Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

Lijun Song, Xiaoguang Wang 2 , Dong Yan 4 , and Yongda Li 1
  • 1 School of Science, Changchun University of Science and Technology, Changchun, 130022, P.R.China
  • 2 Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, HangZhou, 310027, P.R.China
  • 3 Institute of Applied Physics, Changchun University, Changchun, 130022, P.R.China
  • 4 School of Science, Lanzhou University of Technology, Lanzhou, 730050, P.R.China

Abstract

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.

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