每个定域动力学可简化为一个定域子动力学的状态结构
Structure of states for which each localized dynamics reduces to a localized subdynamics
摘要：
我们考虑一个二分量子系统$S$（包括$A$和$B$），通过局域量子动力学$\mathcal{F}_{SE}$与环境$E$相互作用.我们称一个量子动力学$\mathcal{F}_{SE}$局域化，如果，例如，参与方$A$与环境隔离，并且只有$B$与环境交互：$\mathcal{F}_{SE}=id_{A}\otimes \mathcal{F}_{BE}$，其中$id_{A}$是部分$A$上的身份映射，而$\mathcal{F}_{BE}$是$B$和$E$上的完全正（CP）映射。我们将证明系统的约化动力学也被局部化为$\mathcal{E}_{S}=id_{A}\otimes \bar{\mathcal{E}}_{B}$，其中$\bar{\mathcal{E}}_{B}$是$B$上的CP映射，当且仅当系统-环境的初始状态是马尔可夫状态。然后，我们将这一结果推广到以下两种情况：当$A$和$B$与同一环境交互时，以及当每一方与其本地环境交互时。
英文摘要：
We consider a bipartite quantum system $S$ (including parties $A$ and $B$), interacting with an environment $E$ through a localized quantum dynamics $\mathcal{F}_{SE}$ . We call a quantum dynamics $\mathcal{F}_{SE}$ localized if, e.g., the party $A$ is isolated from the environment and only $B$ interacts with the environment: $\mathcal{F}_{SE}=id_{A}\otimes \mathcal{F}_{BE}$, where $id_{A}$ is the identity map on the part $A$ and $\mathcal{F}_{BE}$ is a completely positive (CP) map on the both $B$ and $E$. We will show that the reduced dynamics of the system is also localized as $\mathcal{E}_{S}=id_{A}\otimes \bar{\mathcal{E}}_{B}$, where $\bar{\mathcal{E}}_{B}$ is a CP map on $B$, if and only if the initial state of the system-environment is a Markov state. We then generalize this result to the two following cases: when both $A$ and $B$ interact with a same environment, and when each party interacts with its local environment.
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