Geometric measure of quantum discord under decoherence

  • Authors:

  • Xiao-Ming Lu;Zhengjun Xi;Zhe Sun;Xiaoguang Wang

  • Affiliations:

  • Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, China;Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, China and College of Computer Science, Shaanxi Normal University, Xi'an, China;Department of Physics, Hangzhou Normal University, Hangzhou, China;Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, China

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2010

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Abstract

The dynamics of a geometric measure of the quantum discord (GMQD) under decoher-ence is investigated. We show that the GMQD of a two-qubit state can be alternativelyobtained through the singular values of a 3times;4 matrix whose elements are the expectationvalues of Pauli matrices of the two qubits. By using Heisenberg picture, the analyticresults of the GMQD is obtained for three typical kinds of the quantum decoherencechannels. We compare the dynamics of the GMQD with that of the quantum discordand of entanglement. We show that a sudden change in the decay rate of the GMQD doesnot always imply that of the quantum discord, and vice versa. We also give a generalanalysis on the sudden change in behavior and find that at least for the Bell diagonalstates, the sudden changes in decay rates of the GMQD and that of the quantum discordoccur simultaneously.