论文标题
与可分离和纠缠量子状态的因果特性的任意密度矩阵的通用可分离性标准
Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states
论文作者
论文摘要
揭示了Peres-Horodecki阳性部分转置（PPT-）可分离性标准的一般物理背景。尤其是，局部转置操作的物理意识被证明等于所有可分开的量子系统的“局部因果关系逆转”（LCR-）程序，或在所有纠缠案例中的全局时间箭头方向上的不确定性。 Using these universal causal considerations the heuristic causal separability criterion has been proposed for arbitrary $ D^{N} \times D^{N}$ density matrices acting in $ \mathcal{H}_{D}^{\otimes N} $ Hilbert spaces which describe the ensembles of $ N $ quantum systems of $ D $ eigenstates each.然后，已对所得的一般公式进行了分析，以根据任意维度的最广泛类型的单参数密度矩阵进行分析，该矩阵模拟了等效量子子系统，通过单个Intnaglement参数$ P $相互连接（EC-）。特别是，对于这种EC密度矩阵的家庭，已经发现存在许多$ n $ - 和$ d $依赖性的可分离性（或纠缠）阈值$ p_ p_ {th}（n，d）$，而在Qubit-pair密度密度矩阵中，则在$ \ mathcal {h} _ {h} _ {2} _ \ Mathcal {h} _ {2} $ Hilbert Space显示为佩雷斯[5]和Horodecki [6]获得的众所周知的结果。结果，首次描述了EC密度矩阵的纠缠阈值的许多显着特征。对于任意EC密度矩阵的家族而获得的所有新型结果都适用于广泛的相互作用和非相互作用的和非相互作用的多目标量子系统，例如Qubits的阵列，自旋链，量子振荡器的组合，量子振荡器的组合，与许多体现的量子本地化相关性，等等。
General physical background of Peres-Horodecki positive partial transpose (ppt-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to the "local causality reversal" (LCR-) procedure for all separable quantum systems or to the uncertainty in a global time arrow direction in all entangled cases. Using these universal causal considerations the heuristic causal separability criterion has been proposed for arbitrary $ D^{N} \times D^{N}$ density matrices acting in $ \mathcal{H}_{D}^{\otimes N} $ Hilbert spaces which describe the ensembles of $ N $ quantum systems of $ D $ eigenstates each. Resulting general formulas have been then analyzed for the widest special type of one-parametric density matrices of arbitrary dimensionality, which model equivalent quantum subsystems being equally connected (EC-) with each other by means of a single entnaglement parameter $ p $. In particular, for the family of such EC-density matrices it has been found that there exists a number of $ N $- and $ D $-dependent separability (or entanglement) thresholds $ p_{th}(N,D) $ which in the case of a qubit-pair density matrix in $ \mathcal{H}_{2} \otimes \mathcal{H}_{2} $ Hilbert space are shown to reduce to well-known results obtained earlier by Peres [5] and Horodecki [6]. As the result, a number of remarkable features of the entanglement thresholds for EC-density matrices has been described for the first time. All novel results being obtained for the family of arbitrary EC-density matrices are shown to be applicable for a wide range of both interacting and non-interacting multi-partite quantum systems, such as arrays of qubits, spin chains, ensembles of quantum oscillators, strongly correlated quantum many-body systems with the possibility of many-body localization, etc.
