Abstract

Continuous-variable quantum key distribution (CVQKD) provides an approach for secure communication in optical fiber communication systems. However, its practical implementation has been hindered by low secret key bit rates that are usually limited to several bits/s to hundreds of kbits/s at distances of more than 25 kilometers. In this paper, we use a pair of optical frequency combs (OFCs) for both multiple parallel transmission and coherent reception, which assign multiple sub-channels involving multiple independent secret keys in a single fiber to increase the key bit rate. The first and last sub-channels are selected for propagating phase references to compensate the phase offset between two free-running combs. We analyze possible excess noise caused by dispersive walk-off in the transmission, imperfect phase compensation in the reception and photon leakage from the phase references. Compared to the previous single-channel CVQKD method, simulation results show more than a factor of 20 increase in the secret key rate at a transmission distance of $35$ km and the number of comb lines of $35$.

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

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References

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2019 (2)

2018 (5)

T. Wang, P. Huang, Y. Zhou, W. Liu, and G. Zeng, “Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator,” Phys. Rev. A 97(1), 012310 (2018).
[Crossref]

H. Zhang, Y. Mao, D. Huang, J. Li, L. Zhang, and Y. Guo, “Security analysis of orthogonal-frequency-division-multiplexing–based continuous-variable quantum key distribution with imperfect modulation,” Phys. Rev. A 97(5), 052328 (2018).
[Crossref]

L. Lundberg, M. Karlsson, A. Lorences-Riesgo, M. Mazur, J. Schröder, and P. Andrekson, “Frequency comb-based WDM transmission systems enabling joint signal processing,” Appl. Sci. 8(5), 718 (2018).
[Crossref]

Z. Zhang, C. Chen, Q. Zhuang, F. N. Wong, and J. H. Shapiro, “Experimental quantum key distribution at 1.3 gigabit-per-second secret-key rate over a 10 dB loss channel,” Quantum Sci. Technol. 3(2), 025007 (2018).
[Crossref]

P. Huang, J. Huang, Z. Zhang, and G. Zeng, “Quantum key distribution using basis encoding of gaussian-modulated coherent states,” Phys. Rev. A 97(4), 042311 (2018).
[Crossref]

2017 (3)

Y. Guo, Q. Liao, Y. Wang, D. Huang, P. Huang, and G. Zeng, “Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction,” Phys. Rev. A 95(3), 032304 (2017).
[Crossref]

A. Marie and R. Alléaume, “Self-coherent phase reference sharing for continuous-variable quantum key distribution,” Phys. Rev. A 95(1), 012316 (2017).
[Crossref]

K. Qu, S. Zhao, X. Li, Z. Zhu, D. Liang, and D. Liang, “Ultra-flat and broadband optical frequency comb generator via a single mach–zehnder modulator,” IEEE Photonics Technol. Lett. 29(2), 255–258 (2017).
[Crossref]

2016 (4)

J. N. Kemal, J. Pfeifle, P. Marin-Palomo, M. D. G. Pascual, S. Wolf, F. Smyth, W. Freude, and C. Koos, “Multi-wavelength coherent transmission using an optical frequency comb as a local oscillator,” Opt. Express 24(22), 25432–25445 (2016).
[Crossref]

H. Qin, R. Kumar, and R. Alléaume, “Quantum hacking: Saturation attack on practical continuous-variable quantum key distribution,” Phys. Rev. A 94(1), 012325 (2016).
[Crossref]

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
[Crossref]

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
[Crossref]

2015 (9)

S. Bahrani, M. Razavi, and J. A. Salehi, “Orthogonal frequency-division multiplexed quantum key distribution,” J. Lightwave Technol. 33(23), 4687–4698 (2015).
[Crossref]

J. Pfeifle, V. Vujicic, R. T. Watts, P. C. Schindler, C. Weimann, R. Zhou, W. Freude, L. P. Barry, and C. Koos, “Flexible terabit/s Nyquist-WDM super-channels using a gain-switched comb source,” Opt. Express 23(2), 724–738 (2015).
[Crossref]

V. Ataie, E. Temprana, L. Liu, E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Ultrahigh count coherent WDM channels transmission using optical parametric comb-based frequency synthesizer,” J. Lightwave Technol. 33(3), 694–699 (2015).
[Crossref]

D. Huang, D. Lin, C. Wang, W. Liu, S. Fang, J. Peng, P. Huang, and G. Zeng, “Continuous-variable quantum key distribution with 1 Mbps secure key rate,” Opt. Express 23(13), 17511–17519 (2015).
[Crossref]

F. Xu, M. Curty, B. Qi, L. Qian, and H. K. Lo, “Discrete and continuous variables for measurement-device-independent quantum cryptography,” Nat. Photonics 9(12), 772–773 (2015).
[Crossref]

