Abstract

We propose and study the feasibility of wireless quantum key distribution (QKD) in indoor environments. Such systems are essential in providing wireless access to the developing quantum communications networks. We find a practical regime of operation, where, in the presence of external light sources and loss, secret keys can be exchanged. Our findings identify the trade-off between the acceptable amount of background light and the receiver field of view, where the latter specifies the type of equipment needed for the end user and its range of movements. In particular, we show that, using a proper setting, we can provide mobility for the QKD users without imposing stringent conditions on beam steering.

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References

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2017 (2)

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref]

H. Chun, I. Choi, G. Faulkner, L. Clarke, B. Barber, G. George, C. Capon, A. Niskanen, J. Wabnig, D. O’Brien, and D. Bitauld, “Handheld free space quantum key distribution with dynamic motion compensation,” Opt. Express 25, 6784–6795 (2017).
[Crossref]

2016 (3)

C. Ma, W. D. Sacher, Z. Tang, J. C. Mikkelsen, Y. Yang, F. Xu, T. Thiessen, H.-K. Lo, and J. K. S. Poon, “Silicon photonic transmitter for polarization-encoded quantum key distribution,” Optica 3, 1274–1278 (2016).
[Crossref]

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]

R. Barends, A. Shabani, L. Lamata, J. Kelly, A. Mezzacapo, U. Las Heras, R. Babbush, A. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, E. Lucero, A. Megrant, J. Y. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, C. Quintana, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, E. Solano, H. Neven, and J. M. Martinis, “Digitized adiabatic quantum computing with a superconducting circuit,” Nature 534, 222–226 (2016).
[Crossref]

2015 (4)

S. Bahrani, M. Razavi, and J. A. Salehi, “Orthogonal frequency-division multiplexed quantum key distribution,” J. Lightwave Technol. 33, 4687–4698 (2015).
[Crossref]

G. Vest, M. Rau, L. Fuchs, G. Corrielli, H. Weier, S. Nauerth, A. Crespi, R. Osellame, and H. Weinfurter, “Design and evaluation of a handheld quantum key distribution sender module,” IEEE J. Sel. Top. Quantum Electron. 21, 131–137 (2015).
[Crossref]

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100-Gb/s indoor wide field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27, 367–370 (2015).
[Crossref]

C. Wang, S.-H. Sun, X.-C. Ma, G.-Z. Tang, and L.-M. Liang, “Reference-frame-independent quantum key distribution with source flaws,” Phys. Rev. A 92, 042319 (2015).
[Crossref]

2014 (6)

C. Panayi, M. Razavi, X. Ma, and N. Lütkenhaus, “Memory-assisted measurement-device-independent quantum key distribution,” New J. Phys 16, 043005 (2014).
[Crossref]

K. A. Patel, J. F. Dynes, M. Lucamarini, I. Choi, A. W. Sharpe, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution for 10  Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104, 051123 (2014).
[Crossref]

K. Tamaki, M. Curty, G. Kato, H.-K. Lo, and K. Azuma, “Loss-tolerant quantum cryptography with imperfect sources,” Phys. Rev. A 90, 052314 (2014).
[Crossref]

Z.-Q. Yin, C.-H. F. Fung, X. Ma, C.-M. Zhang, H.-W. Li, W. Chen, S. Wang, G.-C. Guo, and Z.-F. Han, “Mismatched-basis statistics enable quantum key distribution with uncharacterized qubit sources,” Phys. Rev. A 90, 052319 (2014).
[Crossref]

B. Sanguinetti, A. Martin, H. Zbinden, and N. Gisin, “Quantum random number generation on a mobile phone,” Phys. Rev. X 4, 031056 (2014).
[Crossref]

D. Chitnis and S. Collins, “A SPAD-based photon detecting system for optical communications,” J. Lightwave Technol. 32, 2028–2034 (2014).
[Crossref]

2013 (2)

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature 501, 69–72 (2013).
[Crossref]

2012 (1)

M. Razavi, “Multiple-access quantum key distribution networks,” IEEE Trans. Commun. 60, 3071–3079 (2012).
[Crossref]

2011 (2)

2010 (1)

A. Laing, V. Scarani, J. G. Rarity, and J. L. O’Brien, “Reference-frame-independent quantum key distribution,” Phys. Rev. A 82, 012304 (2010).
[Crossref]

2009 (4)

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]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3, 696–705 (2009).
[Crossref]

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001 (2009).
[Crossref]

F. Xu, W. Chen, S. Wang, Z. Yin, Y. Zhang, Y. Liu, Z. Zhou, Y. Zhao, H. Li, D. Liu, Z. Han, and G. Guo, “Field experiment on a robust hierarchical metropolitan quantum cryptography network,” Chin. Sci. Bull. 54, 2991–2997 (2009).
[Crossref]

2007 (1)

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]

2006 (1)

