  The problem of quantum state discrimination, which is a foundational aspect
of quantum information theory, and its relation to the theory of majorization
are discussed. The purpose of this study is to review different approaches to
the problem and analyze different cases of quantum-state discrimination, most
importantly the discrimination of bipartite entangled quantum states under
local operations and classical communication. Two partial results on using
entanglement as a resource for quantum-state discrimination and discrimination
with remaining entanglement is given. The important points are also summarized
and the results are discussed.
