Witnessing the Hierarchy of Quantum Incompatibility Resources in High-Dimensional Systems

• URL: http://arxiv.org/abs/2306.12122v3
• Date: Fri, 3 Nov 2023 00:54:30 GMT
• Title: Witnessing the Hierarchy of Quantum Incompatibility Resources in High-Dimensional Systems
• Authors: Xiaolin Zhang, Rui Qu, Zehong Chang, Yunlong Wang, Zhenyu Guo, Min An, Hong Gao, Fuli Li and Pei Zhang
• Abstract summary: Quantum incompatibility is a phenomenon that some quantum measurements cannot be performed simultaneously. We propose a modified quantum state discrimination protocol that decomposes complex compatibility structures into pair-wise ones. Our approach is able to witness incompatibility structures, i.e., the hierarchy of quantum incompatibility resources.
• Score: 10.661961857558106
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum incompatibility is referred as the phenomenon that some quantum measurements cannot be performed simultaneously, and is also used in various quantum information tasks. However, it is still a challenge to certify whether a given set of multiple high-dimensional measurements respects a specific structure of incompatibility. To address this problem, we propose a modified quantum state discrimination protocol that decomposes complex compatibility structures into pair-wise ones and employs noise robustness to witness incompatibility structures. Our method is capable of detecting genuine $n$-wise incompatibility and some specific general compatibility structures, as demonstrated by our experimental verification of incompatibility structures of $4$ mutually unbiased bases in a qutrit system. The experimental results show that our approach is able to witness incompatibility structures, i.e., the hierarchy of quantum incompatibility resources.

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