Gaussian quantum marginal problem (Q934619)

It is shown that, under large conditions, if \(\rho\) is a Gaussian state of \(n\) modes satisfying some simple conditions on \(sspec(\rho)\), then the possible reduced states \(\rho_{k}\) to each of the individual modes \(k=1,\dots,n\) are also Gaussian states. This property provides a complete characterization of reductions of pure or mixed Gaussian states. The proof of this result is constructive, and by this way could provide new approaches to reductions in multi-mode entangled states.