Disappearance of entanglement: a topological point of view |
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Authors: | Dong Zhou Robert Joynt |
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Affiliation: | 1. Physics Department, University of Wisconsin-Madison, Madison, WI, 53706, USA
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Abstract: | We give a topological classification of the evolution of entanglement, particularly the different ways the entanglement can
disappear as a function of time. Four categories exhaust all possibilities given the initial quantum state is entangled and
the final one is not. Exponential decay of entanglement, entanglement sudden death and sudden birth can all be understood
and visualized in the associated geometrical picture - the polarization vector representation. The entanglement evolution
categories of any model are determined by the topology of the state space and the dynamical subspace, the limiting state and
the memory effect of the environment. Transitions between these types of behaviors as a function of physical parameters are
also possible. These transitions are thus of topological nature. The symmetry of the system is also important, since it determines
the dimension of the dynamical subspace. We illustrate the general concepts with a visualizable model for two qubits, and
give results for extensions to N-qubit GHZ states and W states. |
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