通过对称化计算有限维量子系统的关联界
Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
摘要：
我们提出了一种技术，用于减少计算要求的几个数量级的半定松弛的评价所产生的有限维希尔伯特空间的量子相关的约束集。该技术，我们公开提供通过一个用户友好的软件包，依赖于利用对称性存在的优化问题，以减少变量的数量和块大小的半定松弛。它广泛适用于量子信息理论中遇到的问题，并使以前过于苛刻的计算成为可能。我们证明了它的优点和普遍适用性在几个物理问题。特别是，我们用它来鲁棒地证明在黑盒的情况下，基于自测试的$d$维对称信息完全POVM的高维测量的非投射性。
英文摘要：
We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The technique, which we make publicly available through a user-friendly software package, relies on the exploitation of symmetries present in the optimisation problem to reduce the number of variables and the block sizes in semidefinite relaxations. It is widely applicable in problems encountered in quantum information theory and enables computations that were previously too demanding. We demonstrate its advantages and general applicability in several physical problems. In particular, we use it to robustly certify the non-projectiveness of high-dimensional measurements in a black-box scenario based on self-tests of $d$-dimensional symmetric informationally complete POVMs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
