Quantum key distribution with untrusted detectors

P. González, L. Rebón, T. Ferreira da Silva, M. Figueroa, C. Saavedra, M. Curty, G. Lima, G. B. Xavier, and W. A. T. Nogueira

Phys. Rev. A 92, 022337 – Published 18 August 2015

Abstract

Side-channel attacks currently constitute the main challenge for quantum key distribution (QKD) to bridge theory with practice. So far two main approaches have been introduced to address this problem, (full) device-independent QKD and measurement-device-independent QKD. Here we present a third solution that might exceed the performance and practicality of the previous two in circumventing detector side-channel attacks, which arguably is the most hazardous part of QKD implementations. Our proposal has, however, one main requirement: the legitimate users of the system need to ensure that their labs do not leak any unwanted information to the outside. The security in the low-loss regime is guaranteed, while in the high-loss regime we already prove its robustness against some eavesdropping strategies.

Received 16 May 2013
Revised 14 October 2014

DOI:https://doi.org/10.1103/PhysRevA.92.022337

Authors & Affiliations

P. González^1,2,3, L. Rebón^4,5, T. Ferreira da Silva⁶, M. Figueroa^2,7, C. Saavedra^1,2, M. Curty⁸, G. Lima^1,2,3, G. B. Xavier^2,3,7, and W. A. T. Nogueira^2,3,9

¹Departamento de Física, Universidad de Concepción, 160-C Concepción, Chile
²Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile
³MSI-Nucleus for Advanced Optics, Universidad de Concepción, Concepción, Chile
⁴Instituto de Física de La Plata, Universidad Nacional de La Plata, La Plata, Argentina
⁵Laboratorio de Procesado de Imágenes, Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina
⁶Optical Metrology Division, National Institute of Metrology, Quality and Technology, 25250-020 Duque de Caxias, RJ, Brazil
⁷Departamento de Ingeniería Eléctrica, Universidad de Concepción, 160-C Concepción, Chile
⁸EI Telecomunicación, Department of Signal Theory and Communications, University of Vigo, E-36310 Vigo, Spain
⁹Departamento de Física, ICE, Universidade Federal de Juiz de Fora, Juiz de Fora, CEP 36036-330, Brazil

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Vol. 92, Iss. 2 — August 2015

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Figure 1
(a) Schematic diagram of measurement-device-independent QKD (mdiQKD) [28]. Alice and Bob prepare different quantum states and send them to an untrusted relay Charles, which can be treated as a black box fully controlled by Eve. Charles is supposed to implement a Bell state measurement (BSM) that projects the incoming signals into a Bell state. (b) Schematic diagram of our proposal. Alice generates different quantum states and sends them to Bob. On receiving the signals, Bob encodes his information by means of a trusted linear optics network (LON), which can be regarded as Bob's transmitter (when compared to mdiQKD). This LON does not include any light source but it simply manipulates the state of the incoming signals. Afterwards, Bob implements a BSM, which is treated as a black box. In the figure: (brown box) characterized device; (black box) uncharacterized device; and (light turquoise box) secure laboratory, i.e., the laboratory does not leak any unwanted information to the outside.
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Figure 2
Schematic diagram of an example of a possible implementation of our method. Alice generates phase-randomized weak coherent pulses (WCPs) in different BB84 polarization states [48], and sends them to Bob. In addition, she prepares decoy-states [45, 46, 47] using an intensity modulator (Decoy-IM). Bob employs a trusted LON to encode his information on the incoming signals by using their path degree of freedom. For this, he uses an optical switch that sends the arriving states through one out of three possible optical paths of the same length (paths $a$ , $b$ , and $c$ in the figure). Two additional optical switches are used to guarantee that the selected path is actually connected to the polarizing beam splitter (PBS). The switches are represented in the figure with the standard drawing of arrows and white connectors. The phase modulator $ϕ$ shifts the phase of each pulse by 0 or $π$ . Bob measures the outcoming pulses from the LON with a linear-optics single-photon BSM [50]. A successful BSM result is obtained when only one detector $D_{i}$ clicks. The polarization rotator $R$ changes the horizontal (vertical) polarization to a $45^{\circ} (- 45^{\circ})$ linear polarization. As in Fig. 1: (brown box) characterized device; (black box) uncharacterized device; and (light turquoise box) secure laboratory.
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Figure 3
Lower bound on the secret key rate $R$ given by Eq. (1) in logarithmic scale for the setup illustrated in Fig. 2 with WCPs (green curve). For simulation purposes, we use experimental parameters from Ref. [66]: the loss coefficient of the quantum channel is $0.2$ dB/km, the intrinsic error rate due to misalignment and instability of the optical system is $1.5 %$ , the overall detection efficiency of the detectors $D_{i}$ is $14.5 %$ , and the background count rate is $6.02 \times 10^{- 6}$ . Furthermore, we consider that the parameter $q \approx 1$ [63] and the efficiency of the error correction protocol satisfies $f (E_{i}) = 1.16$ . For comparison, this figure also includes a lower bound on the secret key rate for a standard decoy-state BB84 system with an infinite number of decoy settings and an active measurement setup (red curve) [45, 46, 47].
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Figure 4
Experimental and theoretical (inset) probabilities to obtain a click in detector $D_{i}$ for all possible combinations of states when both Alice and Bob use compatible bases. See Table 2 for further details. The states $| a 〉$ and $| c 〉$ in the figure denote the paths a and c, respectively, while $| b, 0 〉$ and $| b, π 〉$ represent path b with $ϕ = 0$ and $ϕ = π$ , respectively.
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