Reversible Entanglement Beyond Quantum Operations

Schematic hierarchy of operations.

Abstract

We introduce a reversible theory of exact entanglement manipulation by establishing a necessary and sufficient condition for state transfer under trace-preserving transformations that completely preserve the positivity of partial transpose (PPT). Under these free transformations, we show that logarithmic negativity emerges as the pivotal entanglement measure for determining entangled states’ transformations, analogous to the role of entropy in the second law of thermodynamics. Previous results have proven that entanglement is irreversible under quantum operations that completely preserve PPT and leave open the question of reversibility for quantum operations that do not generate entanglement asymptotically. However, we find that going beyond the complete positivity constraint imposed by standard quantum mechanics enables a reversible theory of exact entanglement manipulation, which may suggest a potential incompatibility between the reversibility of entanglement and the fundamental principles of quantum mechanics.

Publication
arXiv:2312.04456
Xin Wang
Xin Wang
Associate Professor

The main focus of my research is to better understand the limits of information processing with quantum systems and the power of quantum artificial intelligence.

Yu-Ao Chen
Yu-Ao Chen
Research Associate

I obtained my BS in Mathematics and Applied Mathematics from University of Science and Technology of China. I obtained my PhD degree in Applied Mathematics from University of Chinese Academy of Sciences under the supervision of Prof. Xiao-Shan Gao. My research interests include quantum computing, symbolic computation and cryptanalysis.

Lei Zhang
Lei Zhang
PhD Student

I obtained my BMath in AMath, CO & joint PMath from the University of Waterloo. My research interests include quantum information theory and quantum machine learning.

Chenghong Zhu
Chenghong Zhu
PhD Student

I obtained my BS and MS degrees in computer science from the University of Melbourne. My research interests include distributed quantum computing, quantum entanglement and quantum machine learning.