Abstract

We report an experimental implementation of free-space quantum secure direct communication based on single photons. The quantum communication scheme uses phase encoding, and the asymmetric Mach–Zehnder interferometer is optimized so as to automatically compensate phase drift of the photons during their transitions over the free-space medium. At a 16 MHz pulse repetition frequency, an information transmission rate of 500 bps over a 10 m free space with a mean quantum bit error rate of 0.49%±0.27% is achieved. The security is analyzed under the scenario that Eve performs the collective attack for single-photon state and the photon number splitting attack for multi-photon state in the depolarizing channel. Our results show that quantum secure direct communication is feasible in free space.

© 2020 Chinese Laser Press

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2020 (2)

H.-Y. Liu, X.-H. Tian, C. Gu, P. Fan, X. Ni, R. Yang, J.-N. Zhang, M. Hu, J. Guo, X. Cao, X. Hu, G. Zhao, Y.-Q. Lu, Y.-X. Gong, Z. Xie, and S.-N. Zhu, “Drone-based entanglement distribution towards mobile quantum networks,” Natl. Sci. Rev. 7, 921–928 (2020).
[Crossref]

Z.-R. Zhou, Y.-B. Sheng, P.-H. Niu, L.-G. Yin, G.-L. Long, and L. Hanzo, “Measurement-device-independent quantum secure direct communication,” Sci. China Phys. Mech. Astron. 63, 230362 (2020).
[Crossref]

2019 (7)

R. Qi, Z. Sun, Z. Lin, P. Niu, W. Hao, L. Song, Q. Huang, J. Gao, L. Yin, and G.-L. Long, “Implementation and security analysis of practical quantum secure direct communication,” Light Sci. Appl. 8, 22 (2019).
[Crossref]

Z. Gao, T. Li, and Z. Li, “Long-distance measurement-device-independent quantum secure direct communication,” Europhys. Lett. 125, 40004 (2019).
[Crossref]

L. Zhou, Y.-B. Sheng, and G.-L. Long, “Device-independent quantum secure direct communication against collective attacks,” Sci. Bull. 65, 12–20 (2019).
[Crossref]

R. Tannous, Z. Ye, J. Jin, K. B. Kuntz, N. Lütkenhaus, and T. Jennewein, “Demonstration of a 6 state-4 state reference frame independent channel for quantum key distribution,” Appl. Phys. Lett. 115, 211103 (2019).
[Crossref]

H. Lu, “Ambiguous discrimination among linearly dependent quantum states and its application to two-way deterministic quantum key distribution,” J. Opt. Soc. Am. B 36, B26–B30 (2019).
[Crossref]

Q. Zhou, R. Valivarthi, C. John, and W. Tittel, “Practical quantum random-number generation based on sampling vacuum fluctuations,” Quantum Eng. 1, e8 (2019).
[Crossref]

J. Wu, Z. Lin, L. Yin, and G.-L. Long, “Security of quantum secure direct communication based on Wyner’s wiretap channel theory,” Quantum Eng. 1, e26 (2019).
[Crossref]

2018 (3)

2017 (5)

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43–47 (2017).
[Crossref]

W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, “Quantum secure direct communication with quantum memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref]

F. Zhu, W. Zhang, Y. Sheng, and Y. Huang, “Experimental long-distance quantum secure direct communication,” Sci. Bull. 62, 1519–1524 (2017).
[Crossref]

S. Cai, H. Shi, J. Li, L. Gu, Y. Ni, Z. Cheng, S. Wang, W.-W. Xiong, L. Li, Z. An, and W. Huang, “Visible-light-excited ultralong organic phosphorescence by manipulating intermolecular interactions,” Adv. Mater. 29, 1701244 (2017).
[Crossref]

W. O. Krawec, “Quantum key distribution with mismatched measurements over arbitrary channels,” Quantum Inf. Comput. 17, 209–241 (2017).

