dorsal/arxiv
View SchemaSemiclassical time-evolution of the reduced density matrix and dynamically assisted generation of entanglement for bipartite quantum systems
| Authors | Philippe Jacquod |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0308099 |
| URL | https://arxiv.org/abs/quant-ph/0308099 |
| DOI | 10.1103/PhysRevLett.92.150403 |
| Journal | Phys. Rev. Lett. 92, 150403 (2004) |
Abstract
Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix $\rho_1$, obtained by integrating out the degrees of freedom of one of the particles. To quantify the generation of entanglement, we calculate the purity ${\cal P}(t)={\rm Tr}[\rho_1(t)^2]$. We find that entanglement generation sensitively depends (i) on the interaction potential, especially on its strength and range, and (ii) on the nature of the underlying classical dynamics. Under general statistical assumptions, and for short-scaled interaction potentials, we find that ${\cal P}(t)$ decays exponentially fast if the two particles are required to interact in a chaotic environment, whereas it decays only algebraically in a regular system. In the chaotic case, the decay rate is given by the golden rule spreading of one-particle states due to the two-particle coupling, but cannot exceed the system's Lyapunov exponent.
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"abstract": "Two particles, initially in a product state, become entangled when they come\ntogether and start to interact. Using semiclassical methods, we calculate the\ntime evolution of the corresponding reduced density matrix $\\rho_1$, obtained\nby integrating out the degrees of freedom of one of the particles. To quantify\nthe generation of entanglement, we calculate the purity ${\\cal P}(t)={\\rm\nTr}[\\rho_1(t)^2]$. We find that entanglement generation sensitively depends (i)\non the interaction potential, especially on its strength and range, and (ii) on\nthe nature of the underlying classical dynamics. Under general statistical\nassumptions, and for short-scaled interaction potentials, we find that ${\\cal\nP}(t)$ decays exponentially fast if the two particles are required to interact\nin a chaotic environment, whereas it decays only algebraically in a regular\nsystem. In the chaotic case, the decay rate is given by the golden rule\nspreading of one-particle states due to the two-particle coupling, but cannot\nexceed the system\u0027s Lyapunov exponent.",
"arxiv_id": "quant-ph/0308099",
"authors": [
"Philippe Jacquod"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"nlin.CD"
],
"doi": "10.1103/PhysRevLett.92.150403",
"journal_ref": "Phys. Rev. Lett. 92, 150403 (2004)",
"title": "Semiclassical time-evolution of the reduced density matrix and dynamically assisted generation of entanglement for bipartite quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0308099"
},
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