Back to Search
Start Over
Entanglement criteria for the bosonic and fermionic induced ensembles
- Source :
- Quant.Inf.Proc., Quant.Inf.Proc., 2022, 21 (11), pp.376. ⟨10.1007/s11128-022-03690-8⟩
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
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.<br />Comment: 37 pages, numerous figures and diagrammatics equations
- Subjects :
- Condensed Matter::Quantum Gases
Quantum Physics
random
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
Probability (math.PR)
matrix model
Hilbert space
FOS: Physical sciences
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Theoretical Computer Science
Electronic, Optical and Magnetic Materials
moment
[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]
Modeling and Simulation
Signal Processing
FOS: Mathematics
Mathematics - Combinatorics
Combinatorics (math.CO)
Electrical and Electronic Engineering
entanglement
Quantum Physics (quant-ph)
density matrix
Mathematical Physics
Mathematics - Probability
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Quant.Inf.Proc., Quant.Inf.Proc., 2022, 21 (11), pp.376. ⟨10.1007/s11128-022-03690-8⟩
- Accession number :
- edsair.doi.dedup.....3cfdb8ba1996e7173430750f2aee33a0
- Full Text :
- https://doi.org/10.48550/arxiv.2111.05638