Abstract

Due to the absorption of water, communication between two parties submersed below the water is normally performed with acoustic waves. However, with the need for higher data rates, the use of RF or optical frequencies is needed. Currently, optical wavelengths have been demonstrated for classical communication over short distances. For these short distances, if a large amount of data needs to be transmitted securely, it is not feasible for both parties to return to the surface to communicate. Additionally, it can be assumed that a third party (Eve) is located in the channel trying to gather information. The solution is to use quantum key distribution (QKD) to generate the secure key, allowing the parties to continuously encrypt and transmit the data. It is assumed the BB84 protocol using pairs of polarization entangled photons generated from a spontaneous parametric down conversion (SPDC) source of Type-II. By using entangled photons, Eve is not able to gain information without being detected. In this work, horizontal oceanic channel is studied for various distances ranging from 10 m to 100 m, depth ranging from 100 m to 200 m, and surface chlorophyll-a concentrations at a wavelength of 532 nm. The secure key rates are calculated, assuming that a low-density parity check (LDPC) error correction code is used for information reconciliation. The maximum secure key rate and optimal number of average entangled photons transmitted are then studied for the various channels.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

2017 (1)

2016 (2)

2015 (1)

2013 (1)

2012 (1)

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

2011 (1)

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

2008 (2)

S. Jaruwatanadilok, “Underwater wireless optical communication channel modeling and performance evaluation using vector radiative transfer theory,” IEEE J. on Sel. Areas Commun. 26, 1620–1627 (2008).
[Crossref]

S. Dong, J. Sprintall, S. T. Gille, and L. Talley, “Southern ocean mixed-layer depth from argo float profiles,” J. Geophys. Res. Ocean. 113, 06013 (2008).
[Crossref]

2007 (1)

X. Ma, C.-H. F. Fung, and H.-K. Lo, “Quantum key distribution with entangled photon sources,” Phys. Rev. A 76, 012307 (2007).
[Crossref]

2006 (1)

B. A. Klinger, B. Huang, B. Kirtman, P. Schopf, and J. Wang, “Monthly climatologies of oceanic friction velocity cubed,” J. Clim. 19, 5700–5708 (2006).
[Crossref]

2005 (1)

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” J. Geophys. Res. Ocean. 111, C08005 (2005).

2004 (1)

2003 (1)

M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett. 90, 057902 (2003).
[Crossref] [PubMed]

1999 (1)

1997 (1)

1995 (1)

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. Ocean. 100, 13321–13332 (1995).
[Crossref]

1992 (1)

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

1991 (1)

A. K. Ekert, “Quantum cryptography based on bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

1989 (1)

C. P. Lombardo and M. C. Gregg, “Similarity scaling of viscous and thermal dissipation in a convecting surface boundary layer,” J. Geophys. Res. Ocean. 94, 6273–6284 (1989).
[Crossref]

1969 (1)

D. Jamieson, J. Tudhope, R. Morris, and G. Cartwright, “Physical properties of sea water solutions: heat capacity,” Desalination. 7, 23–30 (1969).
[Crossref]

Abbas, A.

Alleaume, R.

D. Elkouss, A. Leverrier, R. Alleaume, and J. J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in 2009 IEEE International Symposium on Information Theory, (2009), pp. 1879–1883.

Allevi, A.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Avella, A.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Babin, M.

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. Ocean. 100, 13321–13332 (1995).
[Crossref]

Baringer, M. O.

M. Goes, J. Christophersen, S. Dong, G. Goni, and M. O. Baringer, “An updated estimate of salinity for the atlantic ocean sector using temperature–salinity relationships,” J. Atmospheric Ocean. Technol. 35, 1771–1784 (2018).
[Crossref]

Bartuskova, L.

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Bennett, C. H.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing int,” in Conf. on Computers, Systems and Signal Processing (Bangalore, India, Dec. 1984), (1984), pp. 175–179.

Bettelli, S.

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Blauensteiner, B.

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Böhm, H. R.

Bondani, M.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Bouchard, F.

Boutros, J. J.

D. Elkouss, A. Leverrier, R. Alleaume, and J. J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in 2009 IEEE International Symposium on Information Theory, (2009), pp. 1879–1883.

Boyd, R. w.

Brassard, G.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing int,” in Conf. on Computers, Systems and Signal Processing (Bangalore, India, Dec. 1984), (1984), pp. 175–179.

Bricaud, A.