2016 (2)

J.-Y. Hu, B. Yu, M.-Y. Jing, L.-T. Xiao, S.-T. Jia, G.-Q. Qin, and G.-L. Long, “Experimental quantum secure direct communication with single photons,” Light Sci. Appl. 5, e16144 (2016).
[Crossref]

D. J. Lum, J. C. Howell, M. S. Allman, T. Gerrits, V. B. Verma, S. W. Nam, C. Lupo, and S. Lloyd, “Quantum enigma machine: experimentally demonstrating quantum data locking,” Phys. Rev. A 94, 022315 (2016).
[Crossref]

2015 (1)

C. I. Henao and R. M. Serra, “Practical security analysis of two-way quantum-key-distribution protocols based on nonorthogonal states,” Phys. Rev. A 92, 052317 (2015).
[Crossref]

2014 (4)

A. Carrasco-Casado, N. Denisenko, and V. Fernandez, “Correction of beam wander for a free-space quantum key distribution system operating in urban environment,” Opt. Eng. 53, 084112 (2014).
[Crossref]

J. H. Shapiro, Z. Zhang, and F. N. Wong, “Secure communication via quantum illumination,” Quantum Inf. Process. 13, 2171–2193 (2014).
[Crossref]

H. Sun, S. Liu, W. Lin, K. Y. Zhang, W. Lv, X. Huang, F. Huo, H. Yang, G. Jenkins, Q. Zhao, and W. Huang, “Smart responsive phosphorescent materials for data recording and security protection,” Nat. Commun. 5, 3601 (2014).
[Crossref]

S. Wang, W. Chen, Z.-Q. Yin, H.-W. Li, D.-Y. He, Y.-H. Li, Z. Zhou, X.-T. Song, F.-Y. Li, D. Wang, H. Chen, Y.-G. Han, J.-Z. Huang, J.-F. Guo, P.-L. Hao, M. Li, C.-M. Zhang, D. Liu, W.-Y. Liang, C.-H. Miao, P. Wu, G.-C. Guo, and Z.-F. Han, “Field and long-term demonstration of a wide area quantum key distribution network,” Opt. Express 22, 21739–21756 (2014).
[Crossref]

2012 (1)

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat. Commun. 3, 634 (2012).
[Crossref]

2011 (2)

2010 (1)

2009 (3)

S. Pirandola, S. L. Braunstein, S. Lloyd, and S. Mancini, “Confidential direct communications: a quantum approach using continuous variables,” IEEE J. Sel. Top. Quantum Electron. 15, 1570–1580 (2009).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

S. Lin, Q.-Y. Wen, F. Gao, and F.-C. Zhu, “Eavesdropping on secure deterministic communication with qubits through photon-number-splitting attacks,” Phys. Rev. A 79, 054303 (2009).
[Crossref]

2008 (2)

X. Ma and H.-K. Lo, “Quantum key distribution with triggering parametric down-conversion sources,” New J. Phys. 10, 073018 (2008).
[Crossref]

S. Pirandola, S. L. Braunstein, S. Mancini, and S. Lloyd, “Quantum direct communication with continuous variables,” Europhys. Lett. 84, 20013 (2008).
[Crossref]

2007 (3)

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref]

A. Thangaraj, S. Dihidar, A. R. Calderbank, S. W. McLaughlin, and J.-M. Merolla, “Applications of LDPC codes to the wiretap channel,” IEEE Trans. Inf. Theory 53, 2933–2945 (2007).
[Crossref]

S. L. Zhang, X. Zou, K. Li, C. Jin, and G. C. Guo, “Limitation of decoy-state Scarani-Acin-Ribordy-Gisin quantum-key-distribution protocols with a heralded single-photon source,” Phys. Rev. A 76, 044304 (2007).
[Crossref]

2006 (3)

J.-B. Li and X.-M. Fang, “Nonorthogonal decoy-state quantum key distribution,” Chin. Phys. Lett. 23, 768–775 (2006).
[Crossref]

C.-H. F. Fung, K. Tamaki, and H.-K. Lo, “Performance of two quantum-key-distribution protocols,” Phys. Rev. A 73, 012337 (2006).
[Crossref]

A. M. Marino and C. Stroud, “Deterministic secure communications using two-mode squeezed states,” Phys. Rev. A 74, 022315 (2006).
[Crossref]

2005 (5)

M. Lucamarini and S. Mancini, “Secure deterministic communication without entanglement,” Phys. Rev. Lett. 94, 140501 (2005).
[Crossref]

