Researching | Loss-tolerant measurement device independent quantum key distribution with reference frame misalignment

Journals >Chinese Optics Letters >Volume 20 >Issue 9 >Page 092701 > Article

Chinese Optics Letters
Vol. 20, Issue 9, 092701 (2022)

Loss-tolerant measurement device independent quantum key distribution with reference frame misalignment

Jipeng Wang, Zhenhua Li, Zhongqi Sun, Tianqi Dou..., Wenxiu Qu, Fen Zhou, Yanxin Han, Yuqing Huang and Haiqiang Ma^*|Show fewer author(s)

Author Affiliations

School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China

show less

DOI: 10.3788/COL202220.092701 Cite this Article Set citation alerts

Jipeng Wang, Zhenhua Li, Zhongqi Sun, Tianqi Dou, Wenxiu Qu, Fen Zhou, Yanxin Han, Yuqing Huang, Haiqiang Ma, "Loss-tolerant measurement device independent quantum key distribution with reference frame misalignment," Chin. Opt. Lett. 20, 092701 (2022) Copy Citation Text

show less

Abstract

Reference frame independent and measurement device independent quantum key distribution (RFI-MDI-QKD) has the advantages of being immune to detector side loopholes and misalignment of the reference frame. However, several former related research works are based on the unrealistic assumption of perfect source preparation. In this paper, we merge a loss-tolerant method into RFI-MDI-QKD to consider source flaws into key rate estimation and compare it with quantum coin method. Based on a reliable experimental scheme, the joint influence of both source flaws and reference frame misalignment is discussed with consideration of the finite-key effect. The results show that the loss-tolerant RFI-MDI-QKD protocol can reach longer key rate performance while considering the existence of source flaws in a real-world implementation.

Keywords

measurement device independence quantum key distribution source flaw

Q_{i α, j β}^{M_{a} M_{b}, U} = Q_{i α, j β}^{M_{a} M_{b}} (1 + ξ^{l r}), Q_{i α, j β}^{M_{a} M_{b}, L} = Q_{i α, j β}^{M_{a} M_{b}} (1 - ξ^{l r}), - \frac{f (ϵ^{1.5})}{\sqrt{N^{M_{a} M_{b}} Q_{i α, j β}^{M_{a} M_{b}}}} \leq ξ^{M_{a} M_{b}} \leq \frac{f (ϵ^{4} / 16)}{\sqrt{N^{M_{a} M_{b}} Q_{i α, j β}^{M_{a} M_{b}}}} .

(1)

View in Article

Y_{i α, j β}^{L} = \frac{μ_{a}^{2} μ_{b} S_{1} - v_{a}^{2} v_{b} S_{2}}{μ_{a} μ_{b} v_{a} v_{b} (μ_{a} - v_{a})}, S_{1} = Q_{i α, j β}^{v_{a} ν_{b}, L} e^{(ν_{a} + ν_{b})} + Q_{i α, j β}^{0_{a} 0_{b}, L} - Q_{i α, j β}^{v_{a} 0_{b}, U} e^{v_{a}} - Q_{i α, j β}^{0_{a} v_{b}, U} e^{v_{b}}, S_{2} = Q_{i α, j β}^{μ_{a} μ_{b}, U} e^{(μ_{a} + μ_{b})} + Q_{i α, j β}^{0_{a} 0_{b}, U} - Q_{i α, j β}^{μ_{a} 0_{b}, L} e^{μ_{a}} - Q_{i α, j β}^{0_{a} μ_{b}, L} e^{μ_{b}}, Y_{i α, j β}^{U} = \frac{e^{(v_{a} + v_{b})} Q_{i α, j β}^{0_{a} 0_{b}, U} + Q_{i α, j β}^{v_{a} v_{b}, U} - e^{v_{a}} Q_{i α, j β}^{v_{a} 0_{b}, L} - e^{v_{b}} Q_{i α, j β}^{0_{a} b_{b}, L}}{ν_{a} v_{b}} .

(2)

View in Article

R_{L} = μ_{a} μ_{b} e^{- (μ_{a} + μ_{b})} (1 - I_{E}) \sum_{α = β = Z} Y_{i α, j β}^{L} - λ_{E C}, I_{E} = (1 - E_{Z Z}^{11, U}) h (\frac{1 + v_{\max}}{2}) + E_{Z Z}^{11, U} h [\frac{1 + f (v_{\max})}{2}], f (v_{\max}) = \frac{\sqrt{\frac{C^{L}}{2} - {(1 - E_{Z Z}^{11, U})}^{2} v_{\max}^{2}}}{E_{Z Z}^{11, U}}, v_{\max} = \min (\frac{1}{1 - E_{Z Z}^{11, U}} \sqrt{\frac{C^{L}}{2}}, 1) .

(3)

View in Article

C^{L} = \sum_{α, β \in {X, Y}} min: {(1 - 2 E_{α β}^{11})}^{2}, s.t. E_{α β}^{11, L} \leq E_{α β}^{11} \leq E_{α β}^{11, U} .

