Abstract

Quantum communication has been rapidly developed due to its unconditional security and successfully implemented through optical fibers and free-space air in experiments. To build a complete quantum communication network involving satellites in space and submersibles in ocean, the underwater quantum channel has been investigated in both theory and experiment. However, the question of whether the polarization encoded qubit can survive through a long-distance and high-loss underwater channel, which is considered as the restricted area for satellite-borne radio waves, still remains. Here, we experimentally demonstrate the transmission of blue-green photonic polarization states through 55-m-long water. We prepare six universal quantum states at the single photon level and observe their faithful transmission in a large marine test platform. We obtain complete information of the channel by quantum process tomography. The distance demonstrated in this work reaches a region allowing potential real applications, representing a step further towards air-to-sea quantum communication.

© 2019 Chinese Laser Press

1. INTRODUCTION

Since the BB84 protocol was proposed by Bennett and Brassard, various protocols and methods have appeared to promote the communication efficiency and increase the secure distance of quantum key distribution (QKD) [18]. So far, the distance of quantum communication through optical fiber has reached an order of several hundred kilometers [913], which is applicable for intercity secure communication [1416]. For the situations without an established fiber link, free-space air has been exploited as a new quantum channel [5,1719]. From the first 32-cm demonstration in the laboratory to today’s quantum satellite, the achieved distance through free-space air has been increased to 1200 km [4,2025].

Meanwhile, the free-space quantum communication in a water environment that covers over 70% of the Earth’s area, has attracted much attention for its indispensable role in constructing the global quantum communication network [2628]. In the recent experiment in seawater [27], the transmission of polarization-encoded quantum states and quantum entanglement has been demonstrated in a 3.3-m-long pipe filled with seawater. The obtained high fidelities suggest that underwater quantum communication with photonic polarization is feasible and promising. Very recently, a QKD experiment with photonic orbital angular momentum was performed through a 3-m underwater channel, and the effect of turbulence on transmitted error rates was explored [28].

However, it is still unclear what will happen if single-photon tests go to longer distance and larger tolerance. The theoretically achievable secure communication distances in different single-photon scattering models are not consistent with one another [26,27]. Besides the fundamental interest of verifying theoretical models, it is also very demanding to push the single-photon test into an entirely new region, for boosting applications in special and ultimate scenarios.

For instance, the frequency band of radio waves emitted by communication satellites ranges from 300 MHz to 300 GHz, which can only penetrate the seawater for no more than several meters. Therefore, it is of great importance to experimentally demonstrate an underwater transmission of single-photon states beyond several meters, which may provide a solution of air-to-sea secure communication for submersibles located in the open sea.

2. RESULT

Here, we experimentally demonstrate the underwater transmission of blue-green photonic polarization states in a large marine test platform up to 55 m long, as is shown in Fig. 1(a), which reaches a distance being able to promise practical quantum communication connecting satellites (or aircraft) and submersibles.

 figure: Fig. 1.

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.

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As is shown in Fig. 1(b), our experiment is performed in a marine test platform. The platform space is semiopen with many windows connecting the internal and external environments. The sender and the receiver systems are located on the same side of the water. Photons from the sender system are steered into water by a wireless-controlled cradle head and are guided back into free-space air and finally into the receiver system. The whole link consists of two air-water interfaces and a 55-m-long underwater channel.

The priority in our experiment is to determine the wavelength of photons. There is a blue-green band of 400–450 nm of which light suffers less attenuation in water [29]. On the one hand, the light at 450 nm possesses the highest transmission rate in pure seawater, but the commercially available silicon avalanche photodiode (APD) is rather inefficient at short wavelength, especially in UV-blue band. On the other hand, the light at longer wavelength has a higher transmission rate in eutrophic water (typically in the Pacific Ocean) than oligotrophic water (typically in the Atlantic Ocean). In view of the trade-off above, we eventually choose the wavelength of 532 nm for our experimental test.

