Center for Quantum Information and Quantum Control, Department of Physics, University of Toronto, Toronto, Ontario M5S 3G4, Canada.
Phys Rev Lett. 2011 Nov 4;107(19):190502. doi: 10.1103/PhysRevLett.107.190502.
In this Letter, we investigate the number of measurement and communication rounds needed to implement certain tasks by local quantum operations and classical communication (LOCC), a relatively unexplored topic. To demonstrate the possible strong dependence on the round number, we consider the problem of converting three-qubit entanglement into two-qubit form, specifically in the random distillation setting of [Phys. Rev. Lett. 98, 260501 (2007)]. We find that the number of LOCC rounds needed for a transformation can depend on the amount of entanglement distilled. In fact, for a wide range of transformations, the required number of rounds is infinite (unbounded). This represents the first concrete example of a task needing an infinite number of rounds to implement.
在这封信中，我们研究了通过局部量子操作和经典通信（LOCC）实现某些任务所需的测量和通信轮数，这是一个相对未被探索的话题。为了展示轮数的可能强依赖性，我们考虑了将三量子比特纠缠转换为两量子比特形式的问题，特别是在 [Phys. Rev. Lett. 98, 260501 (2007)] 的随机蒸馏设置中。我们发现，转换所需的 LOCC 轮数可以取决于蒸馏的纠缠量。实际上，对于广泛的转换，所需的轮数是无限的（无界的）。这代表了需要无限轮数来实现的任务的第一个具体例子。
