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We present a simple approach for generation of a diverse set of positive mapsbetween spaces of different dimensions. The proposed method enables theconstruction of Entanglement Witnesses tailored for systems in $d_1 \times d_2$dimensions. With this method, it is possible to construct EntanglementWitnesses that consist solely of a chosen set of desired measurements. Wedemonstrate the effectiveness and generality of our approach using concreteexamples. It is also demonstrated in two examples, how an appropriateentanglement witness can be identified for witnessing the entanglement of agiven state, including a case when the given state is a Positive PartialTranspose (PPT) entangled state.

A simple construction of Entanglement Witnesses for arbitrary and different dimensions