We employ two laser systems at the sending terminal as the signal and the beacon individually, as shown in Fig. 1(b). We use a 532 nm continuous laser with a tunable power range of 0–100 mW as the source of the signal light. With an amplitude modulator, we attenuate the laser to the single-photon level with an intensity required by standard decoy-state protocol. The output power is as low as 1.377×1010W. In addition, a high-power beacon light with a power up to 10 W is used here for the task of underwater alignment. The two lasers are both coupled into a single mode fiber to guarantee a good spatial overlap; meanwhile, they are switchable with a flip mirror.

There are many difficulties for alignment at 1.5-m-deep in an underwater environment. Besides the precise pointing control with cradle head and mirrors, we build a two-lens telescope to expand the light beam to increase its Rayleigh length for better stability and transmission efficiency. The diameters of the lens are 150 mm (f=500mm) and 25 mm (f=50mm), respectively. The diameter of the collimated beam is about 2 mm at the receiving terminal. We use a combination of HWP and QWP to compensate polarization rotation induced by the fiber and the other linear optical devices. The received photons are finally projected on a PBS before being coupled into multimode fibers. By comparing the power between the sending terminal and receiving terminal, we can estimate the underwater channel loss. The measured attenuation coefficient is about α=0.16m1, which is close to the coefficient in coastal seawater (α=0.179m1) [30]. The loss of the overall system is about 40 dB. To retrieve signal photons from very strong background noises at high-loss condition is another main challenge for our experiment. By using two long black tubes as spatial filters at the receiving terminals, we obtain an affordable background noise of 600s1 on APD1 and 200s1 on APD2. After the whole alignment process, we are ready to switch the beacon light to the signal light.

We prepare six universal polarization-encoded quantum states at the sending terminal with the combination of a polarization beam splitter (PBS), a half-wave plate (HWP), and a quarter-wave plate (QWP): |H,|V,|D=12(|H+|V),|A=12(|H|V),|R=12(|H+i|V),|L=12(|Hi|V). The instability of water causes beam wandering and profile distortion, which both lead to the fluctuation of the photon counting numbers. The received signal intensity is about 11,000s1 in average, fluctuating from 9000 to 12,000s1. Here, we use two detectors to detect transmitted and reflected photons under orthogonal projective measurements simultaneously to eliminate the influence of such fluctuation.

First, we verify the polarization correlations between the sent and received states. As is shown in Fig. 2, we prepare the states at |H,|V,|D,|A and project them under different polarization angles at the receiving terminal. The visibilities obtained by fitting the sinusoidal curves are |H:87%,|V:95.2%,|D:85.5%,and|A:95.2%. The visibilities in basis H/V and D/A are slightly different due to the unbalanced background noises on the two detectors. The average visibility is 90.7% without subtracting the background noises.

 figure: Fig. 2.

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.

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To obtain comprehensive and complete information of the received states, we implement quantum state tomography [31]. The density matrices of the six universal states are shown in Fig. 3(a). From the density matrices we calculate the state fidelity according to Fs=trρreceivedρsentρreceived [32,33] and present the results in Fig. 3(b). We see that all fidelities are more than 95%, and the average fidelity is up to 0.976. We further calculate the purity of all these states. As plotted in Fig. 3(c), the average purity of the states is up to 0.942.

 figure: Fig. 3.

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.

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To further reveal the physical process of the underwater channel, we also perform quantum process tomography. Here, we use the matrix χ to represent the effect of the underwater channel, and the output state can be written as

ε(ρ)=mnE˜mρE˜nχmn.
As for one-qubit process tomography, we choose E˜m as: E˜0=I, E˜1=X, E˜2=Y, E˜3=Z. The measured results of quantum process tomography are shown in Fig. 4. Regardless of the loss effect, the operation conducted by the underwater channel is found similar to the ideal case:
χideal=[1000000000000000],
which is the cornerstone for being a reliable quantum channel. We also calculate the fidelity of the process matrix according to the formula FP=trχwaterχidealχwater, and we obtained a result of up to 0.96, which suggests that photonic polarization states can well survive under the conditions of strong scattering and high loss through a long underwater channel.

 figure: Fig. 4.

