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arXiv · 1902.00957

$\ell_1$-norm in three-qubit quantum entanglement constrained by Yang-Baxter equation

Li-Wei Yu·Mo-Lin Ge
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Abstract

Usually the $\ell_2$-norm plays vital roles in quantum physics, acting as the probability of states. In this paper, we show the important roles of $\ell_1$-norm in Yang-Baxter quantum system, in connection with both the braid matrix and quantum entanglements. Concretely, we choose the 2-body and 3-body S-matrices, constrained by Yang-Baxter equation. It has been shown that for 2-body case, the extreme values of $\ell_1$-norm lead to two types of braid matrices and 2-qubit Bell states. Here we show that for the 3-body case, due to the constraint of YBE, the extreme values of $\ell_1$-norm lead to both 3-qubit $|GHZ\rangle$ (local maximum) and $|W\rangle$ (local minimum) states, which cover all 3-qubit genuine entanglements for pure states under SLOCC. This is a more convincing proof for the roles of $\ell_1$-norm in quantum mechanics.

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Li-Wei Yu, Mo-Lin Ge. 2019-02-03. $\ell_1$-norm in three-qubit quantum entanglement constrained by Yang-Baxter equation. https://arxiv.org/abs/1902.00957

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