Skorobagatko Gleb A
Institute for Condensed Matter Physics of National Academy of Sciences of Ukraine, Svientsitskii Str.1, Lviv, 79011, Ukraine.
Sci Rep. 2021 Aug 5;11(1):15866. doi: 10.1038/s41598-021-94804-2.
General physical background of famous Peres-Horodecki positive partial transpose (PH- or PPT-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to what one could call as 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 brand new general relations for the heuristic causal separability criterion have been proposed for arbitrary [Formula: see text] density matrices acting in [Formula: see text] 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 a number of equivalent quantum subsystems being equally connected (EC-) with each other to arbitrary degree by means of a single entanglement 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 [Formula: see text] for the values of the corresponded entanglement parameter p, which in the simplest case of a qubit-pair density matrix in [Formula: see text] Hilbert space are shown to reduce to well-known results obtained earlier independently by Peres (Phys Rev Lett 77:1413-1415, 1996) and Horodecki (Phys Lett A 223(1-2):1-8, 1996). 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 to a wide range of both interacting and non-interacting (at the moment of measurement) 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.
揭示了著名的佩雷斯 - 霍罗德基正偏置转置（PH - 或 PPT -）可分性判据的一般物理背景。特别地，对于所有可分量子系统，偏置转置操作的物理意义被证明等同于所谓的“局部因果性反转”（LCR -）过程；而在所有纠缠情形下，等同于全局时间箭头方向的不确定性。利用这些通用的因果性考量，针对作用于描述具有(D)个本征态的(N)个量子系统系综的(\mathcal{H}D^{\otimes N})希尔伯特空间中的任意(N\times N)密度矩阵，提出了启发式因果可分性判据的全新一般关系。然后针对任意维度的最广泛特殊类型的单参数密度矩阵分析了所得的一般公式，这些密度矩阵通过单个纠缠参数(p)对多个等效量子子系统以任意程度相互平等连接（EC -）的情况进行建模。特别地，对于此类 EC - 密度矩阵族，发现对于相应纠缠参数(p)的值存在许多依赖于(N)和(D)的可分性（或纠缠）阈值(p{sep}^{(N,D)})，在(\mathcal{H}_2^{\otimes 2})希尔伯特空间中双量子比特密度矩阵的最简单情形下，这些阈值被证明可简化为佩雷斯（《物理评论快报》77:1413 - 1415，1996）和霍罗德基（《物理快报 A》223(1 - 2):1 - 8，1996）先前独立得到的著名结果。结果，首次描述了 EC - 密度矩阵纠缠阈值的许多显著特征。针对任意 EC - 密度矩阵族获得的所有新结果被证明适用于广泛的相互作用和非相互作用（在测量时刻）的多体量子系统，例如量子比特阵列、自旋链、量子振子系综、具有多体局域化可能性的强关联量子多体系统等。
