On the structure of LOCC: finite vs. infinite rounds
Scott M. Cohen
备注：
14 pages, 2 figures, comments welcome. For version 2, some terminology and notation have been modified, along with numerous other editorial changes, and a distance measure on quantum measurements has been formally defined. All results are the same as in version 1
Every measurement that can be implemented by local quantum operations and classical communication (LOCC) using an infinite number of rounds is the limit of a sequence of measurements each of which requires only a finite number of rounds. This rather obvious and well-known fact is nonetheless of interest as it shows that these infinite-round measurements can be approximated arbitrarily closely simply by using more and more rounds of communication. Here we demonstrate the perhaps less obvious result that (at least) for bipartite systems, the reverse relationship also holds. Specifically, we show that every finite-round bipartite LOCC measurement is the limit of a continuous sequence of LOCC measurements, where each measurement in that sequence can be implemented by LOCC, but only with the use of an infinite number of rounds. Thus, the set of LOCC measurements that require an infinite number of rounds is dense in the entirety of LOCC, as is the set of finite-round LOCC measurements. This means there exist measurements that can only be implemented by LOCC by using an infinite number of rounds, but can nonetheless be approximated closely by using one round of communication, and actually in some cases, no communication is needed at all. These results follow from a new necessary condition for finite-round LOCC, which is extremely simple to check, is very easy to prove, and which can be violated by utilizing an infinite number of rounds.
Entanglement manipulation of multipartite pure states with finite rounds of classical communication
我们研究了C语言中基于多轮经典通信（$LOCC_{\mathbb{N}}$）的局部操作的纯状态变换。Spee，J.I. de Vicente，D.绍尔温湾Kraus，arXiv：1606.04418（2016）.在这里，我们首先提出的一些证明的细节，并通过$LOCC_{\mathbb{N}}$，这需要一个概率的步骤，推广建设的状态转换的例子。然而，我们也提出了明确的SLOCC类的例子，其中任何可分离的转换可以实现的协议，其中每一步都是确定性的（所有-det- $LOCC_{\mathbb{N}}$）。这样的变换可以被认为是二分变换的自然推广。此外，我们提供了纯状态转换的例子，这是可能的，通过可分离的转换，但不是通过$LOCC_{\mathbb{N}}$。我们还分析了一个有趣的真正多方效应，我们称之为锁定或解锁其他各方的权力。这意味着一方可以阻止或允许其他方实施LOCC转换。此外，我们研究了限制在$LOCC_{\mathbb{N}}$的最大纠缠集，并展示了如何容易计算的限制$LOCC_{\mathbb{N}}$的一些纠缠措施的界限可以得到。
Structure of quantum measurements implementable with one round of classical communication
Universität Siegen（锡根大学）；Universidade Estadual de Campinas（坎皮纳斯州立大学）；Uppsala University（乌普萨拉大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Stockholm University（斯德哥尔摩大学）
A class of unambiguous state discrimination problems achievable by separable measurements but impossible by local operations and classical communication
Random Party Distillation on a Superconducting Processor
University of Toronto（多伦多大学）；National University of Singapore（新加坡国立大学）；Quantum Bridge Technologies Inc.（量子桥技术有限公司）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
Entanglement cost for infinite-dimensional physical systems
The University of Tokyo（东京大学）；University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（理论物理珀尔默特研究所）；Stanford University（斯坦福大学）；Scuola Normale Superiore（比萨高等师范学院）；QuSoft；University of Amsterdam（阿姆斯特丹大学）
