2016/05/13 by Bang-Hai Wang · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.97.050302
published as Physical Review A 97, 050302(R) (2018) · Close to the published version, title was changed to meet the PRA requirement, 6 pages, 2 figures. arXiv admin note: text overlap with arXiv:1605.04073
arxiv created 2020/03/01 · arxiv updated 2020/03/04
Quantum entanglement lies at the heart of quantum mechanics and quantum information processing. In this work, we show a new framework where entangled states play the role of witnesses. We extend the notion of entanglement witnesses, developing a hierarchy of witnesses for classes of observables. This hierarchy captures the fact that entangled states act as witnesses for detecting entanglement witnesses and separable states act as witnesses for the set of non-block-positive Hermitian operators. Indeed, more hierarchies of witnesses exist. We introduce the concept of finer and optimal entangled states. These definitions not only give an unambiguous and non-numeric quantification of entanglement and a new perspective on edge states but also answer the open question of what the remainder of the best separable approximation of a density matrix. Furthermore, we classify all entangled states into disjoint families with optimal entangled states at its heart. This implies that we can focus only on the study of a typical family with optimal entangled states at its core when we investigate entangled states. Our framework also assembles many seemingly different findings with simple arguments that do not require lengthy calculations.