1,157 research outputs found
Non-closure of quantum correlation matrices and factorizable channels that require infinite dimensional ancilla
We show that there exist factorizable quantum channels in each dimension which do not admit a factorization through any finite dimensional von
Neumann algebra, and do require ancillas of type II, thus witnessing new
infinite-dimensional phenomena in quantum information theory. We show that the
set of n by n matrices of correlations arising as second-order moments of
projections in finite dimensional von Neumann algebras with a distinguished
trace is non-closed, for all , and we use this to give a simplified
proof of the recent result of Dykema, Paulsen and Prakash that the set of
synchronous quantum correlations is non-closed. Using a trick
originating in work of Regev, Slofstra and Vidick, we further show that the set
of correlation matrices arising from second-order moments of unitaries in
finite dimensional von Neumann algebras with a distinguished trace is
non-closed in each dimension , from which we derive the first result
above.Comment: 16 pages. An appendix by Narutaka Ozawa has been added. To appear in
Comm. Math. Phy
Working the Field: Rural Experts and the ‘Agrarian Question’ in the Romanian Principalities 1864-1914
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