Separation Between Quantum Lovász Number and Entanglement-Assisted Zero-Error Classical Capacity

Abstract

Quantum Lovász number, as a natural generalization of the celebrated Lovśz number in graph theory, is the best known efficiently computable upper bound of the entanglement-assisted zero-error classical capacity of a quantum channel. However, it remains an intriguing open problem whether this number always coincides with the entanglement-assisted zero-error capacity. Here we show that there is a strict gap between these two quantities for a class of explicitly constructed qutrit-to-qutrit channels. Our key approach is to show that for this class of channels both the one-shot zero-error communication capacity and the one-shot zero-error simulation cost in the presence of quantum no-signalling correlations (QNSC), a more broader class of resources than entanglement, are exactly four, while the quantum Lov’ź number is strictly larger than that. Interestingly, for this class of channels, the quantum fractional packing number is strictly larger than the QNSC-assisted or quantum feedback-assisted zero-error classical capacity. Note that these quantities are all equal for classical channels.

Xin Wang

Associate Professor

Prof. Xin Wang founded the QuAIR lab at HKUST(Guangzhou) in June 2023. His research primarily focuses on better understanding the limits of information processing with quantum systems and the power of quantum artificial intelligence. Prior to establishing the QuAIR lab, Prof. Wang was a Staff Researcher at the Institute for Quantum Computing at Baidu Research, where he concentrated on quantum computing research and the development of the Baidu Quantum Platform. Notably, he spearheaded the development of Paddle Quantum, a Python library designed for quantum machine learning. From 2018 to 2019, Prof. Wang held the position of Hartree Postdoctoral Fellow at the Joint Center for Quantum Information and Computer Science (QuICS) at the University of Maryland, College Park. He earned his doctorate in quantum information from the University of Technology Sydney in 2018, under the guidance of Prof. Runyao Duan and Prof. Andreas Winter. In 2014, Prof. Wang obtained his B.S. in mathematics (with Wu Yuzhang Honor) from Sichuan University.