论文标题
纠缠不可转化的频道
Entanglement-invertible channels
论文作者
论文摘要
在众所周知的结果[Werner2001]中，Werner对所有紧密的量子传送和密集的编码方案进行了分类，表明它们对应于单一误差库。在这里，紧密度是一定的维度限制：要传送的量子系统，并且纠缠的资源必须为dimension d，并且测量必须具有D^2结果。 在这项工作中，我们将此分类概括为完全消除了维度限制，从而解决了在该工作中提出的开放问题。实际上，我们不仅对传送和密集的编码方案进行了分类，而且对纠缠可逆的渠道进行了分类。这些是有限维c*代数之间的渠道，它们借助于纠缠的资源状态可逆，从而概括了通道的普通可逆性。 在Werner的分类中，显示了紧密传送和密集的编码方案之间的徒对应关系：交换Alice和Bob的操作将传送方案变成了密集的编码方案，反之亦然。我们观察到，该属性概括了通道的普通可逆性。我们称之为纠缠的可逆性。我们表明，纠缠不可转化的通道恰恰是先前研究的量子射击量子组合剂[Musto2018]，这些量子是根据量子置换组的表示理论进行分类的。
In a well-known result [Werner2001], Werner classified all tight quantum teleportation and dense coding schemes, showing that they correspond to unitary error bases. Here tightness is a certain dimensional restriction: the quantum system to be teleported and the entangled resource must be of dimension d, and the measurement must have d^2 outcomes. In this work we generalise this classification so as to remove the dimensional restriction altogether, thereby resolving an open problem raised in that work. In fact, we classify not just teleportation and dense coding schemes, but entanglement-reversible channels. These are channels between finite-dimensional C*-algebras which are reversible with the aid of an entangled resource state, generalising ordinary reversibility of a channel. In Werner's classification, a bijective correspondence between tight teleportation and dense coding schemes was shown: swapping Alice and Bob's operations turns a teleportation scheme into a dense coding scheme and vice versa. We observe that this property generalises ordinary invertibility of a channel; we call it entanglement-invertibility. We show that entanglement-invertible channels are precisely the quantum bijections previously studied in the setting of quantum combinatorics [Musto2018], which are classified in terms of the representation theory of the quantum permutation group.
