论文标题
关于choi-jamiolkowski同构的变化
Variations on the Choi-Jamiolkowski isomorphism
论文作者
论文摘要
我们解决了量子信息理论中广泛使用的工具的各个方面：choi-jamiolkowski同构[A. Jamiolkowski，众议员数学。 Phys。，3，275（1972）]。我们回顾了同构的不同版本，它们的特性，并提出了将它们全部结合在一起的统一描述。为此，我们确定了Choi定理中使用的同构中换位（基础依赖性）换位（基础依赖性）操作的物理原因[M.-D。崔，林。 alg。 Appl。，10，285（1975）]。这需要仔细区分约旦代数和它们产生的不同C* - 代数，这些代数由它们的组成顺序区别。从物理上讲，后者编码各个代数中的时间取向的选择，这与最近的许多结果有关，包括从更一般的非信号双分支相关性中表征量子的表征[M. Frembs和A.Döring，Arxiv：2204.11471]和双方纠缠的分类[M. Frembs，Arxiv：2207.00024]。
We address various aspects of a widely used tool in quantum information theory: the Choi-Jamiolkowski isomorphism [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. We review different versions of the isomorphism, their properties and propose a unified description that combines them all. To this end, we identify the physical reason for the appearance of the (basis-dependent) operation of transposition in the isomorphism as used in Choi's theorem [M.-D. Choi, Lin. Alg. Appl., 10, 285 (1975)]. This requires a careful distinction between Jordan algebras and the different C*-algebras they arise from, which are distinguished by their order of composition. Physically, the latter encodes a choice of time orientation in the respective algebras, which relates to a number of recent results, including a characterisation of quantum from more general non-signalling bipartite correlations [M. Frembs and A. Döring, arXiv:2204.11471] and a classification of bipartite entanglement [M. Frembs, arXiv:2207.00024].
