Choi Minjin, Bae Eunok, Lee Soojoon
Division of National Supercomputing, Korea Institute of Science and Technology Information, Daejeon, 34141, Korea.
Qunova Computing, Inc., Daejeon, 34051, Korea.
Sci Rep. 2023 Sep 11;13(1):15013. doi: 10.1038/s41598-023-42052-x.
Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing, and many entanglement measures have been suggested for this purpose. When mathematically defining an entanglement measure, we should consider the distinguishability between entangled and separable states, the invariance under local transformation, the monotonicity under local operations and classical communication, and the convexity. These are reasonable requirements but may be insufficient, in particular when taking into account the usefulness of quantum states in multi-party quantum information processing. Therefore, if we want to investigate multipartite entanglement as a resource, then it can be necessary to consider the usefulness of quantum states in multi-party quantum information processing when we define a multipartite entanglement measure. In this paper, we define new multipartite entanglement measures for three-qubit systems based on the three-party teleportation capability, and show that these entanglement measures satisfy the requirements for being genuine multipartite entanglement measures. We also generalize our entanglement measures for N-qubit systems, where [Formula: see text], and discuss that these quantities may be good candidates to measure genuine multipartite entanglement.
量化纠缠对于理解纠缠作为量子信息处理中的一种资源至关重要，为此人们提出了许多纠缠度量方法。在从数学上定义一种纠缠度量时，我们应考虑纠缠态与可分态之间的可区分性、局部变换下的不变性、局部操作和经典通信下的单调性以及凸性。这些都是合理的要求，但可能并不充分，特别是在考虑量子态在多方量子信息处理中的有用性时。因此，如果我们想将多方纠缠作为一种资源来研究，那么在定义多方纠缠度量时，考虑量子态在多方量子信息处理中的有用性可能是必要的。在本文中，我们基于三方量子隐形传态能力为三量子比特系统定义了新的多方纠缠度量，并表明这些纠缠度量满足作为真正多方纠缠度量的要求。我们还将我们的纠缠度量推广到N量子比特系统，其中[公式：见原文]，并讨论这些量可能是测量真正多方纠缠的良好候选者。
