Average fidelity between random quantum states

Abstract

We analyze mean fidelity between random density matrices of size $N$, generated with respect to various probability measures in the space of mixed quantum states: the Hilbert-Schmidt measure, the Bures (statistical) measure, the measure induced by the partial trace, and the natural measure on the space of pure states. In certain cases explicit probability distributions for the fidelity are derived. The results obtained may be used to gauge the quality of quantum-information-processing schemes.