Measurement incompatibility is one of the most striking examples of how quantum physics is different from classical physics. Two measurements are incompatible if they cannot arise via classical post-processing from a third one. A natural way to quantify incompatibility is in terms of noise robustness. In the present article, we review recent results on the maximal noise robustness of incompatible measurements, which have been obtained by the present authors using free spectrahedra, and rederive them using tensor norms. In this way, we make them accessible to a broader audience from quantum information theory and mathematical physics and contribute to the fruitful interactions between Banach space theory and quantum information theory. We also describe incompatibility witnesses using tensor norm and matrix convex set duality, emphasizing the relation between the different notions of witnesses.
Thermodynamic compatibility, holographic property and wave-function representation of generalized weakly nonlocal self-gravitating non-relativistic fluids
Budapest University of Technology and Economics（布达佩斯科技经济大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络维格纳物理研究中心）；Society for the Unity of Science and Technology（科学与技术统一协会）
Compatibility of any pair of 2-outcome measurements characterizes the Choquet simplex
对于局部凸T2空间的紧凸子集$K $，$A(K)$上的一个度量是$A(K)$中的一个有限的正元素族，归一化为单位常数$1_K$，其中$A(K)$表示$K$上的连续实仿射泛函集。证明了紧凸集$K$是Choquet单形当且仅当任意一对$2$ -结果测度相容，即测量值作为单个测量值的边缘给出。这推广了[Plávala M 2016 Phys.\修订版本\ A \textbf{94}，042108]在量子理论基础的背景下获得。
Efficient Finite Initialization with Partial Norms for Tensorized Neural Networks and Tensor Networks Algorithms
Quantum Technologies and Systems Unit, LKS Next, MONDRAGON Corporation, Goiru 7, 20500 Arrasate-Mondragón, Gipuzkoa, Spain（量子技术与系统单元，LKS Next，MONDRAGON公司，Goiru 7，20500 Arrasate-Mondragón，Gipuzkoa，西班牙）
