Irreversibility of Asymptotic Entanglement Manipulation Under Quantum Operations Completely Preserving Positivity of Partial Transpose
Abstract
We demonstrate the irreversibility of asymptotic entanglement manipulation under quantum operations that completely preserve positivity of partial transpose (PPT), which resolves a major open problem in quantum information theory. To be more specific, we show that for any rank-two mixed state supporting on the $3øtimes3$ antisymmetric subspace, the amount of distillable entanglement by PPT operations is strictly smaller than one entanglement bit (ebit) while its entanglement cost under PPT operations is exactly one ebit. As a byproduct, we find that for this class of quantum states, both the Rains’ bound and its regularization, are strictly less than the asymptotic relative entropy of entanglement with respect to PPT states. So in general there is no unique entanglement measure for the manipulation of entanglement by PPT operations. We further present a feasible sufficient condition for the irreversibility of entanglement manipulation under PPT operations.
Xin Wang
Associate Professor
Prof. Xin Wang founded the QuAIR Lab at HKUST (Guangzhou) in June 2023. His research aims to advance our understanding of the limits of information processing with quantum systems and the potential of quantum artificial intelligence. His current interests include quantum algorithms, quantum resource theory, quantum machine learning, quantum computer architecture, and quantum error processing. Prior to establishing the QuAIR Lab, Prof. Wang was a Staff Researcher at the Institute for Quantum Computing at Baidu Research, where he focused on quantum computing research and the development of the Baidu Quantum Platform. Notably, he led the development of Paddle Quantum, a Python library for quantum machine learning. From 2018 to 2019, he was a Hartree Postdoctoral Fellow at the Joint Center for Quantum Information and Computer Science (QuICS) at the University of Maryland, College Park. Prof. Wang received his Ph.D. in quantum information from the University of Technology Sydney in 2018, under the supervision of Prof. Runyao Duan and Prof. Andreas Winter. He obtained his B.S. in mathematics (Wu Yuzhang Honors) from Sichuan University in 2014.