Asymptotic Entanglement Dynamics and Geometry of Quantum States

Abstract

A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, like entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A classification of the possible situations was given in [M. O. Terra Cunha, {\emph{New J. Phys}} {\bf{9}}, 237 (2007)] but for some classes there were no known examples. In this work we give a better classification for the possibile relaxing dynamics at the light of the geometry of their set of asymptotic states and give explicit examples for all the classes. Although the classification is completely general, in the search of examples it is sufficient to use two qubits with dynamics given by differential equations in Lindblad form (some of them non-autonomous). We also investigate, in each case, the probabilities to find each possible behavior for random initial states.

9 pages, 2 figures; revised version accepted for publication in J. Phys. A: Math. Theor

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• A statistical portrait of the entanglement decay of two-qubit memories
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• Disappearance of entanglement: a topological point of view
• Asymptotic Entanglement Dynamics Phase Diagrams for Two Electromagnetic Field Modes in a Cavity
• Some features of the state-space trajectories followed by robust entangled four-qubit states during decoherence
• Entanglement sudden-death time: a geometric quantity
• Universality of finite time disentanglement