R. Kumar, H. Qin, and R. Alléaume, “Coexistence of continuous variable qkd with intense dwdm classical channels,” New J. Phys. 17(4), 043027 (2015).
[Crossref]

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
[Crossref]

D. B. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

D. Huang, P. Huang, D. Lin, C. Wang, and G. Zeng, “High-speed continuous-variable quantum key distribution without sending a local oscillator,” Opt. Lett. 40(16), 3695–3698 (2015).
[Crossref]

2014 (6)

T. Shao, E. Martin, P. M. Anandarajah, C. Browning, V. Vujicic, R. Llorente, and L. P. Barry, “Chromatic dispersion-induced optical phase decorrelation in a 60 GHz OFDM-RoF system,” IEEE Photonics Technol. Lett. 26(20), 2016–2019 (2014).
[Crossref]

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Theor. Comput. Sci. 560, 7–11 (2014).
[Crossref]

H. K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8(8), 595–604 (2014).
[Crossref]

Z. Li, Y. C. Zhang, F. Xu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 89(5), 052301 (2014).
[Crossref]

X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and power transfer in multiuser OFDM systems,” IEEE Trans. Wirel. Commun. 13(4), 2282–2294 (2014).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref]

2013 (1)

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7(5), 378–381 (2013).
[Crossref]

2012 (3)

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[Crossref]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

K. Yoshino, M. Fujiwara, A. Tanaka, S. Takahashi, Y. Nambu, A. Tomita, S. Miki, T. Yamashita, Z. Wang, M. Sasaki, and A. Tajima, “High-speed wavelength-division multiplexing quantum key distribution system,” Opt. Lett. 37(2), 223–225 (2012).
[Crossref]

2011 (1)

2010 (1)

A. Leverrier and P. Grangier, “Simple proof that gaussian attacks are optimal among collective attacks against continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 81(6), 062314 (2010).
[Crossref]

2009 (3)

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
[Crossref]

J. Z. Zhang, A. B. Wang, J. F. Wang, and Y. C. Wang, “Wavelength division multiplexing of chaotic secure and fiber-optic communications,” Opt. Express 17(8), 6357–6367 (2009).
[Crossref]

S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers,” J. Phys. B: At., Mol. Opt. Phys. 42(11), 114014 (2009).
[Crossref]

2007 (1)

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).
[Crossref]

2006 (2)

R. Garcia-Patron and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[Crossref]

M. Navascués, F. Grosshans, and A. Acin, “Optimality of gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[Crossref]

2004 (1)

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref]

2003 (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[Crossref]

2002 (2)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[Crossref]

Acin, A.

M. Navascués, F. Grosshans, and A. Acin, “Optimality of gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[Crossref]

Alic, N.

Alléaume, R.

A. Marie and R. Alléaume, “Self-coherent phase reference sharing for continuous-variable quantum key distribution,” Phys. Rev. A 95(1), 012316 (2017).
[Crossref]

H. Qin, R. Kumar, and R. Alléaume, “Quantum hacking: Saturation attack on practical continuous-variable quantum key distribution,” Phys. Rev. A 94(1), 012325 (2016).
[Crossref]

R. Kumar, H. Qin, and R. Alléaume, “Coexistence of continuous variable qkd with intense dwdm classical channels,” New J. Phys. 17(4), 043027 (2015).
[Crossref]

R. Kumar, H. Qin, and R. Alléaume, “Experimental demonstration of the coexistence of continuous-variable quantum key distribution with an intense DWDM classical channel,” in CLEO: QELS_Fundamental Science (Optical Society of America, 2014), pp. FM4A–1.

Anandarajah, P.

Anandarajah, P. M.

T. Shao, E. Martin, P. M. Anandarajah, C. Browning, V. Vujicic, R. Llorente, and L. P. Barry, “Chromatic dispersion-induced optical phase decorrelation in a 60 GHz OFDM-RoF system,” IEEE Photonics Technol. Lett. 26(20), 2016–2019 (2014).
[Crossref]

Andrekson, P.

L. Lundberg, M. Karlsson, A. Lorences-Riesgo, M. Mazur, J. Schröder, and P. Andrekson, “Frequency comb-based WDM transmission systems enabling joint signal processing,” Appl. Sci. 8(5), 718 (2018).
[Crossref]

Ataie, V.

Bahrani, S.

Barry, L. P.

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Theor. Comput. Sci. 560, 7–11 (2014).
[Crossref]

Berta, M.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[Crossref]

Bettelli, S.

H. H. Brunner, L. C. Comandar, F. Karinou, S. Bettelli, D. Hillerkuss, F. Fung, D. Wang, S. Mikroulis, Q. Yi, M. Kuschnerov, A. Poppe, C. Xie, and M. Peev, “A low-complexity heterodyne cv-qkd architecture,” in 2017 19th International Conference on Transparent Optical Networks (ICTON), (2017), pp. 1–4.

