Monogamy constraints on entanglement of four-qubit pure states

• URL: http://arxiv.org/abs/2002.00701v3
• Date: Mon, 15 Nov 2021 15:28:51 GMT
• Title: Monogamy constraints on entanglement of four-qubit pure states
• Authors: S. Shelly Sharma
• Abstract summary: We report a set of monogamy constraints on one-tangle, two-tangles, three-tangles and four-way correlations of a general four-qubit pure state.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We report a set of monogamy constraints on one-tangle, two-tangles, three-tangles and four-way correlations of a general four-qubit pure state. It is found that given a two-qubit marginal state $\rho$ of a four qubit pure state $\left\vert \Psi_{4}\right\rangle $, the non-Hermitian matrix $\rho\widetilde{\rho}$ where $\widetilde{\rho}$ $=\left( \sigma_{y} \otimes\sigma_{y}\right) \rho^{\ast}\left( \sigma_{y}\otimes\sigma_{y}\right) $, contains information not only about the entanglement properties of the two-qubits in state $\rho$ but also about three tangles involving the selected pair as well as four-way correlations of the pair of qubits in $\left\vert \Psi_{4}\right\rangle $. To extract information about tangles of a four-qubit state $\left\vert \Psi_{4}\right\rangle $, the coefficients in the characteristic polynomial of matrix $\rho\widetilde{\rho}$ are analytically expressed in terms of $2\times2$ matrices of state coefficients. Four-tangles distinguish between different types of entangled four-qubit pure states.

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