The SPDs are a crucial part of a QKD system as they largely affect its overall performance.
In this section, we first discuss the general performance requirements that they should fulfil, which can vary depending on the operating regime (which is mostly depending on the transmission distance). Then we describe more specifically the two types of detectors which were involved in the experiments: SPADs and SNSPDs.
3.4.1 General requirements of SPDs for QKD
We shall start our discussion with an ideal SPD which has the following characteristics:
• 100 % detection efficiency,
• no timing jitter,
• no dark counts,
• no recovery time (the detector can detect a photon immediately after a detection has occurred),
• no afterpulsing.
3.4. Single-photon detectors
60 80 100 120 140
Jitter (ps) 0.0
0.5 1.0 1.5 2.0 2.5 3.0
QBER induced (%)
Figure 3.6: QBER induced as a function of the detector timing jitter. The simulation was performed considering a time-bin encoding with a repetition rate of 2.5 GHz, detection bins of 100 ps as described in section 3.5.2 and Gaussian jitter distribution.
The resulting SKR as a function of the attenuation is plotted on figure 3.5. In the infinite key regime (continuous blue line), the SKR decreases proportionally to the attenuation.
However, when the block acquisition time is fixed to a finite duration, we note a break at long distance due to the finite key analysis (dash-dotted red line).
In a realistic scenario, the SKR as a function of the distance is instead similar to the dashed green line. In the low-attenuation regime, the SKR is limited by the saturation of the detectors. For every attenuation, the SKR is lower than the ideal case due to limited detection efficiency. Finally, at high attenuation, a break in the SKR appears also because of the DCR of the detectors.
Let’s examine the effect of varying each SPD characteristic individually. A reduction of the detection efficiency is equivalent to a change of the overall attenuation and can therefore be seen as an horizontal displacement of the curve on the figure 3.5. A high detection efficiency is obviously beneficial for the performance of a QKD system but no lower limit can be specified since it is possible to exchange secret keys even with very low detection efficiency.
A growing timing jitter increases the probability that a detection occurs in a neighbouring time-bin, therefore generating an error. The maximum allowable timing jitter depends on the repetition rate of the experiment. Figure 3.6 depicts the QBER contribution of the jitter as a function of the jitter for a time-bin encoding system with a repetition rate of 2.5 GHz. We assumed a Gaussian jitter distribution.
While the detection efficiency and the timing jitter affect the SKR for every attenuation uniformly, the DCR and the recovery time are crucial for the long distance and short distance regimes, respectively. As the attenuation increases, the detection rate decreases but the DCR is constant. The QBER contribution due to the DCR is close to zero for most attenuations because the DCR is negligible compared to the total detection rate. At long distance, when these two quantities become comparable, the DCR is the main QBER contribution. This prevents any secret key exchange at high attenuation and generates a break in the SKR curve, even in the infinite key regime. Two ways can be followed to determine how low the DCR should be. The first approach is based on the fact that for a fixed accumulation time (and a given repetition rate) there is a maximum attenuation achievable with a positive SKR. The second approach is to state that it is impractical and of little use to have a SKR below a certain value (probably around∼ 1 bps [43]).
Therefore, the DCR has to be low enough in order not to reduce significantly the SKR up to the maximum achievable attenuation in the first approach or at least up to the attenuation corresponding to a practical SKR in the second approach.
The recovery time affects the SKR at low attenuation due to the increasing probability of having photons arriving when the detector is inactive. Therefore some photons are not detected, which can be viewed as a decrease in the effective detector efficiency and as a consequence, the resulting SKR is lower than in the unsaturated case. The rule of thumb is that the recovery timeτrshould be much smaller than the inverse of the photon arrival raterγ:
τr1/rγ. (3.2)
Finally, the afterpulsing of the detector acts in a similar way to Alice’s preparation error. Therefore the afterpulsing contribution to the QBER is roughly proportional to the afterpulsing probability.
