  We study the properties of the random quantum states induced from the
uniformly random pure states on a bipartite quantum system by taking the
partial trace over the larger subsystem. Most of the previous studies have
adopted a viewpoint of "concentration of measure" and have focused on the
behavior of the states close to the average. In contrast, we investigate the
large deviation regime, where the states may be far from the average. We prove
the following results: First, the probability that the induced random state is
within a given set decreases no slower or faster than exponential in the
dimension of the subsystem traced out. Second, the exponent is equal to the
quantum relative entropy of the maximally mixed state and the given set,
multiplied by the dimension of the remaining subsystem. Third, the total
probability of a given set strongly concentrates around the element closest to
the maximally mixed state, a property that we call conditional concentration.
Along the same line, we also investigate an asymptotic behavior of coherence of
random pure states in a single system with large dimensions.
