量子态的合成与动力学次可加性
Composition of quantum states and dynamical subadditivity
摘要：
介绍了一种基于密度矩阵重排的二分系统量子态的合成方法。这种非阿贝尔积是结合的，并且源于作用于简单量子系统的量子映射的合成。它在具有最大混合部分迹的状态子集中诱导出一个半群。证明了冯诺伊曼熵关于该乘积的次可加性。它等价于双随机映射的熵关于其合成的次可加性，其中映射的熵是Jamiolkowski同构下对应状态的熵。建立了三个双随机映射级联的强动力次可加性。对于一般的随机映射，导出了组合熵的类似界。在经典的情况下，他们导致新的界限的熵的产品的两个随机矩阵。
英文摘要：
We introduce a composition of quantum states of a bipartite system which is based on the reshuffling of density matrices. This non-Abelian product is associative and stems from the composition of quantum maps acting on a simple quantum system. It induces a semi-group in the subset of states with maximally mixed partial traces. Subadditivity of the von Neumann entropy with respect to this product is proved. It is equivalent to subadditivity of the entropy of bistochastic maps with respect to their composition, where the entropy of a map is the entropy of the corresponding state under the Jamiolkowski isomorphism. Strong dynamical subadditivity of a concatenation of three bistochastic maps is established. Analogous bounds for the entropy of a composition are derived for general stochastic maps. In the classical case they lead to new bounds for the entropy of a product of two stochastic matrices.
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