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The Uhlmann-Jozsa fidelity (or, equivalently, the Bures distance) is a basicconcept of quantum communication and quantum information, which however is verydifficult to measure efficiently without recourse to quantum tomography. Herewe propose a direct experimental method to estimate the fidelity between twounknown two-qubit mixed states via the measurement of the upper and lowerbounds of the fidelity, which are referred to as the superfidelity andsubfidelity, respectively. Our method enables a direct measurement of thefirst- and second-order overlaps between two arbitrary two-qubit states. Inparticular, the method can be applied to measure the purity (or linear entropy)of a single two-qubit mixed state in a direct experiment. We also propose andcritically compare several experimental strategies for measuring the sub- andsuperfidelities of polarization states of photons in various linear-opticalsetups.

Direct method for measuring of purity, superfidelity, and subfidelity of photonic two-qubit mixed states