Streltsov A, Meignant C, Eisert J
Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, Warsaw 02-097, Poland.
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gdańsk 80-233, Poland.
Phys Rev Lett. 2020 Aug 21;125(8):080502. doi: 10.1103/PhysRevLett.125.080502.
The theory of the asymptotic manipulation of pure bipartite quantum systems can be considered completely understood: the rates at which bipartite entangled states can be asymptotically transformed into each other are fully determined by a single number each, the respective entanglement entropy. In the multipartite setting, similar questions of the optimally achievable rates of transforming one pure state into another are notoriously open. This seems particularly unfortunate in the light of the revived interest in such questions due to the perspective of experimentally realizing multipartite quantum networks. In this Letter, we report substantial progress by deriving simple upper and lower bounds on the rates that can be achieved in asymptotic multipartite entanglement transformations. These bounds are based on ideas of entanglement combing and state merging. We identify cases where the bounds coincide and hence provide the exact rates. As an example, we bound rates at which resource states for the cryptographic scheme of quantum secret sharing can be distilled from arbitrary pure tripartite quantum states. This result provides further scope for quantum internet applications, supplying tools to study the implementation of multipartite protocols over quantum networks.
二分纠缠态能够渐近相互转换的速率完全由各自的纠缠熵这一单个数字确定。在多方情形中，将一个纯态最优地转换为另一个纯态的类似可实现速率问题，众所周知仍是开放的。鉴于由于实验实现多分量量子网络的前景，对此类问题重新产生了兴趣，这似乎尤其令人遗憾。在本信函中，我们通过推导渐近多分量纠缠变换中可实现速率的简单上下界，报告了实质性进展。这些界限基于纠缠梳理和态合并的思想。我们确定了界限重合的情形，从而给出了精确速率。例如，我们界定了可从任意纯三方量子态中提取量子秘密共享密码方案的资源态的速率。这一结果为量子互联网应用提供了进一步的空间，提供了研究量子网络上多分量协议实现的工具。
