In the present work, we suggest an approach for describing dynamics of finite-dimensional quantum systems in terms of pseudostochastic maps acting on probability distributions, which are obtained via minimal informationally complete quantum measurements. The suggested method for probability representation of quantum dynamics preserves the tensor product structure, which makes it favourable for the analysis of multi-qubit systems. A key advantage of the suggested approach is that minimal informationally complete positive operator-valued measures (MIC-POVMs) are easier to construct in comparison with their symmetric versions (SIC-POVMs). We establish a correspondence between the standard quantum-mechanical formalism and the MIC-POVM-based probability formalism. Within the latter approach, we derive equations for the unitary von-Neumann evolution and the Markovian dissipative evolution, which is governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generator. We apply the MIC-POVM-based probability representation to the digital quantum computing model. In particular, for the case of spin-1/2 evolution, we demonstrate identifying a transition of a dissipative quantum dynamics to a completely classical-like stochastic dynamics. One of the most important findings is that the MIC-POVM-based probability representation gives more strict requirements for revealing the non-classical character of dissipative quantum dynamics in comparison with the SIC-POVM-based approach. Our results give a physical interpretation of quantum computations and pave a way for exploring the resources of noisy intermediate-scale quantum (NISQ) devices.

中文翻译：

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量子动力学概率表示的最小信息完整测量

在目前的工作中，我们提出了一种方法，根据作用于概率分布的伪随机映射来描述有限维量子系统的动力学，这是通过最小信息完整的量子测量获得的。提出的量子动力学概率表示方法保留了张量积结构，有利于多量子位系统的分析。所建议方法的一个关键优势是，与其对称版本 (SIC-POVM) 相比，最小信息完整的正算子值度量 (MIC-POVM) 更容易构建。我们建立了标准量子力学形式主义和基于 MIC-POVM 的概率形式主义之间的对应关系。在后一种方法中，我们推导出酉冯诺依曼演化和马尔可夫耗散演化方程，后者由 Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) 生成器控制。我们将基于 MIC-POVM 的概率表示应用于数字量子计算模型。特别是，对于自旋 1/2 演化的情况，我们证明了识别耗散量子动力学到完全类似经典的随机动力学的转变。最重要的发现之一是，与基于 SIC-POVM 的方法相比，基于 MIC-POVM 的概率表示对揭示耗散量子动力学的非经典特征提出了更严格的要求。我们的结果给出了量子计算的物理解释，并为探索嘈杂的中尺度量子 (NISQ) 设备的资源铺平了道路。