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.

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In our experiment, the deviations of our measured results from the ideal cases indicate that the noise counts (including APD dark counts and background noise) and the device imperfections remain to be suppressed. In future practical QKD involving an underwater channel, more filtering technologies including time window filtering and ultra-low-dark-count detector can be used to effectively overcome the noise problem. For convenience of light alignment, we choose four large size aluminum coated mirrors shown in Fig. 1 (dielectric coated mirrors in this large size are not commercially available and the coating can be easily eroded by water). The reflectance of two orthogonal polarizations (in Fresnel equations, usually called S and P polarization, corresponding to H and V polarization here) is slightly different when the incident angle is nonzero. Here, we measure the reflectivity of the aluminum coated mirrors using two orthogonal polarizations, respectively, at the incident angle of 45 deg and obtained about 5% unbalance reflectance between the two polarization components, which will cause about 2% decrease of the fidelities in quantum state tomography. Fortunately, in future practical QKD, dielectric coated mirrors will be used because all the optical devices can be integrated in water-proof compartments, and the unbalance can be ignored.

3. CONCLUSION

In summary, we experimentally demonstrate the transmission of blue-green photonic polarization states through a 55-m-long underwater channel. The obtained state and process fidelities confirm the feasibility of implementing secure quantum communication with submersibles located in the open sea. It is noted that the attenuation coefficient in our marine test platform only approaches the quality of costal sea. The results in a blue-green window for the open sea have been found as low as 0.018m1 [30,34], which suggests an even deeper achievable distance. In addition, as the blue-green band is a window of light for both seawater and atmosphere, we therefore expect a long-distance air-to-sea quantum communication from satellites to submersibles at a depth forbidden to the radio wave frequency in the future.

Funding

National Basic Research Program of China (973 Program) (2017YFA0303700); National Natural Science Foundation of China (NSFC) (61734005, 11761141014, 11690033); Science and Technology Commission of Shanghai Municipality (STCSM) (15QA1402200, 16JC1400405, 17JC1400403); Shanghai Municipal Education Commission (SMEC) (16SG09, 2017-01-07-00-02-E00049).

Acknowledgment

The authors thank Jian-Wei Pan, Hang Li, Xiao-Ling Pang, and Jian-Peng Dou for helpful discussions. X.-M.J. acknowledges support from the National Young 1000 Talents Plan.

REFERENCES

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2. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997). [CrossRef]  

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5. H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012). [CrossRef]  

6. T. Sasaki, Y. Yamamoto, and M. Koashi, “Practical quantum key distribution protocol without monitoring signal disturbance,” Nature 509, 475–478 (2014). [CrossRef]  

7. H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over a 404 km optical fiber,” Phys. Rev. Lett. 117, 190501 (2016). [CrossRef]  

8. M. Lucamarini, Z. Yuan, J. Dynes, and A. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–403 (2018). [CrossRef]  

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13. J. Dynes, H. Takesue, Z. Yuan, A. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express 17, 11440–11449 (2009). [CrossRef]  

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16. D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018). [CrossRef]  

17. M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003). [CrossRef]  

18. L.-M. Duan, M. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001). [CrossRef]  

19. X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010). [CrossRef]  

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21. J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Li, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356, 1140–1144 (2017). [CrossRef]  

22. W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett. 91, 057901 (2003). [CrossRef]  

23. X.-B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1–111 (2007). [CrossRef]  

24. B. Huttner, N. Imoto, N. Gisin, and T. Mor, “Quantum cryptography with coherent states,” Phys. Rev. A 51, 1863–1869 (1995). [CrossRef]  

25. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000). [CrossRef]  

26. P. Shi, S.-C. Zhao, W.-D. Li, and Y.-J. Gu, “Feasibility of underwater free space quantum key distribution,” arXiv:1402.4666 (2014).

