四个局部不可区分的Ququad-Ququad正交最大纠缠态
Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
摘要：
我们明确展示了一组四quququad-quququad正交最大纠缠态，不能完全区分通过本地操作和经典通信。在我们的工作之前，对于某个正整数$d$，是否存在一组局部不可分辨的$d\otimes d$正交最大纠缠态是未知的。我们进一步证明了一个$2\otimes 2$最大纠缠态可以在不被消耗的情况下局部区分这组态，从而证明了一种新的“纠缠区分催化”现象。基于这组状态，我们构造了一个新的集合$\mathrm{K}$由四个局部不可区分的状态，使$\mathrm{K}^{\otimes m}$（与$4^m$成员）是局部可区分的一些$m$大于1。作为直接的应用，我们构造了一个有噪声的量子信道，该信道具有一个发送者和两个接收者，其局部零误差经典容量可以实现输入空间的全维，但需要采用多拍协议。
英文摘要：
We explicitly exhibit a set of four ququad-ququad orthogonal maximally entangled states that cannot be perfectly distinguished by means of local operations and classical communication. Before our work, it was unknown whether there is a set of $d$ locally indistinguishable $d\otimes d$ orthogonal maximally entangled states for some positive integer $d$. We further show that a $2\otimes 2$ maximally entangled state can be used to locally distinguish this set of states without being consumed, thus demonstrate a novel phenomenon of "Entanglement Discrimination Catalysis". Based on this set of states, we construct a new set $\mathrm{K}$ consisting of four locally indistinguishable states such that $\mathrm{K}^{\otimes m}$ (with $4^m$ members) is locally distinguishable for some $m$ greater than one. As an immediate application, we construct a noisy quantum channel with one sender and two receivers whose local zero-error classical capacity can achieve the full dimension of the input space but only with a multi-shot protocol.
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