  Schroedinger's disentanglement [E. Schroedinger, Proc. Cambridge Phil. Soc.
31, 555 (1935)], i. e., remote state decomposition, as a physical way to study
entanglement, is carried one step further with respect to previous work in
investigating the qualitative side of entanglement in any bipartite state
vector. Remote measurement (or, equivalently, remote orthogonal state
decomposition) from previous work is generalized to remote linearly-independent
complete state decomposition both in the non-selective and the selective
versions. The results are displayed in terms of commutative square diagrams,
which show the power and beauty of the physical meaning of the (antiunitary)
correlation operator inherent in the given bipartite state vector. This
operator, together with the subsystem states (reduced density operators),
constitutes the so-called correlated subsystem picture. It is the central part
of the antilinear representation of a bipartite state vector, and it is a kind
of core of its entanglement structure. The generalization of previously
elaborated disentanglement expounded in this article is a synthesis of the
antilinear representation of bipartite state vectors, which is reviewed, and
the relevant results of Cassinelli et al. [J. Math. Analys. and Appl., 210, 472
(1997)] in mathematical analysis, which are summed up. Linearly-independent
bases (finite or infinite) are shown to be almost as useful in some quantum
mechanical studies as orthonormal ones. Finally, it is shown that
linearly-independent remote pure-state preparation carries the highest
probability of occurrence. This singles out linearly-independent remote
influence from all possible ones.
