  The density matrix formalism is a fundamental tool in studying various
problems in quantum information processing. In the space of density matrices,
the most well-known and physically relevant measures are the Hilbert-Schmidt
ensemble and the Bures-Hall ensemble. In this work, we propose a generalized
ensemble of density matrices, termed quantum interpolating ensemble, which is
able to interpolate between these two seemingly unrelated ensembles. As a first
step to understand the proposed ensemble, we derive the exact mean formulas of
entanglement entropies over such an ensemble generalizing several recent
results in the literature. We also derive some key properties of the
corresponding orthogonal polynomials relevant to obtaining other statistical
information of the entropies. Numerical results demonstrate the usefulness of
the proposed ensemble in estimating the degree of entanglement of quantum
states.
