We prove that to store n bits x so that each
prefix-sum query Sum(i) := sum_{k < i} x_k can be answered
by non-adaptively probing q cells of log n bits, one needs
memory > n + n/log^{O(q)} n.

Our bound matches a recent upper bound of n +
n/log^{Omega(q)} n by Patrascu (FOCS 2008), also
non-adaptive.

We also obtain a n + n/log^{2^{O(q)}} n lower bound for
storing a string of balanced brackets so that each
Match(i) query can be answered by non-adaptively probing q
cells. To obtain these bounds we show that a too efficient
data structure allows us to break the correlations between
query answers.