neq$ QuantumViolation $\neq$ Quantum

Xingyu Guo, Chen‐Te Ma

The only entanglement quantity is concurrence in a 2-qubit pure state. The maximum violation of Bell's inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the quantum violation. To understand the relation between violation and entanglement, we extend the study to three qubits. We consider all possible 3-qubit operators with a symmetric permutation. When only turning on one entanglement measure, the numerical result shows a contradiction to the expectation. The maximum violation does not have the same behavior as in 2-qubit pure states. Therefore, we conclude Violation $\neq$ Quantum. In the end, we propose the generalized $R$ -matrix or correlation matrix for the new diagnosis of Quantum Entanglement. We demonstrate the evidence by restoring the monotonically increasing result.The only entanglement quantity is concurrence in a 2-qubit pure state. The maximum violation of Bell's inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the quantum violation. To understand the relation between violation and entanglement, we extend the study to three qubits. We consider all possible 3-qubit operators with a symmetric permutation. When only turning on one entanglement measure, the numerical result shows a contradiction to the expectation. The maximum violation does not have the same behavior as in 2-qubit pure states. Therefore, we conclude Violation$\neq$Quantum. In the end, we propose the generalized $R$-matrix or correlation matrix for the new diagnosis of Quantum Entanglement. We demonstrate the evidence by restoring the monotonically increasing result.

Sep 8, 20210 citations

Relativity and Quantum Entanglement

C. S. Unnikrishnan

Fundamental theories of physicsJan 1, 20220 citations

Multipartite entanglement versus nonlocality for two families of N − qubit states

Sanchit Srivastava, Shohini Ghose

Entangled states of multiple qubits can violate Bell-type inequalities indicating nonlocal behavior of multiqubit quantum correlations. We analyze the relation between multipartite entanglement and genuine multipartite nonlocality, characterized by Svetlichny inequality violations, for two families of N − qubit states. We show that for the generalized Greenberger-Horne-Zeilinger family of states, Svetlichny inequality is not violated when the n − tangle is less than 1 / 2 for any even number of qubits. On the other hand, the maximal slice states always violate the Svetlichny inequality when n − tangle is nonzero, and the violation increases monotonically with tangle. Our work generalizes the relations between tangle and Svetlichny inequality violations previously derived for three qubits.Entangled states of multiple qubits can violate Bell-type inequalities indicating nonlocal behavior of multiqubit quantum correlations. We analyze the relation between multipartite entanglement and genuine multipartite nonlocality, characterized by Svetlichny inequality violations, for two families of N − qubit states. We show that for the generalized Greenberger-Horne-Zeilinger family of states, Svetlichny inequality is not violated when the n − tangle is less than 1 / 2 for any even number of qubits. On the other hand, the maximal slice states always violate the Svetlichny inequality when n − tangle is nonzero, and the violation increases monotonically with tangle. Our work generalizes the relations between tangle and Svetlichny inequality violations previously derived for three qubits.

arXiv:2409.10888Physical Review ResearchSep 9, 20250 citations

Quantum Entanglement Under Lorentz Transformation

Ji-Rong Ren, Shi-Xiong Song

International Journal of Theoretical PhysicsMar 23, 20106 citations

_2

molecule and how it is related to electron correlation of the system, which is the difference between the exact and the HF energies.

Violation

\neq

Quantum

\neq

Quantum. In the end, we propose the generalized

R

-matrix or correlation matrix for the new diagnosis of Quantum Entanglement. We demonstrate the evidence by restoring the monotonically increasing result.