3.4.2 Single-photon avalanche diodes
SPADs are a natural choice for single-photon detection in QKD as they are a mature technology which is relatively easy to use and features good performances. They demon-strated their usefulness both in state-of-the-art experiments [13, 14] and in commercial systems. We use InGaAs/InP negative feedback avalanche diodes (NFADs) which have separate absorption and multiplication regions made of InGaAs and InP, respectively.
We operate them in the free-running mode. They are cooled by a free-piston Stirling cooler which can operate to temperatures as low as−130◦C.
Our SPADs have demonstrated the following performance: system detection efficiency approaching 30 %, DCR as low as 1 Hz and timing jitter as low as 52 ps [44, 45]. How-ever, one cannot obtain these numbers all at the same time. Careful optimisation of the detector parameters is required for each operating regime in order to maximize the final
3.4. Single-photon detectors
SKR. The relation between the detector parameters (bias voltage, operating temperature and dead time) and the detector performance (efficiency, DCR, jitter and afterpulsing) can be summarized as following. As the bias voltage is raised, the avalanche probability increases and consequently also the detection efficiency. However, also the DCR grows strongly, which limits the maximum efficiency achievable with a reasonable DCR. More-over, short jitter is obtained with high bias voltage. The SPAD jitter does not exhibit a Gaussian distribution [45], which is detrimental for QKD. Since the dark counts are mostly thermally generated [46], lowering the temperature decreases the DCR. However, the price to pay is that this increases the afterpulsing probability because the lifetime of the charge carrier traps is longer at low temperature. The afterpulsing can be reduced by increasing the dead timeτ[47] but this also influences the maximum detection rate since saturation effect appears as the detection rate approaches 1/τ.
For QKD applications, the detector temperature is generally lowered as the attenuation increases. This allows, at low attenuation, to have a high detection efficiency together with a low afterpulsing probability. This latter permits to choose short dead times which in turn enables high detection rates. At higher attenuation the detection rate is lower, therefore the dead time can be increased without affecting the performance. It is then possible to lower the temperature which reduces the DCR (which is the main QBER contribution at high attenuation) while keeping the afterpulsing probability at the same level as at low attenuation.
3.4.3 Superconducting nanowire single-photon detectors
An SNSPD consists of a nanowire which is cooled down to its superconducting state. It is biased just below its critical current, the current beyond which the nanowire becomes resistive. A photon hitting the nanowire creates a local resistive hotspot which triggers a fast voltage pulse that can be detected by an appropriate electronic readout circuit.
We use in-house-made SNSPDs which are made from amorphous molybdenum silicide (MoSi) (see references [48, 49, 50] for specific information about those detectors). This material enables high detection efficiencies at telecom wavelength as it exhibits a large saturation regime when cooled down around 1 K. The detectors are cooled down in a sorption cryostat reaching 0.8 K. Detector design can be varied depending on the performance requirements and results from a trade-off between the different features.
The majority of the detectors we used, which we denote as standard detectors, have the following characteristics. They are composed of a single nanowire which forms a meander covering an area of 16×16µm2. The nanowire widths are typically∼100 nm and their thicknesses∼5 nm. The photon absorption is enhanced by an optical cavity.
Light is sent on the detector through a SMF which is placed directly on top of the device.
These detectors have system detection efficiencies as high as∼85 %. The DCR is around
few hundreds of Hz and is mainly due to the blackbody radiation coming from the outside of the cryostat. Note that the efficiency and the DCR depend on the bias current.
The vast majority of the devices have jitters lower than 50 ps which is good enough in order not to introduce additional QBER in our QKD system given that the jitter distribution of standard SNSPDs is usually Gaussian [49]. The best detectors have a timing jitter lower than 30 ps. Their recovery time is typically few hundreds of ns which allows for detection rates up to a few MHz. They do not exhibit any afterpulsing.
These characteristics mean that those detectors behave close to an ideal detector in the range of attenuation comprised between∼25 dB and∼50 dB. To go beyond this range, they should be adapted specifically according to the regime under study (low or high attenuation). Such optimisations are described in chapter 4.