论文标题
超密集编码的刚性
Rigidity of superdense coding
论文作者
论文摘要
Bennett和Wiesner的著名超密集编码协议表明，可以通过仅发送一个量子并使用共享的EPR对来传达两个经典信息。我们的第一个结果是，实现此任务的任意协议（在发件人的编码操作或共享纠缠状态的维度没有假设的情况下）在本地等同于规范的Bennett-Wiesner协议。换句话说，超密集的编码任务很严格。特别是，我们表明，发件人和接收器仅使用额外的纠缠（EPR对以外）作为经典随机性的来源。 我们还调查了有关高维超密度编码的几个问题，该问题的目标是通过发送$ d $维量子量的$ d^2 $可能的消息之一传达一般尺寸$ d $。与$ d = 2 $ case（即发送单个量子）不同，可以有不等的超密度编码协议，用于较高的$ d $。我们基于所有$ d> 2 $的不等式的正交统一基础的构造，介绍了不等性协议的具体构造。最后，我们分析了超密集编码方案的性能，其中编码运算符是从单一组上的HAAR度量中独立采样的。我们的分析涉及界定随机最大纠缠状态的区分性，这可能具有独立的利益。
The famous superdense coding protocol of Bennett and Wiesner demonstrates that it is possible to communicate two bits of classical information by sending only one qubit and using a shared EPR pair. Our first result is that an arbitrary protocol for achieving this task (where there are no assumptions on the sender's encoding operations or the dimension of the shared entangled state) is locally equivalent to the canonical Bennett-Wiesner protocol. In other words, the superdense coding task is rigid. In particular, we show that the sender and receiver only use additional entanglement (beyond the EPR pair) as a source of classical randomness. We also investigate several questions about higher-dimensional superdense coding, where the goal is to communicate one of $d^2$ possible messages by sending a $d$-dimensional quantum state, for general dimensions $d$. Unlike the $d=2$ case (i.e. sending a single qubit), there can be inequivalent superdense coding protocols for higher $d$. We present concrete constructions of inequivalent protocols, based on constructions of inequivalent orthogonal unitary bases for all $d > 2$. Finally, we analyze the performance of superdense coding protocols where the encoding operators are independently sampled from the Haar measure on the unitary group. Our analysis involves bounding the distinguishability of random maximally entangled states, which may be of independent interest.
