Gaussian Quantum Marginal Problem

@article{Eisert2008GaussianQM,
  title={Gaussian Quantum Marginal Problem},
  author={Jens Eisert and Tom{\'a}{\vs} Tyc and Terry Rudolph and Barry C. Sanders},
  journal={Communications in Mathematical Physics},
  year={2008},
  volume={280},
  pages={263-280}
}
The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our… 
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