Cost-Efficient Quantum Key Distribution (QKD) Over WDM Networks

Yuan Cao; Yongli Zhao; Jianquan Wang; Xiaosong Yu; Zhangchao Ma; Jie Zhang

doi:10.1364/JOCN.11.000285

Journal of Optical Communications and Networking
Vol. 11,
Issue 6,
pp. 285-298
(2019)
•https://doi.org/10.1364/JOCN.11.000285

Cost-Efficient Quantum Key Distribution (QKD) Over WDM Networks

Yuan Cao, Yongli Zhao, Jianquan Wang, Xiaosong Yu, Zhangchao Ma, and Jie Zhang

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Yuan Cao, Yongli Zhao, Jianquan Wang, Xiaosong Yu, Zhangchao Ma, and Jie Zhang, "Cost-Efficient Quantum Key Distribution (QKD) Over WDM Networks," J. Opt. Commun. Netw. 11, 285-298 (2019)

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Abstract

Quantum key distribution (QKD) uses the laws of quantum mechanics to distribute secret keys with information-theoretic security. To realize QKD for secure communications among multiple distant users, fiber-based QKD networks can be deployed with today’s available technologies. Incorporating QKD into existing wavelength-division multiplexing (WDM) network infrastructure provides a practical way to reduce the difficulty and cost of QKD networking. Nonetheless, the costs of QKD nodes and QKD links are still considered as the major barriers to long-distance QKD network deployment in practice. In this work, we study how to minimize the cost of deploying QKD-over-WDM backbone networks. We introduce a general architecture of QKD-over-WDM backbone networks. A novel cost-oriented model is defined to elaborate the cost-minimized problem, in which various QKD network components including QKD transceivers, QKD auxiliary equipment for QKD backbone nodes and trusted repeater nodes (TRNs), and QKD links are considered. The physical-layer parameters such as secret-key rate, physical distance, and the layout of TRNs are also incorporated in our defined model. We develop an integer linear programming (ILP) model and a novel cost-efficient QKD networking (CEQN) heuristic algorithm to address the cost-minimized problem. The extensive simulations indicate that our proposed approaches are effective in reducing the cost of deploying QKD-over-WDM backbone networks, where the designed CEQN algorithm is efficient to demonstrate similar to the ILP model. Finally, some open issues in future work are discussed, given that this work only presents an early high-level analysis as opposed to a definitive detailed model.

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Notations	Definitions
$G (V, E)$	Substrate QKD-over-WDM backbone network topology
$V$	Set of nodes (including QBNs and OXCs)
$m$ , $n$	Index of the QBNs on the substrate topology $G (V, E)$
$E$	Set of physical links
$L_{m n}$	Physical distance of a fiber link between QBNs $m$ and $n$
$W$	Set of wavelength channels on each fiber link
$W_{Q}$	Set of wavelength channels planned as QChs
$W_{P}$	Set of wavelength channels planned as PChs
$D$	Physical distance between two neighboring QKD nodes
$k$	Secret-key rate corresponding to the physical distance $D$
$R$	Set of QKD requests among network-wide QKD users
$r (s_{r}, d_{r}, v_{r})$	QKD request between two distant QKD users
$s_{r}$	Source QBN of QKD request $r$
$d_{r}$	Destination QBN of QKD request $r$
$L_{s d}$	Physical distance between QBNs $s_{r}$ and $d_{r}$
$v_{r}$	Secret-key rate demand of QKD request $r$
$N_{r}$	Required number of QKD transceivers for QKD request $r$
$N_{r}^{'}$	Required number of TRNs for QKD request $r$
$L_{r}$	Physical length of QKD links for QKD request $r$
$P_{r}$	The shortest QKD path for QKD request $r$
$W_{r}$	Required number of QChs for QKD request $r$
$W_{p}$	Available wavelength channels in $W_{Q}$ along $P_{r}$
$N_{a}$	Total required number of QKD transceivers
$N_{a}^{'}$	Total required number of TRNs
$L_{a}$	Total required physical length of QKD links
$C_{Q}$	Cost of a QKD transceiver
$C_{B}$	Cost of QKD auxiliary equipment for a QBN
$C_{T}$	Cost of QKD auxiliary equipment for a TRN
$C_{W}$	Cost per kilometer of a wavelength channel on a fiber link
$C_{R}$	Total cost of deploying QKD-over-WDM backbone networks
$Z_{(m, n), λ}^{(s_{r}, d_{r}, v_{r})}$	Boolean variable, is 1 if the QKD request $r (s_{r}, d_{r}, v_{r})$ occupies wavelength $λ$ on link ( $m$ , $n$ ), and 0 otherwise

