Reconciliation witness and reliability of a quantum atmospheric channel

The reliability of free-space quantum communication is strongly affected by turbulence present in atmospheric channels. The signal is randomly distorted or gets lost due to the fluctuations of atmospheric refractive index. We consider quantum communication with coherent and squeezed states and derive the fidelities for quantum states transmitted through such a free-space channel. We show that the fidelity can be significantly enhanced by postselecting high transmission events at the expense of decreasing transmission bit rate. Next, we introduce the witness function that characterizes the reliability of the reconciliation procedure between the communicating parties. Based on this measure, we suggest the receiver strategy that further improves the reconciliation quality.