27. L. Ji, J. Gao, A.-L. Yang, Z. Feng, X.-F. Lin, Z.-G. Li, and X.-M. Jin, “Towards quantum communications in free-space seawater,” Opt. Express 25, 19795–19806 (2017). [CrossRef]  

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References

  • View by:

  1. C. H. Bennett, “Quantum cryptography: public key distribution and coin tossing,” in IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175–179.
  2. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
    [Crossref]
  3. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
    [Crossref]
  4. H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
    [Crossref]
  5. H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
    [Crossref]
  6. T. Sasaki, Y. Yamamoto, and M. Koashi, “Practical quantum key distribution protocol without monitoring signal disturbance,” Nature 509, 475–478 (2014).
    [Crossref]
  7. H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over a 404  km optical fiber,” Phys. Rev. Lett. 117, 190501 (2016).
    [Crossref]
  8. M. Lucamarini, Z. Yuan, J. Dynes, and A. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–403 (2018).
    [Crossref]
  9. G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, and H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2000).
    [Crossref]
  10. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
    [Crossref]
  11. T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
    [Crossref]
  12. D. Naik, C. Peterson, A. White, A. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
    [Crossref]
  13. J. Dynes, H. Takesue, Z. Yuan, A. Sharpe, K. Harada, T. Honjo, H. Kamada, O. Tadanaga, Y. Nishida, M. Asobe, and A. J. Shields, “Efficient entanglement distribution over 200 kilometers,” Opt. Express 17, 11440–11449 (2009).
    [Crossref]
  14. K. Azuma, K. Tamaki, and W. J. Munro, “All-photonic intercity quantum key distribution,” Nat. Commun. 6, 10171 (2015).
    [Crossref]
  15. Q.-C. Sun, Y.-L. Mao, S.-J. Chen, W. Zhang, Y.-F. Jiang, Y.-B. Zhang, W.-J. Zhang, S. Miki, T. Yamashita, H. Terai, X. Jiang, T.-Y. Chen, L.-X. You, X.-F. Chen, Z. Wang, J.-Y. Fan, Q. Zhang, and J.-W. Pan, “Quantum teleportation with independent sources and prior entanglement distribution over a network,” Nat. Photonics 10, 671–675 (2016).
    [Crossref]
  16. D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
    [Crossref]
  17. M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
    [Crossref]
  18. L.-M. Duan, M. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
    [Crossref]
  19. X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
    [Crossref]
  20. J.-G. Ren, P. Xu, H.-L. Yong, L. Zhang, S.-K. Liao, J. Yin, W.-Y. Liu, W.-Q. Cai, M. Yang, L. Li, K.-X. Yang, X. Han, Y.-Q. Yao, J. Li, H.-Y. Wu, S. Wan, L. Liu, D.-Q. Liu, Y.-W. Kuang, Z.-P. He, P. Shang, C. Guo, R.-H. Zheng, K. Tian, Z.-C. Zhu, N.-L. Liu, C.-Y. Lu, R. Shu, Y.-A. Chen, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549, 70–73 (2017).
    [Crossref]
  21. J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Li, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356, 1140–1144 (2017).
    [Crossref]
  22. W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett. 91, 057901 (2003).
    [Crossref]
  23. X.-B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1–111 (2007).
    [Crossref]
  24. B. Huttner, N. Imoto, N. Gisin, and T. Mor, “Quantum cryptography with coherent states,” Phys. Rev. A 51, 1863–1869 (1995).
    [Crossref]
  25. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
    [Crossref]
  26. P. Shi, S.-C. Zhao, W.-D. Li, and Y.-J. Gu, “Feasibility of underwater free space quantum key distribution,” arXiv:1402.4666 (2014).
  27. L. Ji, J. Gao, A.-L. Yang, Z. Feng, X.-F. Lin, Z.-G. Li, and X.-M. Jin, “Towards quantum communications in free-space seawater,” Opt. Express 25, 19795–19806 (2017).
    [Crossref]
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2018 (2)

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2017 (3)

