论文标题
Schmidt-Rank-Two多部分统一大门的分类
Classification of Schmidt-rank-two multipartite unitary gates by singular number
论文作者
论文摘要
如果多方统一大门不是任何两者中的产品统一操作员，则称为真实门。我们主要通过关注多Quibit方案来研究施密特排名第二的真正多部分统一门的分类。对于施密特二级的真正多部分（不包括两分）的统一门，这是一个重要的事实，即他们的施密特分解是独一无二的。基于这个事实，我们提出了一个称为单数字的关键概念，以对有关的统一大门进行分类。单数数字定义为施密特分解中局部单数算子的数量。然后，我们确定奇异数的准确范围。对于每个单数数字，我们制定了在局部等效性下的真正多Quipit统一门的参数schmidt分解。最后，由于对角线统一大门与施密特级 - 二级单位之间的密切关系，我们将研究扩展到三分之一的对角线统一门。我们首先讨论施密特等级二的两个典型示例，其中一个是基本的三Q Qubit统一门，即CCZ Gate。然后，我们表征了施密特的对角线统一大门，大于两个。我们表明，一个三分之一的对角统一门最多使施密特排名三，并且为施密特排名第三的这样的单一门提供了必要和充分的条件。这完成了所有真正的三量对角线统一大门的表征。
The multipartite unitary gates are called genuine if they are not product unitary operators across any bipartition. We mainly investigate the classification of genuine multipartite unitary gates of Schmidt rank two, by focusing on the multiqubit scenario. For genuine multipartite (excluding bipartite) unitary gates of Schmidt rank two, there is an essential fact that their Schmidt decompositions are unique. Based on this fact, we propose a key notion named as singular number to classify the unitary gates concerned. The singular number is defined as the number of local singular operators in the Schmidt decomposition. We then determine the accurate range of singular number. For each singular number, we formulate the parametric Schmidt decompositions of genuine multiqubit unitary gates under local equivalence. Finally, we extend the study to three-qubit diagonal unitary gates due to the close relation between diagonal unitary gates and Schmidt-rank-two unitaries. We start with discussing two typical examples of Schmidt rank two, one of which is a fundamental three-qubit unitary gate, i.e., the CCZ gate. Then we characterize the diagonal unitary gates of Schmidt rank greater than two. We show that a three-qubit diagonal unitary gate has Schmidt rank at most three, and present a necessary and sufficient condition for such a unitary gate of Schmidt rank three. This completes the characterization of all genuine three-qubit diagonal unitary gates.