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. Ocean. 100, 13321–13332 (1995).
[Crossref]

Burk, B. D.

B. D. Burk and W. K. Marshall, “Received optical power calculations for optical communications link performance analysis,” Tech. rep., NASA (1986).

Cartwright, G.

D. Jamieson, J. Tudhope, R. Morris, and G. Cartwright, “Physical properties of sea water solutions: heat capacity,” Desalination. 7, 23–30 (1969).
[Crossref]

Chen, K.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

Chen, S.

Chen, T.-Y.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

Christophersen, J.

M. Goes, J. Christophersen, S. Dong, G. Goni, and M. O. Baringer, “An updated estimate of salinity for the atlantic ocean sector using temperature–salinity relationships,” J. Atmospheric Ocean. Technol. 35, 1771–1784 (2018).
[Crossref]

Claustre, H.

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” J. Geophys. Res. Ocean. 111, C08005 (2005).

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. Ocean. 100, 13321–13332 (1995).
[Crossref]

Cui, K.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

Djordjecvic, I. B.

J. Gariano, I. B. Djordjecvic, and Y. Xiang, “Simulation of a submarine to submarine QKD system,” in Quantum Information Science and Technology IV, vol. 10803M. T. Gruneisen, M. Dusek, and J. G. Rarity, eds. (SPIE, 2018).
[Crossref]

Djordjevic, I. B.

X. Yi and I. B. Djordjevic, “Power spectrum of refractive-index fluctuations in turbulent ocean and its effect on optical scintillation,” Opt. Express 26, 10188–10202 (2018).
[Crossref] [PubMed]

J. Gariano and I. B. Djordjevic, “PPLN-waveguide-based polarization entangled QKD simulator,” in Quantum Communications and Quantum Imaging XV,, vol. 10409R. E. Meyers, Y. Shih, and K. S. Deacon, eds. (SPIE, 2017).
[Crossref]

Dong, S.

M. Goes, J. Christophersen, S. Dong, G. Goni, and M. O. Baringer, “An updated estimate of salinity for the atlantic ocean sector using temperature–salinity relationships,” J. Atmospheric Ocean. Technol. 35, 1771–1784 (2018).
[Crossref]

S. Dong, J. Sprintall, S. T. Gille, and L. Talley, “Southern ocean mixed-layer depth from argo float profiles,” J. Geophys. Res. Ocean. 113, 06013 (2008).
[Crossref]

Dusek, M.

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

Elkouss, D.

D. Elkouss, A. Leverrier, R. Alleaume, and J. J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in 2009 IEEE International Symposium on Information Theory, (2009), pp. 1879–1883.

Fedrizzi, A.

Feng, Z.

Fickler, R.

Fry, E. S.

Fung, C.-H. F.

X. Ma, C.-H. F. Fung, and H.-K. Lo, “Quantum key distribution with entangled photon sources,” Phys. Rev. A 76, 012307 (2007).
[Crossref]

Galinis, J.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Gao, J.

Gariano, J.

J. Gariano, I. B. Djordjecvic, and Y. Xiang, “Simulation of a submarine to submarine QKD system,” in Quantum Information Science and Technology IV, vol. 10803M. T. Gruneisen, M. Dusek, and J. G. Rarity, eds. (SPIE, 2018).
[Crossref]

J. Gariano and I. B. Djordjevic, “PPLN-waveguide-based polarization entangled QKD simulator,” in Quantum Communications and Quantum Imaging XV,, vol. 10409R. E. Meyers, Y. Shih, and K. S. Deacon, eds. (SPIE, 2017).
[Crossref]

Gille, S. T.

S. Dong, J. Sprintall, S. T. Gille, and L. Talley, “Southern ocean mixed-layer depth from argo float profiles,” J. Geophys. Res. Ocean. 113, 06013 (2008).
[Crossref]

Goes, M.

M. Goes, J. Christophersen, S. Dong, G. Goni, and M. O. Baringer, “An updated estimate of salinity for the atlantic ocean sector using temperature–salinity relationships,” J. Atmospheric Ocean. Technol. 35, 1771–1784 (2018).
[Crossref]

Goni, G.

M. Goes, J. Christophersen, S. Dong, G. Goni, and M. O. Baringer, “An updated estimate of salinity for the atlantic ocean sector using temperature–salinity relationships,” J. Atmospheric Ocean. Technol. 35, 1771–1784 (2018).
[Crossref]

Green, R. J.

