Entanglement condition for W type multimode states and schemes for experimental realization

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Vol. 73; no. 6; pp. 1 - 7
• Main Authors: Selvan, Karthick, Panigrahi, Prasanta K.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019; Springer Nature B.V
• Subjects: Algebra; Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Beam splitters; Electromagnetic fields; Entangled states; Molecular; Operators (mathematics); Optical and Plasma Physics; Physical Chemistry; Physics; Physics and Astronomy; Quantum entanglement; Quantum Information Technology; Quantum Physics; Regular Article; Spectroscopy/Spectrometry; Spintronics; Uncertainty; Quantum Information
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2019-100012-7

We derive a class of inequality relations, using both the sum uncertainty relations of su (2) algebra operators and the Schrodinger–Robertson uncertainty relation of partially transposed su (1,1) algebra operators, to detect the three-mode entanglement of non-Gaussian states of electromagnetic field. These operators are quadratic in mode creation and annihilation operators. The inseparability condition obtained using su (2) algebra operators is shown to guarantee the violation of Schrodinger–Robertson uncertainty relation of partially transposed su (1,1) algebra operators. The obtained inseparability condition incorporates all the required bipartite entanglement conditions to detect the W type three-mode entangled states and hence it is shown to be a necessary condition for W type three-mode entangled states. A general form for a family of such inseparability conditions is provided. The results derived for three-mode systems are generalized to multimode systems. Experimental schemes using symmetric multiport beam splitters and multi-Λ EIT system are proposed to test the violation of multimode separability condition. Graphical abstract