Nonlocality, Entanglement Witnesses and Supra-Correlations


Alsing, P. (2012). Nonlocality, Entanglement Witnesses and Supra-Correlations. Perimeter Institute. https://pirsa.org/12060076


Alsing, Paul. Nonlocality, Entanglement Witnesses and Supra-Correlations. Perimeter Institute, Jun. 25, 2012, https://pirsa.org/12060076


          @misc{ pirsa_PIRSA:12060076,
            doi = {10.48660/12060076},
            url = {https://pirsa.org/12060076},
            author = {Alsing, Paul},
            keywords = {},
            language = {en},
            title = {Nonlocality, Entanglement Witnesses and Supra-Correlations},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {jun},
            note = {PIRSA:12060076 see, \url{https://pirsa.org}}

Paul Alsing United States Air Force Research Laboratory


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.