X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503 (2005).
[Crossref]

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

C. Wang, F.-G. Deng, Y.-S. Li, X.-S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[Crossref]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

2004 (6)

V. Scarani, A. Acin, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. Rev. Lett. 92, 057901 (2004).
[Crossref]

Y. Feng, R. Duan, and M. Ying, “Unambiguous discrimination between mixed quantum states,” Phys. Rev. A 70, 012308 (2004).
[Crossref]

F.-G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A 69, 052319 (2004).
[Crossref]

J. C. Bienfang, A. J. Gross, A. Mink, B. J. Hershman, A. Nakassis, X. Tang, R. Lu, D. H. Su, C. W. Clark, C. J. Williams, E. W. Hagley, and J. Wen, “Quantum key distribution with 1.25 Gbps clock synchronization,” Opt. Express 12, 2011–2016 (2004).
[Crossref]

F.-G. Deng and G. L. Long, “Bidirectional quantum key distribution protocol with practical faint laser pulses,” Phys. Rev. A 70, 012311 (2004).
[Crossref]

D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325–360 (2004).

2003 (2)

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

F.-G. Deng, G. L. Long, and X.-S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[Crossref]

2002 (2)

G.-L. Long and X.-S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[Crossref]

S. Zhang and M. Ying, “Set discrimination of quantum states,” Phys. Rev. A 65, 062322 (2002).
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2001 (1)

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of free-space QSDC system. Att, attenuator; BS, beam splitter; DL, delay line; FPGA, field-programmable gate array; FR, Faraday rotator; PBS, polarization beam splitter; PC, polarization controller; PM, phase modulator; PMCIR, polarization-maintaining circulator; PMFC, polarization-maintaining fiber coupler; SPD, single-photon detector; TFOC, triplet fiber-optic collimator. Blue, yellow, and red lines are the electric line, optical fiber line, and free-space path, respectively.
Fig. 2.
Fig. 2. Interference fringes. Driving voltage ranges from 6  V to +6  V with a half-wave voltage 4.8 V and a step of about 0.1 V. The interference fringe of a single-trip (photons transmitted from Bob-to-Alice) is obtained from Alice’s detection. More specifically, the counts are recorded by Alice’s SPD at each step when she drives the voltage of her PM. By contrast, when the photons are received by Bob (after their trip Bob-Alice-Bob), he drives the voltage of his PM and records counts by his SPD to obtain the interference fringe of the round-trip.
Fig. 3.
Fig. 3. Error rates during image file transmission. Dashed lines represent the mean values of DBER, and dash-dotted lines show the mean values of QBER. The definition of DBER and QBER is given in Section 2.A, while the experimental approach for accessing them is introduced in Section 2.B.
Fig. 4.
Fig. 4. Illustration of Eve’s attack strategies. n, the number of photons in a pulse in the forward quantum channel; EμBA is the error rate of the Bob-Alice channel, which is also called as DBER; QμBA, the overall signal gain of Alice; edetBA, the erroneous signal detection of Alice; ρBE, the joint state after Eve’s attack in the forward quantum channel; QμBAE, the overall signal gain of Eve; ρBAE, the joint state after Alice’s information encoding and Eve’s attacks in the two quantum channels; EμBAB is QBER; QμBAB, the overall signal gain of Bob; edetBAB is the erroneous signal detection of Bob.
Fig. 5.
Fig. 5. Secrecy capacities versus the attenuation given the collective attack as well as the PNS and USD attack under the framework of GLLP analysis. The curves labeled by different markers represent the data with different mean photon numbers.
Fig. 6.
Fig. 6. Comparison of the secrecy capacities calculated by the GLLP theory and the decoy-state method. Simulations in the decoy-state method using μ=0.1, ν1=0.07, ν2=0.0445, and ν3=0.03 and in the GLLP theory using μ=0.1 are performed. In the secrecy capacity Cs,1+2, we have considered the contribution both from single-photon states and two-photon states, while Cs,1 has not considered the contribution from two-photon states. The two yellow areas represent the contribution of two-photon states to the secrecy capacity.