Gregg, M. C.

C. P. Lombardo and M. C. Gregg, “Similarity scaling of viscous and thermal dissipation in a convecting surface boundary layer,” J. Geophys. Res. Ocean. 94, 6273–6284 (1989).
[Crossref]

Gu, Y.-J.

Haltrin, V. I.

Heshami, K.

Hooker, S. B.

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” J. Geophys. Res. Ocean. 111, C08005 (2005).

Huang, B.

B. A. Klinger, B. Huang, B. Kirtman, P. Schopf, and J. Wang, “Monthly climatologies of oceanic friction velocity cubed,” J. Clim. 19, 5700–5708 (2006).
[Crossref]

Huebel, H.

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Hufnagel, F.

Jamieson, D.

D. Jamieson, J. Tudhope, R. Morris, and G. Cartwright, “Physical properties of sea water solutions: heat capacity,” Desalination. 7, 23–30 (1969).
[Crossref]

Jaruwatanadilok, S.

S. Jaruwatanadilok, “Underwater wireless optical communication channel modeling and performance evaluation using vector radiative transfer theory,” IEEE J. on Sel. Areas Commun. 26, 1620–1627 (2008).
[Crossref]

Jennewein, T.

Ji, L.

Jin, X.-M.

Johnson, L. J.

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

Karimi, E.

Kasai, K.

K. Kasai, R. Matsumoto, and K. Sakaniwa, “Information reconciliation for QKD with rate-compatible non-binary LDPC codes,” in 2010 International Symposium On Information Theory Its Applications, (2010), pp. 922–927.

Kaushal, H.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

Kirtman, B.

B. A. Klinger, B. Huang, B. Kirtman, P. Schopf, and J. Wang, “Monthly climatologies of oceanic friction velocity cubed,” J. Clim. 19, 5700–5708 (2006).
[Crossref]

Klinger, B. A.

B. A. Klinger, B. Huang, B. Kirtman, P. Schopf, and J. Wang, “Monthly climatologies of oceanic friction velocity cubed,” J. Clim. 19, 5700–5708 (2006).
[Crossref]

Koashi, M.

M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett. 90, 057902 (2003).
[Crossref] [PubMed]

Kurtsiefer, C.

Lanzagorta, M.

J. Uhlmann, M. Lanzagorta, and S. E. Venegas-Andraca, “Quantum communications in the maritime environment,” in OCEANS 2015 - MTS/IEEE Washington, (IEEE, 2015).
[Crossref]

Leeson, M. S.

Leuchs, G.

Leverrier, A.

D. Elkouss, A. Leverrier, R. Alleaume, and J. J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in 2009 IEEE International Symposium on Information Theory, (2009), pp. 1879–1883.

Li, H.

Li, W.-D.

Li, Z.-G.

Liang, H.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

Lin, S.-Z.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

Lin, X.-F.

Liu, X.

Lo, H.-K.

X. Ma, C.-H. F. Fung, and H.-K. Lo, “Quantum key distribution with entangled photon sources,” Phys. Rev. A 76, 012307 (2007).
[Crossref]

Lombardo, C. P.

C. P. Lombardo and M. C. Gregg, “Similarity scaling of viscous and thermal dissipation in a convecting surface boundary layer,” J. Geophys. Res. Ocean. 94, 6273–6284 (1989).
[Crossref]

Lorunser, T.

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Lorünser, T.

Luo, C.-L.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

Ma, X.

X. Ma, C.-H. F. Fung, and H.-K. Lo, “Quantum key distribution with entangled photon sources,” Phys. Rev. A 76, 012307 (2007).
[Crossref]

Machulka, R.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Marquardt, C.

Marshall, W. K.

B. D. Burk and W. K. Marshall, “Received optical power calculations for optical communications link performance analysis,” Tech. rep., NASA (1986).

Mataloni, P.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Matsumoto, R.

K. Kasai, R. Matsumoto, and K. Sakaniwa, “Information reconciliation for QKD with rate-compatible non-binary LDPC codes,” in 2010 International Symposium On Information Theory Its Applications, (2010), pp. 922–927.

Maurhardt, O.

Meng, W.

Mermin, N. D.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

Milani, G.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Morel, A.

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” J. Geophys. Res. Ocean. 111, C08005 (2005).

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. Ocean. 100, 13321–13332 (1995).
[Crossref]

Morris, R.

