$\ell_1$-norm in three-qubit quantum entanglement constrained by Yang-Baxter equation
| Autor: | Yu, Li-Wei, Ge, Mo-Lin |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 5 pages, 4 figures + supplementary material |
| Databáze: | arXiv |
| Externí odkaz: |
|