J.-G. Ren, P. Xu, H.-L. Yong, L. Zhang, S.-K. Liao, J. Yin, W.-Y. Liu, W.-Q. Cai, M. Yang, L. Li, K.-X. Yang, X. Han, Y.-Q. Yao, J. Li, H.-Y. Wu, S. Wan, L. Liu, D.-Q. Liu, Y.-W. Kuang, Z.-P. He, P. Shang, C. Guo, R.-H. Zheng, K. Tian, Z.-C. Zhu, N.-L. Liu, C.-Y. Lu, R. Shu, Y.-A. Chen, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549, 70–73 (2017).
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2016 (2)

Q.-C. Sun, Y.-L. Mao, S.-J. Chen, W. Zhang, Y.-F. Jiang, Y.-B. Zhang, W.-J. Zhang, S. Miki, T. Yamashita, H. Terai, X. Jiang, T.-Y. Chen, L.-X. You, X.-F. Chen, Z. Wang, J.-Y. Fan, Q. Zhang, and J.-W. Pan, “Quantum teleportation with independent sources and prior entanglement distribution over a network,” Nat. Photonics 10, 671–675 (2016).
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H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over a 404  km optical fiber,” Phys. Rev. Lett. 117, 190501 (2016).
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2015 (1)

K. Azuma, K. Tamaki, and W. J. Munro, “All-photonic intercity quantum key distribution,” Nat. Commun. 6, 10171 (2015).
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2014 (1)

T. Sasaki, Y. Yamamoto, and M. Koashi, “Practical quantum key distribution protocol without monitoring signal disturbance,” Nature 509, 475–478 (2014).
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2012 (2)

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
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J. R. Johansson, P. D. Nation, and F. Nori, “Qutip: an open-source python framework for the dynamics of open quantum systems,” Comput. Phys. Commun. 183, 1760–1772 (2012).
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2010 (1)

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
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2009 (1)

2008 (1)

B. M. Cochenour, L. J. Mullen, and A. E. Laux, “Characterization of the beam-spread function for underwater wireless optical communications links,” IEEE J. Ocean. Eng. 33, 513–521 (2008).
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2007 (1)

X.-B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1–111 (2007).
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2005 (1)

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
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2003 (2)

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
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2001 (2)

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
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2000 (5)

G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, and H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2000).
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T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000).
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G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
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1997 (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
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1995 (1)

B. Huttner, N. Imoto, N. Gisin, and T. Mor, “Quantum cryptography with coherent states,” Phys. Rev. A 51, 1863–1869 (1995).
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1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
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Abbas, A.

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv:1801.10299 (2018).

Asobe, M.

Aspelmeyer, M.

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
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Azuma, K.

K. Azuma, K. Tamaki, and W. J. Munro, “All-photonic intercity quantum key distribution,” Nat. Commun. 6, 10171 (2015).
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C. H. Bennett, “Quantum cryptography: public key distribution and coin tossing,” in IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175–179.

Berglund, A.

D. Naik, C. Peterson, A. White, A. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000).
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Böhm, H. R.

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
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Bouchard, F.

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv:1801.10299 (2018).

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
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Boyd, R. W.

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Underwater quantum key distribution in outdoor conditions with twisted photons,” arXiv:1801.10299 (2018).

Boynton, N.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
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G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
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Brendel, J.

G. Ribordy, J. Brendel, J.-D. Gautier, N. Gisin, and H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A 63, 012309 (2000).
[Crossref]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
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Bunandar, D.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
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Cai, H.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
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J.-G. Ren, P. Xu, H.-L. Yong, L. Zhang, S.-K. Liao, J. Yin, W.-Y. Liu, W.-Q. Cai, M. Yang, L. Li, K.-X. Yang, X. Han, Y.-Q. Yao, J. Li, H.-Y. Wu, S. Wan, L. Liu, D.-Q. Liu, Y.-W. Kuang, Z.-P. He, P. Shang, C. Guo, R.-H. Zheng, K. Tian, Z.-C. Zhu, N.-L. Liu, C.-Y. Lu, R. Shu, Y.-A. Chen, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549, 70–73 (2017).
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J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Li, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356, 1140–1144 (2017).
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Camacho, R.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
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J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Li, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356, 1140–1144 (2017).
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J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Li, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356, 1140–1144 (2017).
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Chen, C.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
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H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over a 404  km optical fiber,” Phys. Rev. Lett. 117, 190501 (2016).
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Chen, K.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
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H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
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Chen, S.-J.

