LAUSR

We study entanglement witnesses (EWs) and construct a linear map by taking two groups of mutually unbiased bases (MUBs) of two Hilbert spaces. We provide two new relations about matrices (may not be square matrices) with properties similar to unitary matrix. Using these two new relations, we obtain a positive map between two different linear spaces of complex matrices. Finally, we calculate a special case by applying our map to get an EW on ℂ 3 ⊗ ℂ 4 $\mathbb {C}^{3}\otimes \mathbb {C}^{4}$ . We also find three entangled states detected by this EW.