Disappearance of entanglement: a topological point of view

Disappearance of entanglement: a topological point of view 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Disappearance of entanglement: a topological point of view

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Publisher
Springer US
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Physics; Physics, general; Theoretical, Mathematical and Computational Physics; Quantum Physics; Computer Science, general; Mathematics, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0272-8
Publisher site
See Article on Publisher Site

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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 2, 2011

References

  • Quantum entanglement
    Horodecki, R.; Horodecki, P.; Horodecki, M.; Horodecki, K.
  • Disentanglement and decoherence from classical non-Markovian noise: random telegraph noise
    Zhou, D.; Lang, A.; Joynt, R.
  • Environment-induced sudden death of entanglement
    Almeida, M.P.; Melo, F.; Hor-Meyll, M.; Salles, A.; Walborn, S.P.; Ribeiro, P.H.S.; Davidovich, L.
  • The bloch vector for n-level systems
    Kimura, G.

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