如何结合三个量子态
How to combine three quantum states
摘要：
我们设计了一个三元操作来组合三个量子态：它包括以连续的方式排列输入系统，然后丢弃所有的，但其中之一。这推广了Audenaert等人最近研究的二元运算。[arXiv：1503.04213]在熵功率不等式的背景下。我们的三进制操作在所有这样的嵌套二进制操作之间连续插值。我们的建设是基于一个单一版本的凯莱定理：使用表示理论，我们表明，任何有限群可以自然地嵌入到一个连续子群的酉群。形式上，这相当于表征某些排列的线性组合何时是酉的。
英文摘要：
We devise a ternary operation for combining three quantum states: it consists of permuting the input systems in a continuous fashion and then discarding all but one of them. This generalizes a binary operation recently studied by Audenaert et al. [arXiv:1503.04213] in the context of entropy power inequalities. Our ternary operation continuously interpolates between all such nested binary operations. Our construction is based on a unitary version of Cayley's theorem: using representation theory we show that any finite group can be naturally embedded into a continuous subgroup of the unitary group. Formally, this amounts to characterizing when a linear combination of certain permutations is unitary.
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