Entanglement criteria for the bosonic and fermionic induced ensembles
- URL: http://arxiv.org/abs/2111.05638v1
- Date: Wed, 10 Nov 2021 11:10:11 GMT
- Title: Entanglement criteria for the bosonic and fermionic induced ensembles
- Authors: Stephane Dartois, Ion Nechita and Adrian Tanasa
- Abstract summary: 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.
- Score: 1.2891210250935143
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 bosonic density matrices fail the PPT
criterion, being thus entangled. We also relate moment computations for
tensor-symmetric random matrices to evaluations of the circuit-counting and
interlace graph polynomials for directed graphs.
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