Bounds on quantum process fidelity from minimum required number of quantum state fidelity measurements

摘要

To certify that an experimentally implemented quantum transformation is acertain unitary operation U on a d-dimensional Hilbert space, it suffices todetermine fidelities of output states for d+1 suitably chosen pure input states[Reich et al., Phys. Rev. A 88, 042309 (2013)]. The set of these d+1 probestates can consist of d orthogonal states that form a basis and one additionalstate which is a balanced superposition of all d basis states. Here we providean analytical lower bound on quantum process fidelity for two-qubit quantumgates which results from the knowledge of average state fidelity for the basisstates and the fidelity of the superposition state. We compare this bound withthe Hofmann bound that is based on knowledge of average state fidelities fortwo mutually unbiased bases. We also discuss possible extension of our findingsto N-qubit operations.