D. Jamieson, J. Tudhope, R. Morris, and G. Cartwright, “Physical properties of sea water solutions: heat capacity,” Desalination. 7, 23–30 (1969).
[Crossref]

Pan, J.-W.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

Peev, M.

A. Poppe, A. Fedrizzi, R. Ursin, H. R. Böhm, T. Lorünser, O. Maurhardt, M. Peev, M. Suda, C. Kurtsiefer, H. Weinfurter, T. Jennewein, and A. Zeilinger, “Practical quantum key distribution with polarization entangled photons,” Opt. Express 12, 3865–3871 (2004).
[Crossref] [PubMed]

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Perego, A. M.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Pope, R. M.

Poppe, A.

A. Poppe, A. Fedrizzi, R. Ursin, H. R. Böhm, T. Lorünser, O. Maurhardt, M. Peev, M. Suda, C. Kurtsiefer, H. Weinfurter, T. Jennewein, and A. Zeilinger, “Practical quantum key distribution with polarization entangled photons,” Opt. Express 12, 3865–3871 (2004).
[Crossref] [PubMed]

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Preskill, J.

M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett. 90, 057902 (2003).
[Crossref] [PubMed]

Querasser, E.

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Sakaniwa, K.

K. Kasai, R. Matsumoto, and K. Sakaniwa, “Information reconciliation for QKD with rate-compatible non-binary LDPC codes,” in 2010 International Symposium On Information Theory Its Applications, (2010), pp. 922–927.

Schmidt, J. D.

J. D. Schmidt, Numerical simulation of optical wave propagation: with examples in MATLAB, vol. 199;199.; (SPIE, 2010).

Schneier, B.

B. Schneier, Applied cryptography: protocols, algorithms, and source code in C (Wiley-India, 2007).

Schopf, P.

B. A. Klinger, B. Huang, B. Kirtman, P. Schopf, and J. Wang, “Monthly climatologies of oceanic friction velocity cubed,” J. Clim. 19, 5700–5708 (2006).
[Crossref]

Sciarrino, F.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Shi, P.

Sit, A.

Spasibko, K. Y.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Sprintall, J.

S. Dong, J. Sprintall, S. T. Gille, and L. Talley, “Southern ocean mixed-layer depth from argo float profiles,” J. Geophys. Res. Ocean. 113, 06013 (2008).
[Crossref]

Suda, M.

Talley, L.

S. Dong, J. Sprintall, S. T. Gille, and L. Talley, “Southern ocean mixed-layer depth from argo float profiles,” J. Geophys. Res. Ocean. 113, 06013 (2008).
[Crossref]

Tang, K.

Tudhope, J.

D. Jamieson, J. Tudhope, R. Morris, and G. Cartwright, “Physical properties of sea water solutions: heat capacity,” Desalination. 7, 23–30 (1969).
[Crossref]

Uhlmann, J.

J. Uhlmann, M. Lanzagorta, and S. E. Venegas-Andraca, “Quantum communications in the maritime environment,” in OCEANS 2015 - MTS/IEEE Washington, (IEEE, 2015).
[Crossref]

Uitz, J.

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” J. Geophys. Res. Ocean. 111, C08005 (2005).

Ursin, R.

Vallone, G.

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Venegas-Andraca, S. E.

J. Uhlmann, M. Lanzagorta, and S. E. Venegas-Andraca, “Quantum communications in the maritime environment,” in OCEANS 2015 - MTS/IEEE Washington, (IEEE, 2015).
[Crossref]

Voelz, D. G.

D. G. Voelz, Computational Fourier optics: a MATLAB tutorial, vol. TT89;v. TT 89.; (SPIE, Bellingham, Wash. (1000 20th St. Bellingham WA 98225-6705 USA), 2011).

Wang, J.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

B. A. Klinger, B. Huang, B. Kirtman, P. Schopf, and J. Wang, “Monthly climatologies of oceanic friction velocity cubed,” J. Clim. 19, 5700–5708 (2006).
[Crossref]

Wang, Z.

Weinfurter, H.

Wu, Z.

Xiang, Y.

J. Gariano, I. B. Djordjecvic, and Y. Xiang, “Simulation of a submarine to submarine QKD system,” in Quantum Information Science and Technology IV, vol. 10803M. T. Gruneisen, M. Dusek, and J. G. Rarity, eds. (SPIE, 2018).
[Crossref]

Xie, X.

Yang, A.-L.

Yang, X.

Yi, X.

You, L.

Zeilinger, A.

