Towards Quantum Communication in Free-Space Seawater

Long-distance quantum channels capable of transferring quantum states faithfully for unconditionally secure quantum communication have been so far confirmed feasible in both fiber and free-space air. However, it remains unclear whether seawater, which covers more than 70% of the earth, can also be utilized, leaving global quantum communication incomplete. Here we experimentally demonstrate that polarization quantum states including general qubits and entangled states can well survive after travelling through seawater. We performed experiments in a 3.3-meter-long tube filled with seawater samples collected in a range of 36 kilometers in Yellow sea, which conforms to Jerlov water type I. For single photons at 405 nm in blue-green window, we obtained average process fidelity above 98%. For entangled photons at 810 nm, even with high loss, we observe violation of Bell inequality with 33 standard deviations. This work confirms feasibility of seawater quantum channel, representing the first step towards underwater quantum communication.

seawater quantum channel, we experimentally explore polarization preservation properties of single photon and quantum entanglement.
As shown in Fig.1, Our seawater samples were collected from the surface of costal sea in the zone between Dalian city and Zhangzi island. Six sampling sites are several kilometers apart from one another. The distance between site I and VI is up to 36 kilometers. Investigations in such a large scale would ensure generalizability of our experimental results. A schematic layout of the experimental setup is shown in Fig. 2 (Table 1).
Besides the loss associated with maximum secure distance, it is more important to find a desirable degree of freedom of photon with which quantum states can be encoded and transferred with high fidelity, i.e. without significant degrade induced by seawater. As water is a uniform isotropic medium, it is very likely that seawater, though incorporating dissolved salts and microbes, does not lead to massive polarization rotation or depolarization of photon. Multi random scattering on suspended particulate matter can introduce depolarization accompanying with transverse angle diffusion 23 . However, we can spatially filter the depolarized photons with small receiving angle defined by optical fiber.
We prepare single photons by driving the semiconductor laser to 2-ns pulse with a repetition rate of 50 MHz and strongly attenuating it to 0.3~0.6 photon per pulse typically adopted in decoy state protocols 24,25,26 . We encode single photons with six initial input where H and V represent horizontal and vertical polarization. After going through seawater, we project each output state on these three sets of orthogonal basis (Fig. 2a). We employ quantum state tomography 27 method to reconstruct the density matrixes of output states with the counts of avalanche photodiode detectors APD1 and APD2. By making coincidence with synchronization signal of laser pulse from photodiode, we suppress noisy counts including background count and dark count of avalanche photodiode detectors from 500 cps to 150 cps, when the coincidence window of FPGA is 3.5 ns. Fig. 2b shows fidelities of receiving states for six initial states in six seawater samples, distilled water and air (empty tube), see their average value in Table 1. We can see that fidelities are all above 98%, which far exceed the classical limit 2/3 28 . As an example, Fig. 2c shows density matrix of six receiving states through seawater sample VI.
To reveal physical processes of seawater quantum channel, we employ quantum process tomography 29 , which can provide complete information of the channel changing arbitrary input state into another state. Any quantum process can be written as Once the set of operators m A are fixed, the density matrix of process mn χ can detail the dynamics of the system. We measure mn χ with each sample and air. We derive the process fidelities as In spite of attenuation difference, we obtain high process fidelities in all seawater samples as well as distilled water (see Table 1).
Quantum entanglement is the main resource for quantum communication. The randomness and correlations inherent in quantum entanglement can be exploited to enable entanglement-based quantum cryptography 2 , quantum teleportation 3 , quantum repeater 30 and distributed quantum computing 31 . It is therefore of practical interest to see whether entanglement can be preserved in seawater channel. Furthermore, since the polarization state of entangled photons is completely uncertainty before detection, the survival of entanglement will reveal that seawater channel allow faithful transmission of arbitrary unknown polarization states, consistent with the result of high process fidelity of seawater channel.
In Fig. 3a, polarization entangled photon-pair source at 810 nm is generated by a blue laser beam (power 11mw, wavelength 405nm) pumping a quasi-phase matched periodically-poled KTiOPO 4 (PPKTP) crystal with type II spontaneous parametric down conversion 32 . The source is prepared as the singlet state where the subscripts A and B label the spatial modes. Locally we obtain more than 300k cps in each path, and 55k cps coincidence events. Photon B is sent through the glass tube connected by a 3-meter-long single mode fiber. We analyze photon A locally and photon B at the receiving site with state tomography.

Methods
Loss budget and measurement. Loss caused by seawater could not be measured directly because of additional loss of optical devices and possible fluctuation of the laser's power.
We use a reference beam to remove the influence. Reference beam and signal beam are divided by a polarization beam splitter and for every sample the splitting ratio is constant.
Real loss induced by seawater can be derived by subtract the value of empty tube out of full tube. Differential reflection at glass-seawater and glass-air interface must be taken into account, which can be figured out by Fresnel formula.
where i 1 ( i 2 ) is incident angle (transmission angle). Refractive index of medium can influence the transmission of light. n air = 1 , n water = 1.34 ( T C = 20 ! C , λ = 405nm )， n BK 7 = 1.5302(λ = 405nm) . Seawater water is a complex system, whose refractive index is related to its salinity, temperature and the incident light wavelength 40 , which can be written as Assuming that the intensity of reference beam is a 1 (b 1 ) and the intensity of output signal beam is a 2 (b 2 ) , corresponding to the condition empty tube (full tube), we can obtain attenuation coefficient by The attenuation coefficient of Jerlov type I coastal water is To eliminate differential loss and detection efficiency, we correct the counts by . By using the same method, we can get η DA = C D1 C A1 C D2 C A2 , Beam wandering in seawater. In the experiment, single count of detector present slow and quasi-periodical variation. We attribute this to the beam wandering associated with decoupling to optical fiber. Ambient condition change including mechanical vibration, temperature fluctuation and varying salinity may result in variational and inhomogenous refractive index distribution along propagating direction of the beam. According to the data collected in sample VI, the counts of two detectors present nearly synchronous variation. Such beam wandering issue, though in a faster speed, also exists as a main problem to solve in free-space quantum communication. It suggests that the active feedback system adopted in free-space air should also be applied to free-space seawater.      cases appear to be highly entangled in polarization, which demonstrate entanglement can well preserved in seawater. This complements the evidence of high process fidelities provided by Fig. 2 and Table 1.