  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.
