Tensor product operators on finite dimensional Hilbert spaces are studied. The focus is on bilinear tensor product operators. A tensor product operator on a pair of Hilbert spaces is a maximally general bilinear operator into a target Hilbert space. By 'maximally general' is meant every bilinear operator from the same pair of spaces to any Hilbert space factors into the composition of the tensor product operator with a uniquely determined linear mapping on the target space. There are multiple distinct tensor product operators of the same type; there is no "the" tensor product. Distinctly different tensor product operators can be associated with different parts of a multipartite system without difficulty. Separability of states, and locality of operators and observables is tensor product operator dependent. The same state in the target state space can be inseparable with respect to one tensor product operator but separable with respect to another, and no tensor product operator is distinguished relative to the others; the unitary operator used to construct a Bell state from a pair of |0>'s being highly tensor product operator-dependent is a prime example. The relationship between two tensor product operators of the same type is given by composition with a unitary operator. There is an equivalence between change of tensor product operator and change of basis in the target space. Among the gains from change of tensor product operator is the localization of some nonlocal operators as well as separability of inseparable states. Examples are given.

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多个同类型张量积算子的交互：介绍

研究了有限维希尔伯特空间上的张量积算子。重点是双线性张量积算子。一对 Hilbert 空间上的张量积算子是到目标 Hilbert 空间的最大一般双线性算子。“最大一般”是指从同一对空间到任何 Hilbert 空间的每个双线性算子，将其分解为张量积算子的组合，并在目标空间上具有唯一确定的线性映射。有多个不同的相同类型的张量积算子；没有“那个”张量积。明显不同的张量积算子可以毫无困难地与多部分系统的不同部分相关联。状态的可分性以及运算符和可观察对象的局部性取决于张量积运算符。目标状态空间中的相同状态对于一个张量积算子可以是不可分的，但对于另一个可以分，并且没有张量积算子相对于其他算子是可区分的；用于从一对 |0> 高度依赖于张量积算子构建贝尔状态的幺正算子就是一个典型的例子。两个相同类型的张量积算子之间的关系由一个酉算子组合给出。张量积算子的变化和目标空间中基的变化是等价的。张量积算子变化的好处之一是一些非局部算子的局部化以及不可分离状态的可分离性。给出了例子。