J. L. Duligall, M. S. Godfrey, K. A. Harrison, W. J. Munro, and J. G. Rarity, “Low cost and compact quantum key distribution,” New J. Phys. 8, 249 (2006).
[Crossref]

2005 (3)

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

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

H.-K. Lo, H.-F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” J. Cryptol. 18, 133–165 (2005).
[Crossref]

2003 (1)

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

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

2000 (1)

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

1999 (1)

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594–2597 (1999).
[Crossref]

1997 (1)

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[Crossref]

1979 (1)

F. R. Gfeller and U. Bapst, “Wireless in-house data communication via diffuse infrared radiation,” Proc. IEEE 67, 1474–1486 (1979).
[Crossref]

1978 (1)

R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM 21, 120–126 (1978).
[Crossref]

Adleman, L.

R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM 21, 120–126 (1978).
[Crossref]

Allacher, A.

Alléaume, R.

M. Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. Dynes, S. Fasel, S. Fossier, M. Fürst, J.-D. Gautier, O. Gay, N. Gisin, P. Grangier, A. Happe, Y. Hasani, M. Hentschel, H. Hübel, G. Humer, T. Länger, M. Legré, R. Lieger, J. Lodewyck, T. Lorünser, N. Lütkenhaus, A. Marhold, T. Matyus, O. Maurhart, L. Monat, S. Nauerth, J.-B. Page, A. Poppe, E. Querasser, G. Ribordy, S. Robyr, L. Salvail, A. W. Sharpe, A. J. Shields, D. Stucki, M. Suda, C. Tamas, T. Themel, R. T. Thew, Y. Thoma, A. Treiber, P. Trinkler, R. Tualle-Brouri, F. Vannel, N. Walenta, H. Weier, H. Weinfurter, I. Wimberger, Z. L. Yuan, H. Zbinden, and A. Zeilinger, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001 (2009).
[Crossref]

Amin, M.

M. Johnson, M. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A. Berkley, J. Johansson, P. Bunyk, E. M. Chapple, C. Enderud, J. P. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, C. J. S. Truncik, S. Uchaikin, J. Wang, B. Wilson, and G. Rose, “Quantum annealing with manufactured spins,” Nature 473, 194–198 (2011).
[Crossref]

Ardehali, M.

H.-K. Lo, H.-F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” J. Cryptol. 18, 133–165 (2005).
[Crossref]

Asai, T.

Azuma, K.

K. Tamaki, M. Curty, G. Kato, H.-K. Lo, and K. Azuma, “Loss-tolerant quantum cryptography with imperfect sources,” Phys. Rev. A 90, 052314 (2014).
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K. A. Patel, J. F. Dynes, M. Lucamarini, I. Choi, A. W. Sharpe, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution for 10  Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104, 051123 (2014).
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Figures (9)

Fig. 1.
Fig. 1. Wireless QKD link in an indoor setup. The transmitter is mobile, while the QKD receiver is fixed on the ceiling. For illustration purposes, the QKD receiver is depicted away from the center. In practice, it should be optimally placed at the center of the ceiling.
Fig. 2.
Fig. 2. Power spectral density of two LED bulbs, equivalent to a 60-W incandescent lamp: a 650-lumen cool white LED manufactured by AURAGLOW (dashed), and a 805-lumen warm white LED bulb manufactured by INTEGRAL (solid). The wriggly form of the curves at the two far ends of the spectrum is due to the measurement precision.
Fig. 3.
Fig. 3. Total loss, 10 log 10 ( η d H DC / 2 ) , for the QKD source in center and corner positions. Path loss depends on the semi-angle at half power, the position of the QKD source, and the receiver’s FOV.
Fig. 4.
Fig. 4. Secret key rate per transmitted pulse when the lighting source is off, and the background noise is only due to the ambient noise. The QKD source is sending light upward with Θ 1 / 2 = 30 ° . The decoy-state BB84 protocol with an infinite number of decoy states and perfect encoders are employed here.
Fig. 5.
Fig. 5. (a) Background noise (BN) in count per pulse (c/p), generated by the artificial light source, collected by the QKD receiver versus FOV. (b) The channel loss, 1 / H DC , and QBER, E μ , versus FOV. The QKD source is located either at the center or at the corner of the room floor. The PSD of the bulb is 10 5    W / nm .
Fig. 6.
Fig. 6. Secret key rate per transmitted pulse for a QKD source ( Θ 1 / 2 = 30 ° ) at the center of the floor in the presence of a lighting source. The decoy-state BB84 protocol with an infinite number of decoy states and perfect encoders are assumed here.
Fig. 7.
Fig. 7. Secret key rate per transmitted pulse for a QKD source with ( Θ 1 / 2 = 30 ° ) in a corner of the room in the presence of a lighting source. The decoy-state BB84 protocol with an infinite number of decoy states and perfect encoders are employed.
Fig. 8.
Fig. 8. Secret key rate per transmitted pulse for the QKD source in a corner of the room with additional beam steering: the QKD beam is directed into the receiver with Θ 1 / 2 = 5 ° . The decoy-state BB84 protocol with an infinite number of decoy states and perfect encoders are employed.
Fig. 9.
Fig. 9. Secret key rate per transmitted pulse versus the QKD receiver FOV for different QKD protocols (PE, perfect encoding; DS, decoy state; SF, source flaw; V + W, vacuum + weak). (a) The QKD source is located at the center of the room. (b) The QKD source is located at a corner of the room. The PSD of the bulb is 10 6    W / nm .

