Managing the three-party entanglement challenge

Abstract

We introduce the challenges of multi-party quantum entanglement and explain a recent success in learning to take its measure. Given the widely accepted reputation of entanglement as a counter-intuitive feature of quantum theory, we first describe pure-state entanglement itself. We restrict attention to multi-party qubit states. Then we introduce the features that have made it challenging for several decades to extend an entanglement measure beyond the 2-qubit case of Bell states. We finish with a description of the current understanding that solves the 3-qubit entanglement challenge. This necessarily takes into account the fundamental division of the 3-qubit state space into two completely independent sectors identified with the so-called GHZ and W states.

Keywords:

• Qubit systems
• multipartite entanglement
• triangle measure
• concurrence Fill

Acknowledgments

We thank M. A. Alonso and X.-F. Qian for several key initial discussions, and we thank Y.-Y. Zhao for valuable conversations.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Financial support was provided by National Science Foundation Grants PHY-1501589 and PHY-1539859 (INSPIRE), and a competitive award from the University of Rochester.

Notes on contributors

Songbo Xie

Songbo Xie is a PhD Candidate in Physics at the University of Rochester, studying quantum entanglement. He received his B.S. in Physics in 2017 from Shanghai Jiao Tong University in China, supervised by Prof. Zhiguo Lv. His researches cover the geometric quantification of entanglement in multi-qubit systems, bizarre behavior of entanglement in quantum dynamical systems, and the evaluation of entanglement with experimental measurements.

J.H. Eberly

Joseph Eberly received his degrees from Penn State and Stanford where E.T. Jaynes was his PhD advisor. He is now the Andrew Carnegie Professor of Physics and Professor of Optics in the University of Rochester where his research in theoretical quantum optics and atomic physics has engaged more than 40 PhD students in interesting topics such as time-dependent spectra, multiphoton ionization, atomic state collapse and revival in cavity QED, first observation of Bessel beams, and both sudden death and freezing of quantum entanglement. Professor Eberly is a Fellow of APS and of Optica (formerly OSA) and has served as Chair of the Division of Laser Science of APS and President of OSA. He was the Founding Editor of Optics Express. Professor Eberly has received the Distinguished Alumnus Award of the Penn State College of Science, Smoluchowski Medal of the Physical Society of Poland, the Georgen Award for Artistry in Undergraduate Teaching at the University of Rochester, Frederick Ives Medal and Quinn Prize of OSA, and has been elected as Honorary Member of Optica. He is a Foreign Member of the Academy of Science of Poland.