Different Scenarios	$N_{a}$	$C_{Q}$ (US$)	$C_{B}$ (US$)	$C_{T}$ (US$)	$C_{W}$ (US$)
Rather pessimistic scenario with fixed cost values	$\geq 1$	40,000	30,000	20,000	8
Optimized scenario with fixed cost values	$\geq 1$	10,000	10,000	5,000	5
Dynamic scenario with flexible cost values	1	40,000	30,000	20,000	8
	2–2000	$- 15 \cdot N_{a} + 40,000$	$- 10 \cdot N_{a} + 30,000$	$- 7.5 \cdot N_{a} + 20,000$	$- 0.0015 \cdot N_{a} + 8$
	$> 2000$	10,000	10,000	5,000	5

Notations	Definitions
$G (V, E)$	Substrate QKD-over-WDM backbone network topology
$V$	Set of nodes (including QBNs and OXCs)
$m$ , $n$	Index of the QBNs on the substrate topology $G (V, E)$
$E$	Set of physical links
$L_{m n}$	Physical distance of a fiber link between QBNs $m$ and $n$
$W$	Set of wavelength channels on each fiber link
$W_{Q}$	Set of wavelength channels planned as QChs
$W_{P}$	Set of wavelength channels planned as PChs
$D$	Physical distance between two neighboring QKD nodes
$k$	Secret-key rate corresponding to the physical distance $D$
$R$	Set of QKD requests among network-wide QKD users
$r (s_{r}, d_{r}, v_{r})$	QKD request between two distant QKD users
$s_{r}$	Source QBN of QKD request $r$
$d_{r}$	Destination QBN of QKD request $r$
$L_{s d}$	Physical distance between QBNs $s_{r}$ and $d_{r}$
$v_{r}$	Secret-key rate demand of QKD request $r$
$N_{r}$	Required number of QKD transceivers for QKD request $r$
$N_{r}^{'}$	Required number of TRNs for QKD request $r$
$L_{r}$	Physical length of QKD links for QKD request $r$
$P_{r}$	The shortest QKD path for QKD request $r$
$W_{r}$	Required number of QChs for QKD request $r$
$W_{p}$	Available wavelength channels in $W_{Q}$ along $P_{r}$
$N_{a}$	Total required number of QKD transceivers
$N_{a}^{'}$	Total required number of TRNs
$L_{a}$	Total required physical length of QKD links
$C_{Q}$	Cost of a QKD transceiver
$C_{B}$	Cost of QKD auxiliary equipment for a QBN
$C_{T}$	Cost of QKD auxiliary equipment for a TRN
$C_{W}$	Cost per kilometer of a wavelength channel on a fiber link
$C_{R}$	Total cost of deploying QKD-over-WDM backbone networks
$Z_{(m, n), λ}^{(s_{r}, d_{r}, v_{r})}$	Boolean variable, is 1 if the QKD request $r (s_{r}, d_{r}, v_{r})$ occupies wavelength $λ$ on link ( $m$ , $n$ ), and 0 otherwise

Different Scenarios	$N_{a}$	$C_{Q}$ (US$)	$C_{B}$ (US$)	$C_{T}$ (US$)	$C_{W}$ (US$)
Rather pessimistic scenario with fixed cost values	$\geq 1$	40,000	30,000	20,000	8
Optimized scenario with fixed cost values	$\geq 1$	10,000	10,000	5,000	5
Dynamic scenario with flexible cost values	1	40,000	30,000	20,000	8
	2–2000	$- 15 \cdot N_{a} + 40,000$	$- 10 \cdot N_{a} + 30,000$	$- 7.5 \cdot N_{a} + 20,000$	$- 0.0015 \cdot N_{a} + 8$
	$> 2000$	10,000	10,000	5,000	5

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Journal of Optical Communications and Networking