Average fidelity in n-qubit systems

This Letter generalizes the expression for the average fidelity of single qubits, as found by Bowdrey et al. [M.D. Bowdrey, D.K.L. Oi, A.J. Short, K. Banaszek, J.A. Jones, Phys. Lett. A 294 (2002) 258], to the case of n qubits. We use a simple algebraic approach with basis elements for the density-matrix expansion expressed as Kronecker products of n Pauli spin matrices. An explicit integration over initial states is avoided by invoking the invariance of the state average under unitary transformations of the initial density matrix. The results have applications to measurements of quantum information, for example in ion-trap and NMR experiments.