While entanglement is believed to underlie the power of
quantum computation
and communication, it is not generally well understood
for multipartite
systems. Recently, it has been appreciated that there
exists proper
no-signaling probability distributions derivable from
operators that do not
represent valid quantum states. Such systems exhibit supra-correlations
that are stronger than allowed by quantum mechanics, but
less than the
algebraically allowed maximum in Bell-inequalities (in
the bipartite case).
Some of these probability distributions are derivable
from an entanglement
witness W, which is a non-positive Hermitian operator
constructed such that
its expectation value with a separable quantum state
(positive density
matrix) rho_sep is non-negative (so that Tr[W rho]< 0
indicates entanglement
in quantum state rho). In the bipartite case, it is known
that by a
modification of the local no-signaling measurements by
spacelike separated
parties A and B, the supra-correlations exhibited by any
W can be modeled as
derivable from a physically realizable quantum state ρ.
However, this result
does not generalize to the n-partite case for n>2.
Supra-correlations can
also be exhibited in 2- and 3-qubit systems by explicitly
constructing
"states" O (not necessarily positive quantum
states) that exhibit PR
correlations for a fixed, but arbitrary number, of
measurements available to
each party. In this paper we examine the structure of
"states" that exhibit
supra-correlations. In addition, we examine the affect
upon the distribution
of the correlations amongst the parties involved when
constraints of
positivity and purity are imposed. We investigate
circumstances in which
such "states" do and do not represent valid
quantum states.