In this paper we examine the average R\'{e}nyi entropy Sα of a
subsystem A when the whole composite system AB is a random pure state. We
assume that the Hilbert space dimensions of A and AB are m and mn
respectively. First, we compute the average R\'{e}nyi entropy analytically for
m=α=2. We compare this analytical result with the approximate
average R\'{e}nyi entropy, which is shown to be very close. For general case we
compute the average of the approximate R\'{e}nyi entropy
Sα(m,n) analytically. When 1≪n,
Sα(m,n) reduces to lnm−2nα(m−m−1), which is in agreement with the asymptotic expression of the average
von Neumann entropy. Based on the analytic result of Sα(m,n) we plot the lnm-dependence of the quantum information derived from
Sα(m,n). It is remarkable to note that the nearly
vanishing region of the information becomes shorten with increasing α,
and eventually disappears in the limit of α→∞. The
physical implication of the result is briefly discussed.Comment: 14 pages, 3 figure