# 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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