Equations (26)

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Cs=max{p0}{I(A:B)I(A:E)},
U|0B|0B|E=|0B|0B|E0000+|0B|1B|E0001=|φ1,U|1B|1B|E=|1B|0B|E1110+|1B|1B|E1111=|φ2,U|+B|+B|E=|φ3,U|B|B|E=|φ4,
YU|0B|0B|E=|0B|1B|E0000+|0B|0B|E0001=|φ5,YU|1B|1B|E=|1B|1B|E1110+|1B|0B|E1111=|φ6,YU|+B|+B|E=|φ7,YU|B|B|E=|φ8.
ρBEA=p0·ρBE0+p1·ρBE1=14(p0|φ1φ1|+p0|φ2φ2|+p0|φ3φ3|+p0|φ4φ4|+p1|φ5φ5|+p1|φ6φ6|+p1|φ7φ7|+p1|φ8φ8|),
I(A:E)χ=max{U}{S(ρBEA)p0·S(ρBE0)p1·S(ρBE1)},
G=14[p0φ1|φ1p0φ1|φ2p0p1φ1|φ8p0φ2|φ1p0φ2|φ2p0p1φ2|φ8p0p1φ8|φ1p0p1φ8|φ2p1φ8|φ8].
E0000|E1110=E0001|E1111=0,E0000|E0001=E1110|E1111=0,E0001|E1110=0,E0000|E1111=12e2BA,
I(A:E)n=2=12h(2e2BA)+12.
tBA=10(αBA10),tBAB=10(αBAB10),
ηBA=tBAηoptBAηDA,ηBAB=tBABηoptBABηDB,
QμBA=n=0Qμ,nBA=n=0p(n,μ)YnA=Y0A+1eηBAμ,QμBAE=n=0Qμ,nBAEn=0[Qμ,nBAp(n,μ)Y0A]max{1,γEγA},QμBAB=n=0Qμ,nBAB=n=0p(n,μ)YnB=Y0B+1eηBABμ,
EμBA=e0Y0A+edetBA(1eηBAμ)QμBA,EμBAB=e0Y0B+edetBAB(1eηBABμ)QμBAB,
I(A:B)=QμBAB[1h(EμBAB)],
I(A:E)n=1=Qμ,n=1BAEh(2e1BA),
Cs=QμBAB[1h(EμBAB)]Qμ,n=1BAEh(2e1BA)Qμ,n=2BAE[12h(2e2BA)+12]Qμ,n3BAE·1.
e1BA=EμBA1p(n2,μ)QμBA,
e1BA,U=Eν3BAQν3BAeν3e0Y0AY1A,Lν3,
e2BA,U=2(Eν2BAQν2BAeν2ν2ν3Eν3BAQν3BAeν3+ν2ν3ν3e0Y0A)Y2A,Lν2(ν2ν3),
Y1A,L=μ2(Qν2BAeν2Qν3BAeν3)(ν22ν32)(QμBAeμY0A)μ(ν2ν3)(μν2ν3),
Y2A,L=2μ(Qν1BAeν1Qν2BAeν2)2(ν1ν2)(QμBAeμY0A)μ(ν1ν2)(ν1+ν2μ).
0<ν3<ν223μ<ν134μ,ν1+ν2>μ,ν2+ν3<μ,ν1ν2ν13ν23μ2=0.
YnAY0A=m=0fn(m,μ){1(1γA)m[1(1γA)m]Y0A}m=0fn(m,μ)[1(1γA)m]
YnE=m=0fn(m,μ){1(1γE)m[1(1γE)m]Y0E}+Y0Em=0fn(m,μ)[1(1γE)m],
YnE=(YnAY0A)m=0fn(m,μ)[1(1γE)m]m=0fn(m,μ)[1(1γA)m](YnAY0A)max{1,γEγA},
{m=0fn(m,μ)[1(1γE)m]m=0fn(m,μ)[1(1γA)m]1          ifγAγE,m=0fn(m,μ)[1(1γE)m]m=0fn(m,μ)[1(1γA)m]γEγA          ifγA<γE.
Qμ,nBAE=p(n,μ)YnE[Qμ,nBAp(n,μ)YnA]max{1,γEγA}.