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- Nonlocality, Entanglement Witnesses and Supra-Correlations

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PIRSA Number:

12060076

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

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.

©2012 Perimeter Institute for Theoretical Physics