Entanglement criteria for the bosonic and fermionic induced ensembles

@article{Dartois2021EntanglementCF,
  title={Entanglement criteria for the bosonic and fermionic induced ensembles},
  author={St{\'e}phane Dartois and Ion Nechita and Adrian Tanasa},
  journal={Quantum Information Processing},
  year={2021},
  volume={21}
}
We introduce the bosonic and fermionic ensembles of density matrices and study their entanglement. In the fermionic case, we show that random bipartite fermionic density matrices have non-positive partial transposition; hence, they are typically entangled. The similar analysis in the bosonic case is more delicate, due to a large positive outlier eigenvalue. We compute the asymptotic ratio between the size of the environment and the size of the system Hilbert space for which random bipartite… 
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