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We provide a new extension of entanglement witnesses for$\mathbb{C}^{d_{1}}\otimes\mathbb{C}^{d_{2}}$ systems. Our constructionpreserves the properties of indecomposability and spanning property ofentanglement witnesses. We show how our concept of extended entanglementwitnesses is connected with the idea of measurement device independententanglement witnesses.

Tensor product extension of entanglement witnesses and their connection with measurement device independent entanglement