Strassen’s theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite, Strassen’s theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen’s theorem in this case can be stated and solved using semidefinite programming. The aim of this paper is to give analogs of Strassen’s theorem to density trace class operators on a product of two separable Hilbert spaces, where at least one of the Hilbert spaces is infinite-dimensional.

中文翻译：

---

量子施特拉森定理

大约 1965 年的 Strassen 定理给出了在给定支持和两个边际的两个产品空间上存在概率测度的必要和充分条件。在每个乘积空间是有限的情况下，Strassen 定理被简化为可以使用流动理论解决的线性规划问题。二分量子系统的密度矩阵是概率矩阵在两个有限乘积空间上的量子模拟。密度矩阵的部分迹线是边缘的类似物。密度矩阵的支持是它的范围。在这种情况下，Strassen 定理的类比可以使用半定规划来表述和求解。本文的目的是将 Strassen 定理与两个可分离 Hilbert 空间乘积上的密度迹类算子类似，