论文标题
多方量子纯度蒸馏与有限的经典交流
Multi-Party Quantum Purity Distillation with Bounded Classical Communication
论文作者
论文摘要
我们考虑将局部纯度从嘈杂的量子状态$ρ{abc} $中提取的任务，其中我们为三方（爱丽丝，鲍勃和查理）提供了一个协议，以将局部纯度（以$ p $为$ p $）从许多给定的量子状态$ρ^{abc} $的独立副本中提炼出来。这三方可以访问其各自的子系统$ρ^{abc} $，并且在协议结束后催化纯粹的Ancilla催化了纯粹的Ancilla。此外，爱丽丝（Alice）和鲍勃（Bob）可以分别使用链接率的单向多访问渠道与查理（Charlie）进行交流，分别分别为$ r_1 $和$ r_2 $。该协议的目的是最大程度地减少Dephasing渠道的使用（就$ r_1 $和$ r_2 $而言），同时最大化可以从$ρ^{ABC} $共同提炼的渐近纯度。为了实现这一目标，我们采用分布式测量压缩协议中的想法，然后在$（p，r_1，r_2）$上表征量子信息理论量的一组足够条件（p，r_1，r_2）$。最后，我们还结合了渐近代数结构化编码的技术，并提供了表征性能极限的统一方法。
We consider the task of distilling local purity from a noisy quantum state $ρ^{ABC}$, wherein we provide a protocol for three parties, Alice, Bob and Charlie, to distill local purity (at a rate $P$) from many independent copies of a given quantum state $ρ^{ABC}$. The three parties have access to their respective subsystems of $ρ^{ABC}$, and are provided with pure ancilla catalytically, i.e., with the promise of returning them unaltered after the end of the protocol. In addition, Alice and Bob can communicate with Charlie using a one-way multiple-access dephasing channel of link rates $R_1$ and $R_2$, respectively. The objective of the protocol is to minimize the usage of the dephasing channel (in terms of rates $R_1$ and $R_2$) while maximizing the asymptotic purity that can be jointly distilled from $ρ^{ABC}$. To achieve this, we employ ideas from distributed measurement compression protocols, and in turn, characterize a set of sufficient conditions on $(P,R_1,R_2)$ in terms of quantum information theoretic quantities such that $P$ amount of purity can be distilled using rates $R_1$ and $R_2$. Finally, we also incorporate the technique of asymptotic algebraic structured coding, and provide a unified approach of characterizing the performance limits.
