Research ArticleAPPLIED MATHEMATICS

Hacking the Bell test using classical light in energy-time entanglement–based quantum key distribution

See allHide authors and affiliations

Science Advances  18 Dec 2015:
Vol. 1, no. 11, e1500793
DOI: 10.1126/sciadv.1500793
  • Fig. 1 Experimental setup of the Franson interferometer.

    The setup consists of a source, 2 × 2 couplers (C), delay loops (ΔT), phase modulators φA and φB, and detectors (D).

  • Fig. 2 The faked Bell value of our source is 2.5615 ± 0.0064 (solid black line), which clearly violates the CHSH inequality S2 ≤ 2.

    It is possible to increase the faked Bell value up to 3.6386 ± 0.0096 (dotted blue line, data for time slots where pr < 1/2 − p or 1/2 + pr < 1 − p). In both cases, the faked efficiency is 97.6%. Each point in the diagram corresponds to the S2 value for 1 s worth of data.

  • Fig. 3 The blinding attack causes the detector to click only for pulses of greater intensity than IT.

    If Eve sends three pulses of equal intensity I, they will arrive as four after the interferometer. By changing the phase shifts ωE and ωL between the pulses at the source, she can control the intensity of the early and late middle pulses at the ± output ports, giving clicks as desired. Here, φ = 0, ωE = π/8, and ωL = π/4. The first and last pulses have a constant intensity of I/4.

  • Fig. 4 Discretized LHV model (23) that can give any Bell value between 2 and 4.

    The hidden variables are 0 ≤ r < 1 (a real number in the unit interval) and Embedded Image, where 0 ≤ n ≤ 7 is an integer. The parameter 0 ≤ p ≤ 1/4 can be chosen freely, and the output Bell value is S2 = 4 − 8p, so that the “classical” S2 = 2 is obtained with p = 1/4, the “quantum” Embedded Image is obtained with Embedded Image (as in the figure), and the “nonlocal box” S2 = 4 is obtained with p = 0, all at 100% faked efficiency and 50% postselection.

  • Fig. 5 Experimental setup of the attack on the Franson interferometer.

    The source consists of a CW laser for blinding the detectors, a pulsed laser for generating the bright classical light pulses, fiber optic couplers (C) delay loops (ΔT), phase modulators (ω and φ), and detectors (D). Alice and Bob have the same analysis stations as in Fig. 1.

Related Data

Navigate This Article