Bobrek, M.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
[Crossref]

Bowen, W. P.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref]

Brasch, V.

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Li, J.

H. Zhang, Y. Mao, D. Huang, J. Li, L. Zhang, and Y. Guo, “Security analysis of orthogonal-frequency-division-multiplexing–based continuous-variable quantum key distribution with imperfect modulation,” Phys. Rev. A 97(5), 052328 (2018).
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Liu, L.

Liu, W.

T. Wang, P. Huang, Y. Zhou, W. Liu, and G. Zeng, “Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator,” Phys. Rev. A 97(1), 012310 (2018).
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F. Xu, M. Curty, B. Qi, L. Qian, and H. K. Lo, “Discrete and continuous variables for measurement-device-independent quantum cryptography,” Nat. Photonics 9(12), 772–773 (2015).
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Appl. Sci. (1)

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J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

J. Phys. B: At., Mol. Opt. Phys. (1)

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R. Kumar, H. Qin, and R. Alléaume, “Coexistence of continuous variable qkd with intense dwdm classical channels,” New J. Phys. 17(4), 043027 (2015).
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Figures (8)

Fig. 1.
Fig. 1. The OFC-based multichannel parallel CVQKD system. Alice splits an OFC with center frequency of $f_0^s$ and repetition rate of $f_r^s$ , generating $N$ sub-channels followed by independent Gaussian modulation. Bob detects the received comb by a locally generated OFC with the same parameters as Alice. The outermost two sub-channels are selected as pilot channel for phase compensation.
Fig. 2.
Fig. 2. Schematic presentation of the phase compensation process. $f^s_{n_{min}}$ and $f^s_{n_{max}}$ are the outermost two comb lines of the signal comb that sent by Alice, $f^L_{n_{min}}$ and $f^L_{n_{max}}$ are the outermost two comb lines of the LO comb that generated by Bob.
Fig. 3.
Fig. 3. Temporal decorrelation between quantum and reference signals.
Fig. 4.
Fig. 4. (a) The the excess noise of each sub-channel in terms of the ratio $\langle \hat {N}^{Alice}_{n_{min}}\rangle /V_a$ when $N=7$ . $k$ is the channel index. (b) The excess noise in each sub-channel when the extinction ratio $Re=\{40,50,60\}$ dB. The number of sub-channel is set as $N=15$ .
Fig. 5.
Fig. 5. (a) The secret key rate of the OFC-based CVQKD system against collective attacks in the asymptotic limit with the variable parameter ${\Delta }\nu =\{10^4,10^5,10^6,10^7\}$ Hz. The value of $\langle \hat {N}^{Alice}_{n_{min}}\rangle /V_a$ is chosen to optimize the key rate and the repetition rate of the comb is set as $f_r^s=10$ GHz. (b) The secret key rate of the OFC-based CVQKD system against collective attacks in the asymptotic limit with the variable parameter $f_r^s=\{10,20,30,40\}$ GHz. The value of $\langle \hat {N}^{Alice}_{n_{min}}\rangle /V_a$ is chosen to optimize the key rate and the linewidth is given by $\Delta \nu =10^5$ Hz.
Fig. 6.
Fig. 6. (a) The secret key bit rate of each sub-channel when $N=15$ . (b) The secret key bit rate for the first and last sub-channels when $N={7,15,35}$ . The value of $\langle \hat {N}^{Alice}_{n_{min}}\rangle /V_a$ is chosen to optimize the key rate. Other parameters are $f^s_r=10$ GHz, $\Delta \nu =100$ kHz, and $Re=60$ dB.
Fig. 7.
Fig. 7. (a) Secret key bit rate $R_{tot}$ as a function of modulation variance $V_a$ and transmission distance $L$ . The number of sub-channels are $N=7$ , $N=15$ , and $N=35$ , respectively. (b) The top view of the surface in Fig. 7(a) when $N=35$ . The black solid line represents the bound between positive and negative secret key rate. The value of $\langle \hat {N}^{Alice}_{n_{min}}\rangle /V_a$ is set as 500. Other parameters are $f^s_r=10$ GHz, $\Delta \nu =100$ kHz, and $Re=60$ dB.
Fig. 8.
Fig. 8. (a) The secret key bit rate as a function of the transmission distance. Curves from top to bottom are $N=35$ , $N=15$ , $N=7$ , and the single channel case, respectively. (b) The multichannel gain of the system. Curves from top to bottom are $N=35$ , $N=15$ , and $7$ , respectively. The value of $\langle \hat {N}^{Alice}_{n_{min}}\rangle /V_a$ is chosen to optimize the key rate. Other parameters are $f^s_r=10$ GHz, $\Delta \nu =100$ kHz, and $Re=60$ dB.

