Semiclassical Time Evolution of the Reduced Density Matrix and Dynamically Assisted Generation of Entanglement for Bipartite Quantum Systems
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 ρ_{1}, obtained by integrating out the degrees of freedom of one of the particles. 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 shortranged interaction potentials, we find that P(t) decays exponentially fast 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 oneparticle states due to the twoparticle coupling, but cannot exceed the system's Lyapunov exponent.
 Publication:

Physical Review Letters
 Pub Date:
 April 2004
 DOI:
 10.1103/PhysRevLett.92.150403
 arXiv:
 arXiv:quantph/0308099
 Bibcode:
 2004PhRvL..92o0403J
 Keywords:

 03.65.Ud;
 03.67.Mn;
 05.45.Mt;
 05.70.Ln;
 Entanglement and quantum nonlocality;
 Entanglement production characterization and manipulation;
 Quantum chaos;
 semiclassical methods;
 Nonequilibrium and irreversible thermodynamics;
 Quantum Physics;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 Final version, to appear in Physical Review Letters