The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e., basis-independent, notion of dimensionality for ensembles of quantum states. It is based on whether a quantum ensemble can be simulated with states confined to arbitrary lower-dimensional subspaces and classical postprocessing. In order to determine the absolute dimension of quantum ensembles, we develop both analytical witness criteria and a semidefinite programming criterion based on the ensemble’s information capacity. Furthermore, we construct explicit simulation models for arbitrary ensembles of pure quantum states subject to white noise, and in natural cases we prove their optimality. Also, efficient numerical methods are provided for simulating generic ensembles. Finally, we discuss the role of absolute dimensionality in high-dimensional quantum information processing. Published by the American Physical Society 2024

中文翻译：

---

量子系综的绝对维数


量子态的维度传统上被视为给定基中叠加的可区分态的数量。我们提出了一个绝对的，即与基无关的量子态系积的维数概念。它基于是否可以使用仅限于任意低维子空间的状态和经典后处理来模拟量子集成。为了确定量子集合的绝对维度，我们根据集合的信息容量开发了分析见证标准和半定编程标准。此外，我们为受白噪声影响的纯量子态的任意系分构建了显式仿真模型，并在自然情况下证明了它们的最优性。此外，还提供了用于模拟通用集成的有效数值方法。最后，我们讨论了绝对维数在高维量子信息处理中的作用。美国物理学会 2024 年出版