Experimental Lower Bounds to the Classical Capacity of Quantum Channels

We show an experimental procedure to certify the classical capacity for noisy qubit channels. The method makes use of a fixed bipartite entangled state, where the system qubit is sent to the channel input and the set of local measurements $\sigma_{x}\otimes\sigma_{x}$, $\sigma_{y}\otimes\sigma_{y}$ and $\sigma_{z}\otimes\sigma_{z}$ is performed at the channel output and the ancilla qubit, thus without resorting to full quantum process tomography. The witness to the classical capacity is achieved by reconstructing sets of conditional probabilities, noise deconvolution, and classical optimisation of the pertaining mutual information. The performance of the method to provide lower bounds to the classical capacity is tested by a two-photon polarization entangled state in Pauli channels and amplitude damping channels. The measured lower bounds to the channels are in high agreement with the simulated data, which take into account both the experimental entanglement fidelity $F=0.979\pm 0.011$ of the input state and the systematic experimental imperfections.