It is shown that, in the interaction of a field and a qubit, there exists a relation between the linear entropy and the von Neumann entropy. The Cayley–Hamilton theorem is used to obtain such relation. In the case we study, the qubit is given by the internal degrees of freedom of an ion trapped in a Paul trap and the field given by its external (vibrational) degrees of freedom.

中文翻译：

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离子-激光相互作用中熵与线性熵的关系

结果表明，在场和量子比特的相互作用中，线性熵与冯诺依曼熵之间存在关系。Cayley-Hamilton 定理用于获得这种关系。在我们研究的案例中，量子位由被困在保罗陷阱中的离子的内部自由度和由其外部（振动）自由度给出的场给出。