Some applications of equiangular tight frames in quantum information

Finite tight frames are interesting in their own rights as well as for applications including quantum information topics. Each complex tight frame leads to a non-orthogonal resolution of the identity in the Hilbert space. In many respects, equiangular tight frames (ETFs) are similar to the maximal sets that provide symmetric informationally complete measurements. Using known ETFs, new ones can be generated via the method related to Naimark's extension. For a measurement assigned to an ETF, the index of coincidence is estimated from above. Hence, several uncertainty relations follow. As is well known, uncertainty relations can lead to some criteria useful in quantum infomation processing. In particular, we consider the use of ETFs to detect entanglement and steerability.