Possibility of entanglement of purification to be less than half of the reflected entropy

作     者：Josiah Couch Phuc Nguyen Sarah Racz Georgios Stratis Yuxuan Zhang 

作者机构：Beth Israel Deaconess Medical Center Boston Massachusetts 02215 USA Martin A. Fisher School of Physics Brandeis University Waltham Massachusetts 02453 USA Theory Group Weinberg Institute Department of Physics The University of Texas at Austin Austin Texas 78712 USA Department of Electrical and Computer Engineering Northeastern University Boston Massachusetts 02115 USA Department of Physics The University of Texas at Austin Austin Texas 78712 USA Department of Physics and Centre for Quantum Information and Quantum Control University of Toronto 60 Saint George St. Toronto Ontario Canada M5S 1A7 Vector Institute MaRS Centre Toronto Ontario Canada M5G 1M1 

出 版 物：《Physical Review A》 (物理学评论A辑：原子、分子和光学物理学)

年 卷 期：2024年第109卷第2期

页      面：022426-022426页

核心收录：

学科分类：070207[理学-光学] 07[理学] 08[工学] 0803[工学-光学工程] 0702[理学-物理学] 

基　　金：National Science Foundation, NSF, (2210562) National Science Foundation, NSF U.S. Department of Energy, USDOE, (DE-SC0009986, DE-SC0022102) U.S. Department of Energy, USDOE Air Force Office of Scientific Research, AFOSR, (FA9550-19-1-0360) Air Force Office of Scientific Research, AFOSR Simons Foundation, SF University of Toronto, U of T 

主　　题：Quantum gravity Quantum information theory 

摘      要：In recent work, Akers et al. [arXiv:2306.06163] proved that the entanglement of purification Ep(A:B) is bounded below by half of the q-Rényi reflected entropy SR(q)(A:B) for all q≥2, showing that Ep(A:B)=12SR(q)(A:B) for a class of random tensor-network states. Naturally, the authors raise the question of whether a similar bound holds at q=1. Our work answers that question in the negative by finding explicit counterexamples, which we arrive at through numerical optimization. Nevertheless, this result does not preclude the possibility that restricted sets of states, such as conformal field theory states with semiclassical gravity duals, could obey the bound in question.