  It is well-known in classical frame theory that overcomplete representations
of a given vector space provide robustness to additive noise on the frame
coefficients of an unknown vector. We describe how the same robustness can be
shown to exist in the context of quantum state estimation. A key element of the
discussion is the application of classical frame theory to operator-valued
vector spaces, or operator spaces, which arise naturally in quantum mechanics.
Specifically, in the problem we describe the frame vectors are represented by
the elements of an informationally complete or overcomplete (IC or IOC) POVM,
the frame coefficients are represented by the outcome probabilities of a
quantum measurement made on an unknown state, and the error on the frame
coefficients arises from finite sample size estimations of the probabilities.
We show that with this formulation of the problem, there is a tradeoff in
estimation performance between the number of copies of the unknown system and
the number of POVM elements. Lastly, we present evidence through simulation
that the same tradeoff is present in the context of quantum binary state
detection -- the probability of error can be reduced either by increasing the
number of copies of the unknown system or by increasing the number of POVM
elements.
