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Journal of Lanzhou University of Technology

Separability criteria for higher-order multimode systems

Fan Kang-kang

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

The separation discrimination conditions of higher-order two-particle multiple mode were derived by using Heisenberg and Schrdinger-Robertson uncertainty relations.After comparing these two uncertainty relations,the entanglement discrimination conditions were obtained.It was found that a stronger separation discrimination condition could be obtained based on the derivation with Schrdinger-Robertson uncertain relation.

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The separation discrimination conditions of higher-order two-particle multiple mode were derived by using Heisenberg and Schrdinger-Robertson uncertainty relations.After comparing these two uncertainty relations,the entanglement discrimination conditions were obtained.It was found that a stronger separation discrimination condition could be obtained based on the derivation with Schrdinger-Robertson uncertain relation.
Compared with the Heisenberg uncertainty relation, Schrodinger-Robertson uncertain relation generally provides stronger bound on product of uncertainties for two noncommutation observables, so the stricter separability condition can be provided by using Schrodinger-Robertson uncertainty relation. In this paper, using the Schrodinger Robertson uncertainty relation, the separability condition previously proposed by L. M. Duan is improved into the stricter separability condition. Then we extend the above ideas to the general two-mode situation and multi-mode terms, some new separation conditions are obtained.
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 stronger separability condition provided by Schrodinger-Robertson uncertainty relation of partially transposed su(1, 1) algebra operators. The obtained inseparability condition is also shown to be a necessary condition for W type entangled states and it is used to derive the general form for a family of such inseparability conditions. An experimental scheme is proposed to test the violation of separability condition. The results derived for three-mode systems are generalized to multimode systems.