Research ArticlePHYSICS

Provably secure and high-rate quantum key distribution with time-bin qudits

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Science Advances  24 Nov 2017:
Vol. 3, no. 11, e1701491
DOI: 10.1126/sciadv.1701491
  • Fig. 1 Schematic of the experimental setup.

    At Alice’s transmitter, the quantum photonic states (signal and decoy) are created using a frequency-stabilized continuous laser (Wavelength Reference, Clarity-NLL-1550-HP) operating at 1550 nm, which passes through three intensity modulators (only two are shown for clarity) and one phase modulator (all intensity and phase modulators are from EOSpace). The entire system is controlled by serial pattern generators realized with a field-programmable gate array (FPGA; Altera Stratix V 5SGXEA7N2F40C2), operating at a 10-GHz clock rate. In greater detail, a 5-GHz sine-wave generator phase locked to the FPGA drives an intensity modulator (not shown), which creates a periodic train of 66-ps-duration (full width at half maximum) optical pulses. These pulses pass through an intensity modulator (IM 1), which is driven by the FPGA-based pattern generator to define the data pattern for either the time-bin or phase states. A second intensity modulator (IM 2), driven by an independent FPGA channel, adjusts the amplitude of the phase and decoy states relative to the primary time-bin signal states. Finally, the states pass through an FPGA-driven phase modulator (PM) to encode the different phase states. The time-bin basis and the phase basis are chosen with probabilities of 0.90 and 0.10, respectively. An attenuator (ATT) reduces the level of the states to the single-photon level. An additional attenuator is used to simulate the loss of the quantum channel. At Bob’s receiver, the incoming signals are split using a 90/10 beam splitter (BS) to direct 90% of the states to the temporal basis measurement system and 10% to the phase basis system. For both measurement bases, we use commercially available superconducting nanowire single-photon detectors (Quantum Opus), and the detection events are recorded with a 50-ps-resolution time-to-digital converter (Acqiris U1051A, Agilent), which is synchronized with Alice’s clock over a public channel.

  • Fig. 2 Time-bin and phase states for d = 4 and the phase-state measurement scheme.

    (A) Temporal (left) and phase (right) states for d = 4, with the phases determined from Eq. 1. (B) Probability of detection when each input state is measured in both bases. (C) Measuring the phase states with a cascaded interferometric tree, where the relative time delay of the first unequal-path delay-line interferometer (DI 1) is twice the delay of DI 2 and DI 3. The phase of DI 3 is set to π/2. (D) Expected photon probability distribution at the output of the interferometers when the phase state |f0〉 is injected into the system.

  • Fig. 3 Observation of high-rate and secure QKD.

    (A) Experimentally achievable secret key rates as a function of the channel loss for the case when the number of signals transmitted by Alice is N = 6.25 × 1010 (100-s-duration communication session). The orange solid line is the simulated secret key rate. For the simulation, we set the probabilities of sending signal, decoy, and vacuum intensities to 0.8, 0.1, and 0.1, respectively. The intrinsic error rate in the time and phase basis is set to 0.03 and 0.025, respectively. (B) Experimentally observed quantum bit error rate in temporal and phase basis signal states as a function of channel loss.

  • Table 1 Comparison of some notable high-rate QKD systems.

    The protocol implemented by Lucamarini et al. (37) is a d = 2 time-bin BB84 protocol, where the two bases are chosen with asymmetric probability. Zhong et al. (21) and Lee et al. (23) implement high-dimensional QKD (HD-QKD) using time-bin encoding schemes.

    ProtocolLoss (dB)Equivalent fiber length (km)Secret key rate (megabits/s)Security level
    Lucamarini et al. (37)T127
    10
    13
    16
    35
    50
    65
    80
    2.20
    1.09
    0.40
    0.12
    Collective
    Zhong et al. (21)HD-QKD0.02
    4
    0.1
    20
    7.0
    2.7
    Collective
    Lee et al. (23)HD-QKD0.1
    7.6
    12.7
    0
    38
    63
    23.0
    5.3
    1.2
    Collective
    This workHD-QKD4
    8
    10
    14
    16.6
    20
    40
    50
    70
    83
    26.2
    11.9
    7.71
    3.40
    1.07
    Coherent/general*

    *For the definition of coherent attacks, we refer readers to the study of Sheridan and Scarani (12).

    Supplementary Materials

    • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/11/e1701491/DC1

      section S1. Finite-key estimates for the experiment

      section S2. Secret key rate simulation

      section S3. Detector efficiency calibration

      section S4. Numerically optimized secret key rate

      section S5. Experimental parameters

      section S6. Generation of the phase states

      fig. S1. Efficiency of single-photon detectors.

      fig. S2. Numerical simulation.

      fig. S3. Graphical illustration of all phase states in d = 4.

      fig. S4. Generation of phase states.

      table S1. Length of sifted data.

      References (3840)

    • Supplementary Materials

      This PDF file includes:

      • section S1. Finite-key estimates for the experiment
      • section S2. Secret key rate simulation
      • section S3. Detector efficiency calibration
      • section S4. Numerically optimized secret key rate
      • section S5. Experimental parameters
      • section S6. Generation of the phase states
      • fig. S1. Efficiency of single-photon detectors.
      • fig. S2. Numerical simulation.
      • fig. S3. Graphical illustration of all phase states in d = 4.
      • fig. S4. Generation of phase states.
      • table S1. Length of sifted data.
      • References (38–40)

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