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We study the scaling properties of the conductance fluctuations due to quantum interference in linear quantum-dot arrays. The key finding of our study is of a common scaling behaviour of the fluctuations, according to which their amplitude varies in direct proportion to the total conductance of the system, independently of the size of the arrays. We argue that such behaviour is inconsistent with a classical scaling of incoherently coupled dots, but is reasonable for that expected when dephasing arises from the interaction of the quantum system with its external environment.