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Abstract
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We propose an experimentally feasible criterion for the detection of entanglement
in an arbitrary four-partite quantum system. It is written as local sum uncertainty relations
for suitably chosen observables of the subsystems. The relations are satisfied by all separable
states so that their violation implies the presence of the entanglement. This criterion
generalizes the tighter criterion for tripartite systems introduced in our previous work (Y.
Akbari-Kourbolagh and M. Azhdargalam, Phys. Rev. A 97, 2018) to the four-partite cases.
It can be used to detect the entanglement of both discrete- and continuous-variable quantum
states without having to know their complete density matrices. Moreover, in contrast to the
well-established positive partial transpose criterion, it is also able to detect bound entangled
states. Its efficiency is shown by the examples of four-qubit and Gaussian four-mode states.
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