A. Poppe, A. Fedrizzi, R. Ursin, H. R. Böhm, T. Lorünser, O. Maurhardt, M. Peev, M. Suda, C. Kurtsiefer, H. Weinfurter, T. Jennewein, and A. Zeilinger, “Practical quantum key distribution with polarization entangled photons,” Opt. Express 12, 3865–3871 (2004).
[Crossref] [PubMed]

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

Zhang, H.-F.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

Zhang, L.

Zhang, W.

Zhang, Y.

Zhang, Z.

Zhao, S.-C.

Zhou, L.

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

Appl. Opt. (3)

Desalination. (1)

D. Jamieson, J. Tudhope, R. Morris, and G. Cartwright, “Physical properties of sea water solutions: heat capacity,” Desalination. 7, 23–30 (1969).
[Crossref]

IEEE Access (1)

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

IEEE J. on Sel. Areas Commun. (1)

S. Jaruwatanadilok, “Underwater wireless optical communication channel modeling and performance evaluation using vector radiative transfer theory,” IEEE J. on Sel. Areas Commun. 26, 1620–1627 (2008).
[Crossref]

J. Atmospheric Ocean. Technol. (1)

M. Goes, J. Christophersen, S. Dong, G. Goni, and M. O. Baringer, “An updated estimate of salinity for the atlantic ocean sector using temperature–salinity relationships,” J. Atmospheric Ocean. Technol. 35, 1771–1784 (2018).
[Crossref]

J. Clim. (1)

B. A. Klinger, B. Huang, B. Kirtman, P. Schopf, and J. Wang, “Monthly climatologies of oceanic friction velocity cubed,” J. Clim. 19, 5700–5708 (2006).
[Crossref]

J. Geophys. Res. Ocean. (4)

S. Dong, J. Sprintall, S. T. Gille, and L. Talley, “Southern ocean mixed-layer depth from argo float profiles,” J. Geophys. Res. Ocean. 113, 06013 (2008).
[Crossref]

C. P. Lombardo and M. C. Gregg, “Similarity scaling of viscous and thermal dissipation in a convecting surface boundary layer,” J. Geophys. Res. Ocean. 94, 6273–6284 (1989).
[Crossref]

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” J. Geophys. Res. Ocean. 111, C08005 (2005).

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. Ocean. 100, 13321–13332 (1995).
[Crossref]

J. Light. Technol. (1)

H.-F. Zhang, J. Wang, K. Cui, C.-L. Luo, S.-Z. Lin, L. Zhou, H. Liang, T.-Y. Chen, K. Chen, and J.-W. Pan, “A real-time qkd system based on fpga,” J. Light. Technol. 30, 3226–3234 (2012).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Express (5)

Phys. Rev. A (1)

X. Ma, C.-H. F. Fung, and H.-K. Lo, “Quantum key distribution with entangled photon sources,” Phys. Rev. A 76, 012307 (2007).
[Crossref]

Phys. Rev. Lett. (3)

M. Koashi and J. Preskill, “Secure quantum key distribution with an uncharacterized source,” Phys. Rev. Lett. 90, 057902 (2003).
[Crossref] [PubMed]

A. K. Ekert, “Quantum cryptography based on bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

The Eur. Phys. J. Special Top. (1)

F. Sciarrino, G. Vallone, G. Milani, A. Avella, J. Galinis, R. Machulka, A. M. Perego, K. Y. Spasibko, A. Allevi, M. Bondani, and P. Mataloni, “High degree of entanglement and nonlocality of a two-photon state generated at 532 nm,” The Eur. Phys. J. Special Top. 199, 111–125 (2011).
[Crossref]

Other (12)

D. G. Voelz, Computational Fourier optics: a MATLAB tutorial, vol. TT89;v. TT 89.; (SPIE, Bellingham, Wash. (1000 20th St. Bellingham WA 98225-6705 USA), 2011).

J. D. Schmidt, Numerical simulation of optical wave propagation: with examples in MATLAB, vol. 199;199.; (SPIE, 2010).

NASA Earth Observatory, “Chlorophyll & sea surface temperature,” (2018).

B. D. Burk and W. K. Marshall, “Received optical power calculations for optical communications link performance analysis,” Tech. rep., NASA (1986).

B. Schneier, Applied cryptography: protocols, algorithms, and source code in C (Wiley-India, 2007).

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing int,” in Conf. on Computers, Systems and Signal Processing (Bangalore, India, Dec. 1984), (1984), pp. 175–179.

