We study the quantum separability problem by using general symmetric informationally complete measurements and present a separability criterion for arbitrary dimensional bipartite systems. We show by detailed examples that our criterion is more powerful than the existing ones in entanglement detection.

Unambiguous state discrimination of two mixed bipartite states via local operations and classical communications (LOCC) is studied and compared with the result of a scheme realized via global measurement. We show that the success probability of a global scheme for mixed-state discrimination can be achieved perfectly by the local scheme. In addition, we simulate this discrimination via a pair of pure entangled bipartite states. This simulation is perfect for local rather than global schemes due to the existence of entanglement and global coherence in the pure states. We also prove that LOCC protocol and the sequential state discrimination (SSD) can be interpreted in a unified view. We then hybridize the LOCC protocol with three protocols (SSD, reproducing and broadcasting) relying on classical communications. Such hybridizations extend the gaps between the optimal success probability of global and local schemes, which can be eliminated only for the SSD rather than the other two protocols.

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We study entanglement witness and present a construction of entanglement witnesses in terms of the mutually unbiased measurements (MUMs). These witnesses include the entanglement witnesses constructed from mutually unbiased bases (MUBs) as a special case. Comparing with the dimension dependence of MUBs, the witnesses can be always constructed from a complete set of d + 1 MUMs for any dimension d. We show that our witness can detect entanglement better than previous separability criterion given also by MUMs. And the approach can be experimentally implemented. *