有限量子系统的素分解与关联测度
Prime decomposition and correlation measure of finite quantum systems
摘要：
在素分解（pd）的名义下，引入了一种将任意$N$维密度矩阵$ρ$分解为维数由$N$的互质因子给出的可分密度矩阵之和的唯一分解.对于一类密度矩阵，得到了完全张量积分解。该结构是基于中国剩余定理和离散海森堡群$H_N$对$Z_N$的射影酉表示。的PD同构是酉实现的，它被证明是coassociative和作用于$H_N$作为commultiplication。具有完全pd的密度矩阵被解释为$H_N$的类群元素。为了量化$ρ$与其pd之间的距离，引入了迹范数相关指数$\cal E$，并确定了其不变性群.
英文摘要：
Under the name prime decomposition (pd), a unique decomposition of an arbitrary $N$-dimensional density matrix $ρ$ into a sum of seperable density matrices with dimensions given by the coprime factors of $N$ is introduced. For a class of density matrices a complete tensor product factorization is achieved. The construction is based on the Chinese Remainder Theorem and the projective unitary representation of $Z_N$ by the discrete Heisenberg group $H_N$. The pd isomorphism is unitarily implemented and it is shown to be coassociative and to act on $H_N$ as comultiplication. Density matrices with complete pd are interpreted as grouplike elements of $H_N$. To quantify the distance of $ρ$ from its pd a trace-norm correlation index $\cal E$ is introduced and its invariance groups are determined.
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