论文标题
开放量子随机步行和树木上的量子马尔可夫链I：相变
Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
论文作者
论文摘要
在本文中，我们构建了与开放量子随机步行相关的QMC（量子马尔可夫链），以使链的过渡算子由OQRW定义，并且QMC限制对交换性亚位式的限制与OQRW的分布$P_ρ$相吻合。但是，我们将把概率分布视为Cayley树上的马尔可夫字段。这种考虑使我们能够研究QMC方案中与OQRW相关的相变现象。此外，我们首先提出了在树上的QMC新结构，这是参考文献中考虑的QMC的扩展。 [10]。使用这种结构，我们能够在与OQRW关联的TRESS上构造QMC。我们的研究导致在拟议方案中检测到相变现象。这种现象首次朝这个方向出现。此外，计算QMC的平均熵。
In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution $P_ρ$ of OQRW. However, we are going to look at the probability distribution as a Markov field over the Cayley tree. Such kind of consideration allows us to investigated phase transition phenomena associated for OQRW within QMC scheme. Furthermore, we first propose a new construction of QMC on trees, which is an extension of QMC considered in Ref. [10]. Using such a construction, we are able to construct QMCs on tress associated with OQRW. Our investigation leads to the detection of the phase transition phenomena within the proposed scheme. This kind of phenomena appears first time in this direction. Moreover, mean entropies of QMCs are calculated.
