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Keywords
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Entanglement criterion, Uncertainty relation, Three-qubit state,
Three-mode Gaussian state, Bound entangled state.
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Abstract
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We propose a sufficient criterion for the entanglement of tripartite systems based on local sum uncertainty
relations for arbitrarily chosen observables of subsystems. This criterion generalizes the tighter criterion for
bipartite systems introduced by Zhang et al. [C.-J. Zhang, H. Nha, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 81,
012324 (2010)] and can be used for both discrete- and continuous-variable systems. It enables us to detect the
entanglement of quantum states without having a complete knowledge of them. Its utility is illustrated by some
examples of three-qubit, qutrit-qutrit-qubit, and three-mode Gaussian states. It is found that, in comparison with
other criteria, this criterion is able to detect some three-qubit bound entangled states more efficiently.
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