量子系综的绝对维度
Absolute dimensionality of quantum ensembles
AI总结：
提出与基无关的量子系综绝对维度概念，开发解析见证和半定规划准则以确定绝对维度，构建受白噪声影响的纯态系综模拟模型，并探讨其在高维量子信息处理中的作用。
摘要：
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。我们提出了一种绝对的，即与基无关的量子态系综维度概念。它基于量子系综是否能用局限于任意低维子空间的态和经典后处理来模拟。为了确定量子系综的绝对维度，我们开发了基于系综信息容量的解析见证准则和半定规划准则。此外，我们为受白噪声影响的任意纯量子态系综构建了显式模拟模型，并在自然情况下证明了其最优性。同时，提供了用于模拟一般系综的高效数值方法。最后，我们讨论了绝对维度在高维量子信息处理中的作用。
英文摘要：
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.
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