面包师映射的纠缠能力：对称性的作用
Entangling power of baker's map: Role of symmetries
摘要：
量子贝克映射具有两种对称性：一种是规范的“空间”对称性，另一种是时间反演对称性。我们表明，即使考虑到这些功能，面包师的地图的渐近纠缠功率并不总是同意随机矩阵理论的预测。证明了Hilbert空间的维数是决定面包师纠缠性质是否普适的关键参数。对于二维幂，即，在量子比特系统中，观察到异常的纠缠功率;否则面包师的行为与随机矩阵理论一致。我们还推导出一个一般公式，涉及的渐近纠缠功率的任意酉与其约化特征向量的属性。
英文摘要：
The quantum baker map possesses two symmetries: a canonical "spatial" symmetry, and a time-reversal symmetry. We show that, even when these features are taken into account, the asymptotic entangling power of the baker's map does not always agree with the predictions of random matrix theory. We have verified that the dimension of the Hilbert space is the crucial parameter which determines whether the entangling properties of the baker are universal or not. For power-of-two dimensions, i.e., qubit systems, an anomalous entangling power is observed; otherwise the behavior of the baker is consistent with random matrix theories. We also derive a general formula that relates the asymptotic entangling power of an arbitrary unitary with properties of its reduced eigenvectors.
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