Tables (1)

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Table 1. Numerical Parameters

Equations (35)

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s ^ ( t ) = n = n m i n n m a x a ^ n exp { j [ φ ( t ) + 2 π f n s t ] } ,
V k Ra ( σ ) = V k σ 2 e V k 2 2 σ 2 ,
( X r B P r B ) = ( cos θ ^ r sin θ ^ r sin θ ^ r cos θ ^ r ) ( X r A P r A ) .
θ ^ r = tan 1 ( P r B X r A X r B P r A X r B X r A + P r B P r A ) .
θ ^ k = θ ^ n m i n + k n m i n n m a x n m i n ( θ ^ n m a x θ ^ n m i n ) .
( X ^ k B P ^ k B ) = ( cos θ ^ k sin θ ^ k sin θ ^ k cos θ ^ k ) ( X k A P k A ) .
Δ θ n m i n = θ ^ n m i n θ n m i n , Δ θ n m a x = θ ^ n m a x θ n m a x .
Δ θ k e r r o r = θ ^ k θ k = k n m i n n m a x n m i n ( Δ θ n m a x Δ θ n m i n ) + Δ θ n m i n .
V k e r r o r = V n m i n e r r o r + ( k n m i n n m a x n m i n ) 2 ( V n m a x e r r o r + V n m i n e r r o r ) ,
V n m a x e r r o r = χ n m a x + 1 | α n m a x | 2 , V n m i n e r r o r = χ n m i n + 1 | α n m i n | 2 ,
χ n m a x = χ n m i n = 2 η T η T + 2 v e l η T + ε ,
τ i j = D L Δ λ i j ,
θ ^ n m a x = φ n m a x B ( t ) φ n m a x A ( t A ) , θ ^ n m i n = φ n m i n B ( t ) φ n m i n A ( t A ) ,
θ ^ n m a x = φ n m a x B ( t τ k n m a x ) φ n m a x A ( t A ) , θ ^ n m i n = φ n m i n B ( t + τ k n m i n ) φ n m i n A ( t A ) .
φ n m a x B ( t ) = φ n m a x B ( t τ k n m a x ) + 2 π f n m a x τ k n m a x + N n m a x , φ n m i n B ( t + τ k n m i n ) = φ n m i n B ( t ) + 2 π f n m i n τ k n m i n + N n m i n .
θ ^ k = φ n m i n B ( t + τ k n m i n ) φ n m i n A ( t A ) + k n m i n n m a x n m i n [ φ n m a x B ( t τ k n m a x ) φ n m i n B ( t + τ k n m i n ) ] .
V k d i s p = < ( Δ φ ( τ k n m i n ) ) 2 > + ( k n m i n n m a x n m i n ) 2 ( < ( Δ φ ( τ k n m a x ) ) 2 > + < ( Δ φ ( τ k n m i n ) ) 2 > ) ,
< ( Δ φ ( τ k n m a x ) ) 2 > = 2 τ k n m a x t n m a x c , < ( Δ φ ( τ k n m i n ) ) 2 > = 2 τ k n m i n t n m i n c ,
t n m a x c = t n m i n c = 1 π Δ ν .
ε L E = 2 N ^ n m a x A l i c e R e + 2 N ^ n m i n A l i c e R e
ε k = V a ( V k e r r o r + V k d i s p ) + ε L E .
ε k a t t a c k = V a ( V ~ k e r r o r + V k d i s p ) + ε L E + ε E v e ,
V a V ~ k e r r o r + ε E v e V a V k e r r o r .
V a r ( θ ^ k θ k a t t a c k ) < V a r ( θ ^ k θ k ) .
V a r ( θ ^ k a t t a c k θ k ) < V a r ( θ ^ k θ k ) .
R t o t = k R k ,
K k = β I A B χ B E .
G = R t o t R s ,
I A B = 1 2 log 2 V B V B | A = 1 2 log 2 V + χ t o l 1 + χ t o l ,
χ B E = S ( ρ E ) d m B p ( m B ) S ( ρ E m B ) ,
χ B E = i = 1 2 G ( λ i 1 2 ) i = 3 5 G ( λ i 1 2 ) ,
λ 1 , 2 2 = 1 2 ( A ± A 2 4 B ) ,
A = V 2 + T 2 ( V + χ l i n e ) 2 + 2 T ( 1 V 2 ) , B = T 2 ( 1 + V χ l i n e ) 2 ,
λ 3 , 4 2 = 1 2 ( C ± C 2 4 D ) ,
C = A χ h o m + V B + T ( V + χ l i n e ) T ( V + χ t o t ) , D = B V + B χ h o m T ( V + χ t o t ) ,

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