  In spite of many results in quantum information theory, the complex nature of
compound systems is far from being clear. In general the information is a
mixture of local, and non-local ("quantum") information. To make this point
more clear, we develop and investigate the quantum information processing
paradigm in which parties sharing a multipartite state distill local
information. The amount of information which is lost because the parties must
use a classical communication channel is the deficit. This scheme can be viewed
as complementary to the notion of distilling entanglement. After reviewing the
paradigm, we show that the upper bound for the deficit is given by the relative
entropy distance to so-called psuedo-classically correlated states; the lower
bound is the relative entropy of entanglement. This implies, in particular,
that any entangled state is informationally nonlocal i.e. has nonzero deficit.
We also apply the paradigm to defining the thermodynamical cost of erasing
entanglement. We show the cost is bounded from below by relative entropy of
entanglement. We demonstrate the existence of several other non-local
phenomena. For example,we prove the existence of a form of non-locality without
entanglement and with distinguishability. We analyze the deficit for several
classes of multipartite pure states and obtain that in contrast to the GHZ
state, the Aharonov state is extremely nonlocal (and in fact can be thought of
as quasi-nonlocalisable). We also show that there do not exist states, for
which the deficit is strictly equal to the whole informational content (bound
local information). We then discuss complementary features of information in
distributed quantum systems. Finally we discuss the physical and theoretical
meaning of the results and pose many open questions.