D. Elkouss, A. Leverrier, R. Alleaume, and J. J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in 2009 IEEE International Symposium on Information Theory, (2009), pp. 1879–1883.

K. Kasai, R. Matsumoto, and K. Sakaniwa, “Information reconciliation for QKD with rate-compatible non-binary LDPC codes,” in 2010 International Symposium On Information Theory Its Applications, (2010), pp. 922–927.

J. Gariano and I. B. Djordjevic, “PPLN-waveguide-based polarization entangled QKD simulator,” in Quantum Communications and Quantum Imaging XV,, vol. 10409R. E. Meyers, Y. Shih, and K. S. Deacon, eds. (SPIE, 2017).
[Crossref]

S. Bettelli, T. Lorunser, M. Peev, E. Querasser, M. Dusek, L. Bartuskova, B. Blauensteiner, H. Huebel, A. Poppe, and A. Zeilinger, “Effect of double pair emission to entanglement based qkd,” in 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, (IEEE, 2007), JSI2_2.

J. Uhlmann, M. Lanzagorta, and S. E. Venegas-Andraca, “Quantum communications in the maritime environment,” in OCEANS 2015 - MTS/IEEE Washington, (IEEE, 2015).
[Crossref]

J. Gariano, I. B. Djordjecvic, and Y. Xiang, “Simulation of a submarine to submarine QKD system,” in Quantum Information Science and Technology IV, vol. 10803M. T. Gruneisen, M. Dusek, and J. G. Rarity, eds. (SPIE, 2018).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 a) QKD System model with an entangled photon source located at Alice’s side of the channel. b) The detection apparatus used to implement the BB84 protocol.
Fig. 2
Fig. 2 a) Probability that a photon lands on a detector for different propagation distances b) The attenuation profile for different surface chlorophyll-a concentrations as a function as underwater depth.
Fig. 3
Fig. 3 a) Optimum SKR at various distances and depths with data set S4. b) Optimum SKR at various distances and depths with data set S5. c) Optimum μ at various distances and depths with data set S4. d) Optimum μ at various distances and depths with data set S5

Tables (1)

Tables Icon

Table 1 Channel Conditions

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

P S ( n ) = ( n + 1 ) ( μ / 2 ) n ( 1 + ( μ / 2 ) ) n + 2 ,
R SKR = P Key [ 1 f ( δ ) H 2 ( δ ) H 2 ( δ ) ] ,
f ( δ T ) = 1 R H 2 ( δ T ) ,
α ( λ , d ) = a ( λ , d ) + b ( λ , d ) ,
C c ( d ) = Chla ¯ Zeu ( C b s × d Z eu + C Max exp ( d / Z eu ζ Max ) 2 Δ ζ 2 ) ,
C f ( d ) = 1.74098 C c ( d ) exp ( 0.12327 C c ( d ) ) ,
C h ( d ) = 0.19334 C c ( d ) exp ( 0.12343 C c ( d ) ) ,
C s ( d ) = 0.01739 C c ( d ) exp ( 0.11631 C c ( d ) ) ,
C l ( d ) = 0.76284 C c ( d ) exp ( 0.03092 C c ( d ) ) .
a ( λ , d ) = a w ( λ ) + a f C f ( d ) exp ( k f λ ) + a h 0 C h ( d ) exp ( k h λ ) + a c 0 C c ( d ) 0.602 ,
b ( λ , C c ( d ) ) = b w ( λ ) + b s 0 ( λ ) C s ( d ) + b l 0 ( λ ) C l ( d ) ,
b w ( λ ) = 0.005826 ( 400 / λ ) 4.3222 ,
b s 0 ( λ ) = 0.1.1513 ( 400 / λ ) 1.7 ,
b l 0 ( λ ) = 0.3411 ( 400 / λ ) 0.3 .
Φ n ( κ ) = ( 4 π ) 1 A 2 β χ T 1 / 3 κ 11 / 3 [ g ( κ η , Pr T ) + d r ω 2 g ( κ η , Pr S ) ( 1 d r ) ω g ( κ η , Pr T S ) ] ,
g ( x , Pr ) = [ 1 + n = 1 n a n x n ] exp ( δ x ) ,
L Sol = E Sol R L fac π exp ( α Dav D )
N Background = λ h c τ s L Sol π Θ 2 4 π D r x 2 4 Δ λ η r η λ ,

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