Geometric measure of quantum discord for a two-parameter class of states in a qubit–qutrit system under various dissipative channels

Geometric measure of quantum discord for a two-parameter class of states in a qubit–qutrit... Quantum discord, as a measure of all quantum correlations, has been proposed as the key resource in certain quantum communication tasks and quantum computational models without containing much entanglement. Dakić et al. (Phys Rev Lett 105:190502, 2010) introduced a geometric measure of quantum discord (GMQD) and derived an explicit formula for any two-qubit state. Luo and Fu (Phys Rev A 82:034302, 2010) introduced another form of GMQD and derived an explicit formula for arbitrary state in a bipartite quantum system. However, the explicit analytical expression for any bipartite system was not given. In this work, we give out the explicit analytical expressions of the GMQD for a two-parameter class of states in a qubit–qutrit system and study its dynamics for the states under various dissipative channels in the first time. Our results show that all these dynamic evolutions do not lead to a sudden vanishing of GMQD. Quantum correlations vanish at an asymptotic time for local or multi-local dephasing, phase-flip, and depolarizing noise channels. However, it does not disappear even though t → ∞ for local trit-flip and local trit-phase-flip channels. Our results maybe provide some important information for the application of GMQD in hybrid qubit–qutrit systems in quantum information. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Geometric measure of quantum discord for a two-parameter class of states in a qubit–qutrit system under various dissipative channels

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Publisher
Springer US
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-012-0458-8
Publisher site
See Article on Publisher Site

Abstract

Quantum discord, as a measure of all quantum correlations, has been proposed as the key resource in certain quantum communication tasks and quantum computational models without containing much entanglement. Dakić et al. (Phys Rev Lett 105:190502, 2010) introduced a geometric measure of quantum discord (GMQD) and derived an explicit formula for any two-qubit state. Luo and Fu (Phys Rev A 82:034302, 2010) introduced another form of GMQD and derived an explicit formula for arbitrary state in a bipartite quantum system. However, the explicit analytical expression for any bipartite system was not given. In this work, we give out the explicit analytical expressions of the GMQD for a two-parameter class of states in a qubit–qutrit system and study its dynamics for the states under various dissipative channels in the first time. Our results show that all these dynamic evolutions do not lead to a sudden vanishing of GMQD. Quantum correlations vanish at an asymptotic time for local or multi-local dephasing, phase-flip, and depolarizing noise channels. However, it does not disappear even though t → ∞ for local trit-flip and local trit-phase-flip channels. Our results maybe provide some important information for the application of GMQD in hybrid qubit–qutrit systems in quantum information.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 29, 2012

References

  • Geometric measure of quantum discord
    Luo, S.L.; Fu, S.S.
  • Entanglement sudden death in qubit–qutrit systems
    Ann, K.; Jaeger, G.
  • Correlation dynamics of qubit–qutrit systems in a classical dephasing environment
    Karpat, G.; Gedik, Z.

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