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M.-J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over a 404  km optical fiber,” Phys. Rev. Lett. 117, 190501 (2016).
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Chen, T.-Y.

Q.-C. Sun, Y.-L. Mao, S.-J. Chen, W. Zhang, Y.-F. Jiang, Y.-B. Zhang, W.-J. Zhang, S. Miki, T. Yamashita, H. Terai, X. Jiang, T.-Y. Chen, L.-X. You, X.-F. Chen, Z. Wang, J.-Y. Fan, Q. Zhang, and J.-W. Pan, “Quantum teleportation with independent sources and prior entanglement distribution over a network,” Nat. Photonics 10, 671–675 (2016).
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Chen, X.-F.

Q.-C. Sun, Y.-L. Mao, S.-J. Chen, W. Zhang, Y.-F. Jiang, Y.-B. Zhang, W.-J. Zhang, S. Miki, T. Yamashita, H. Terai, X. Jiang, T.-Y. Chen, L.-X. You, X.-F. Chen, Z. Wang, J.-Y. Fan, Q. Zhang, and J.-W. Pan, “Quantum teleportation with independent sources and prior entanglement distribution over a network,” Nat. Photonics 10, 671–675 (2016).
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Chen, Y.-A.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Li, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356, 1140–1144 (2017).
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J.-G. Ren, P. Xu, H.-L. Yong, L. Zhang, S.-K. Liao, J. Yin, W.-Y. Liu, W.-Q. Cai, M. Yang, L. Li, K.-X. Yang, X. Han, Y.-Q. Yao, J. Li, H.-Y. Wu, S. Wan, L. Liu, D.-Q. Liu, Y.-W. Kuang, Z.-P. He, P. Shang, C. Guo, R.-H. Zheng, K. Tian, Z.-C. Zhu, N.-L. Liu, C.-Y. Lu, R. Shu, Y.-A. Chen, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549, 70–73 (2017).
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Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).

Cirac, J. I.

L.-M. Duan, M. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
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Cochenour, B. M.

B. M. Cochenour, L. J. Mullen, and A. E. Laux, “Characterization of the beam-spread function for underwater wireless optical communications links,” IEEE J. Ocean. Eng. 33, 513–521 (2008).
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Curty, M.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
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Dai, H.

J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Dai, G.-B. Li, Q.-M. Lu, Y.-H. Gong, Y. Xu, S.-L. Li, F.-Z. Li, Y.-Y. Yin, Z.-Q. Jiang, M. Li, J.-J. Jia, G. Ren, D. He, Y.-L. Zhou, X.-X. Zhang, N. Wang, X. Chang, Z.-C. Zhu, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356, 1140–1144 (2017).
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Davids, P.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
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B. Wozniak and J. Dera, Light Absorption in Sea Water (Springer, 2007), Vol. 33.

DeRose, C.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
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Duan, L.-M.

L.-M. Duan, M. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
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M. Lucamarini, Z. Yuan, J. Dynes, and A. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–403 (2018).
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Eibl, M.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
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Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
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Englund, D.

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
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Fan, J.-Y.

Q.-C. Sun, Y.-L. Mao, S.-J. Chen, W. Zhang, Y.-F. Jiang, Y.-B. Zhang, W.-J. Zhang, S. Miki, T. Yamashita, H. Terai, X. Jiang, T.-Y. Chen, L.-X. You, X.-F. Chen, Z. Wang, J.-Y. Fan, Q. Zhang, and J.-W. Pan, “Quantum teleportation with independent sources and prior entanglement distribution over a network,” Nat. Photonics 10, 671–675 (2016).
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Feng, Z.

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Figures (4)

Fig. 1.
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.
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.
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.
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.

Equations (2)

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ε(ρ)=mnE˜mρE˜nχmn.
χideal=[1000000000000000],

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