  We investigate the performance of a Kennedy receiver, which is known as a
beneficial tool in optical coherent communications, to the quantum state
discrimination of the two superpositions of vacuum and single photon states
corresponding to the $\hat\sigma_x$ eigenstates in the single-rail encoding of
photonic qubits. We experimentally characterize the Kennedy receiver in
vacuum-single photon two-dimensional space using quantum detector tomography
and evaluate the achievable discrimination error probability from the
reconstructed measurement operators. We furthermore derive the minimum error
rate obtainable with Gaussian transformations and homodyne detection. Our proof
of principle experiment shows that the Kennedy receiver can achieve a
discrimination error surpassing homodyne detection.
