Nonlocality, Entanglement Witnesses and Supra-Correlations

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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] 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

"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.