(4)

View in Article

| Ψ_{A} 〉 = \frac{1}{\sqrt{2}} ({| 0_{Z} 〉}_{A 1} \otimes {| ϕ_{0 Z} 〉}_{A 2 E} + {| 1_{Z} 〉}_{A 1} \otimes {| ϕ_{1 Z} 〉}_{A 2 E}),

(5)

View in Article

| Ψ_{A} 〉 = \frac{1}{\sqrt{2}} ({| 0_{X} 〉}_{A 1} \otimes {| ϕ_{0 X}^{vir} 〉}_{A 2 E} + {| 1_{X} 〉}_{A 1} \otimes {| ϕ_{1 X}^{vir} 〉}_{A 2 E}), | Ψ_{A} 〉 = \frac{1}{\sqrt{2}} ({| 0_{Y} 〉}_{A 1} \otimes {| ϕ_{0 Y}^{vir} 〉}_{A 2 E} + {| 1_{Y} 〉}_{A 1} \otimes {| ϕ_{1 Y}^{vir} 〉}_{A 2 E}) .

(6)

View in Article

Y_{i α, j β}^{vir} = P_{i α}^{vir} P_{j β}^{vir} [S_{σ_{t}^{A}}^{i α, vir} {(S_{σ_{t}^{B}}^{j β, vir})}^{T}] \cdot q_{σ_{t}^{A} \otimes σ_{t}^{B}},

(7)

View in Article

S_{σ_{t}^{A}}^{i α, vir} = [S_{I^{A}}^{i α, vir}, S_{X^{A}}^{i α, vir}, S_{Y^{A}}^{i α, vir}, S_{Z^{A}}^{i α, vir}], S_{σ_{t}^{B}}^{j β, vir} = [S_{I^{B}}^{j β, vir}, S_{X^{B}}^{j β, vir}, S_{Y^{B}}^{j β, vir}, S_{Z^{B}}^{j β, vir}], q_{σ_{t}^{A} \otimes σ_{t}^{B}} = [q_{I^{A} \otimes I^{B}}, q_{I^{A} \otimes X^{B}}, q_{I^{A} \otimes Y^{B}}, q_{I^{A} \otimes Z^{B}}, q_{X^{A} \otimes I^{B}}, q_{X^{A} \otimes X^{B}}, q_{X^{A} \otimes Y^{B}}, q_{X^{A} \otimes Z^{B}}, q_{Y^{A} \otimes I^{B}}, q_{Y^{A} \otimes X^{B}}, q_{Y^{A} \otimes Y^{B}}, q_{Y^{A} \otimes Z^{B}}, q_{Z^{A} \otimes I^{B}}, q_{Z^{A} \otimes X^{B}}, q_{Z^{A} \otimes Y^{B}}, q_{Z^{A} \otimes Z^{B}}] .

(8)

View in Article

q_{σ_{t}^{A} \otimes σ_{t}^{B}} = \frac{Y_{i α, j β}}{P_{i α} P_{j β} [S_{σ_{t}^{A}}^{i α} {(S_{σ_{t}^{B}}^{j β})}^{T}]} .

(9)

View in Article

{| ϕ_{0 Z} 〉}_{A} = | 0_{Z} 〉, {| ϕ_{1 Z} 〉}_{A} = | 1_{Z} 〉, {| ϕ_{0 X} 〉}_{A} = \frac{| 0_{Z} 〉 + | 1_{Z} 〉}{\sqrt{2}} = | 0_{X} 〉, {| ϕ_{0 Y} 〉}_{A} = \frac{| 0_{Z} 〉 + i | 1_{Z} 〉}{\sqrt{2}} = | 0_{Y} 〉,

(10)

View in Article

{| ϕ_{0 Z} 〉}_{B} = \cos (δ_{1}) | 0_{Z} 〉 + \sin (δ_{1}) | 1_{Z} 〉, {| ϕ_{1 Z} 〉}_{B} = \sin (δ_{2}) | 0_{Z} 〉 + \cos (δ_{2}) | 1_{Z} 〉, {| ϕ_{0 X} 〉}_{B} = \sin (\frac{π}{4} + δ_{3}) | 0_{Z} 〉 + \cos (\frac{π}{4} + δ_{3}) e^{i (θ_{1} + ω)} | 1_{Z} 〉, {| ϕ_{0 Y} 〉}_{B} = \sin (\frac{π}{4} + δ_{3}) | 0_{Z} 〉 + \cos (\frac{π}{4} + δ_{3}) e^{i (\frac{π}{2} + θ_{2} + ω)} | 1_{Z} 〉 .

(11)

View in Article

Q_{0} = \frac{1}{2 π} \int_{0}^{2 π} 1 - (1 - e_{dark}) \exp (- {| A + e^{i Δ ϕ} B |}^{2}) d Δ ϕ, Q_{1} = \frac{1}{2 π} \int_{0}^{2 π} 1 - (1 - e_{dark}) \exp (- {| A + e^{i π} e^{i Δ ϕ} B |}^{2}) d Δ ϕ,

(12)

View in Article

Figures&Tables (6)

References (37)

Copy Citation Text

Jipeng Wang, Zhenhua Li, Zhongqi Sun, Tianqi Dou, Wenxiu Qu, Fen Zhou, Yanxin Han, Yuqing Huang, Haiqiang Ma, "Loss-tolerant measurement device independent quantum key distribution with reference frame misalignment," Chin. Opt. Lett. 20, 092701 (2022)

Download Citation

Set citation alerts for the article

Set citation alerts for the article

Save the article for my favorites

Paper Information

Recommended Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology

Set citation alerts for the article

Please enter your email address