Tables (1)

Tables Icon

Table 1. Nominal Values Used for Our System Parameters

Equations (30)

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H DC = { A ( m + 1 ) 2 π d 2 cos ( ϕ ) m T s ( ψ ) × g ( ψ ) cos ( ψ ) , 0 ψ Ψ c , 0 elsewhere ,
m = ln 2 ln ( cos ( Θ 1 / 2 ) )
g ( ψ ) = { n 2 sin 2 ( Ψ c ) , 0 ψ Ψ c 0 ψ > Ψ c ,
P n , isotropic ( λ ) = p n ( λ ) Δ λ T s A n 2 .
n B ( 1 ) = P n , isotropic ( λ ) τ η d / 2 h c / λ ,
H Ref = { A ( m 1 + 1 ) 2 π 2 d 1 2 d 2 2 cos ( ϕ ) m 1 r T s ( ψ ) g ( ψ ) × d A cos ( α ) cos ( β ) cos ( ψ ) , 0 ψ Ψ c , 0 elsewhere ,
n B ( 2 ) = S ( λ ) Δ λ τ η d / 2 h c / λ walls , floor H Ref .
R decoy q { Q 1 ( 1 h ( e 1 ) f Q μ h ( E μ ) } ,
Q 1 = Y 1 μ e μ ,
Y 1 = 1 ( 1 η ) ( 1 n N ) 2 ,
e 1 = e 0 Y 1 ( e 0 e d ) η ( 1 n N ) Y 1 ,
Q μ = 1 e η μ ( 1 n N ) 2 .
E μ = e 0 Q μ ( e 0 e d ) ( 1 e η μ ) ( 1 n N ) Q μ .
h ( x ) = x log 2 x ( 1 x ) log 2 ( 1 x ) .
Y 1 Y 1 L , ν 1 , ν 2 = μ μ ν 1 μ ν 2 ν 1 2 + ν 2 2 [ Q ν 1 e ν 1 Q ν 2 e ν 2 ν 1 2 ν 2 2 μ 2 ( Q μ e μ Y 0 L ) ] ,
Q 1 Q 1 L , ν 1 , ν 2 = μ 2 e μ μ ν 1 μ ν 2 ν 1 2 + ν 2 2 [ Q ν 1 e ν 1 Q ν 2 e ν 2 ν 1 2 ν 2 2 μ 2 ( Q μ e μ Y 0 L ) ] ,
e 1 e 1 U , ν 1 , ν 2 = E ν 1 Q ν 1 e ν 1 E ν 2 Q ν 2 e ν 2 ( ν 1 ν 2 ) Y 1 L , ν 1 , ν 2 ,
Y 0 Y 0 L = max { ν 1 Q ν 2 e ν 2 ν 2 Q ν 1 e ν 1 ν 1 ν 2 , 0 } .
R = Q 1 [ 1 h ( e x ( 1 ) ) ] Q μ f h ( E μ ) ,
e x ( 1 ) = Y 1 X | 0 X + Y 0 X | 1 X Y 1 X | 0 X + Y 0 X | 1 X + Y 1 X | 1 X + Y 0 X | 0 X ,
Y s X | j X = η [ P s X | j X ( 1 n N ) + 1 2 n N ] + ( 1 η ) [ n N ( 1 n N ) + n N 2 / 2 ] ,
X B = cos ( ξ ) X A + sin ( ξ ) Y A and Y B = cos ( ξ ) Y A sin ( ξ ) X A .
C = X A X B 2 + X A Y B 2 + Y A X B 2 + Y A Y B 2 ,
C = ( 1 2 E X X ) 2 + ( 1 2 E X Y ) 2 + ( 1 2 E Y X ) 2 + ( 1 2 E Y Y ) 2 ,
C = 2 ( 1 2 e 1 ) 2 .
I E = ( 1 e 1 ) h [ 1 + ν max 2 ] + e 1 h [ 1 + f ( ν max ) 2 ] ,
ν max = min [ 1 1 e 1 C / 2 , 1 ]
f ( ν max ) = C / 2 ( 1 e 1 ) 2 ν max 2 e 1 .
I E = e 1 + ( 1 e 1 ) h [ ( 1 3 e 1 / 2 ) ( 1 e 1 ) ] .
R Q 1 ( 1 I E ) Q μ f h ( E μ ) ,

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