Fig. 1. Sketch of the experiment. (a) Schematic of the scenarios that have already been practically useful. (b) Experimental setup and real field-test environment. The marine test platform is the biggest multiple function towing tank in Asia, with the length of 300 m, the width of 16 m, and the depth of 7.5 m. The platform space is actually semiopen in terms of background noises, because there are many windows and they cannot be blocked. Six polarization states for testing are marked on Bloch sphere. SMF, single-mode fiber; PBS, polarization beam splitter; HWP, half-wave plate; QWP, quarter-wave plate; MMF, multimode fiber; AM, amplitude modulator; SF, spatial filter.

Fig. 2. Experimental results of polarization correlations between the sent and received states. Four curves in chart are obtained by projecting the initial states, |H⟩, |V⟩, |D⟩, and |A⟩ at different polarization angles at the receiving terminal. Error bars are too small to be visible.

Fig. 3. Experimental results of underwater transmission of photonic polarization states up to 55 m. (a) The measured density matrices of the received polarization states are presented together with the states marked on Bloch sphere. (b) The fidelities were obtained by quantum state tomography. All the fidelities are over 0.95, and the average fidelity is 0.976. (c) The purities were obtained by quantum state tomography. The average purity is 0.942. The error bars are too small to be visible in the histograms.

Fig. 4. Experimental results of quantum process tomography for the 55-m-long underwater channel. The measured χwater matrix in bases of E˜0=I, E˜1=X, E˜2=Y, E˜3=Z. The modulus and argument of the process matrix elements are represented by the height and color of the bars, respectively. The fidelity between the matrix χwater and χideal is 0.96.