4.3 Simulation of decoy-state BB84 protocol with SNSPDs
4.3.1 High secret-key-rate optimization
Here we shall now discuss the optimization of the proposed QKD system to achieve the highest possible SKR. The SKR for a QKD system is ultimately limited by the loss in the quantum chan-nel [113], hence this optimization will concentrate on short distances. A more technological constraint is the maximum count rate of the single-photon detectors. As discussed in Sec. 3.2.4 the typical maximum count rate of SNSPDs is in the range of tens of megahertz. In order to 46
4.3. Simulation of decoy-state BB84 protocol with SNSPDs
increase the system detection rate, one can use multiple detectors, which is facilitated by the fact that the read-out electronics are rather simple for SNSPDs and it is possible to put many devices into a single cryostat. In our cryogenic system, there are 8 readout channels (see Sec. 3.2), hence this optimization will take this into account. By using a 1-to-8 fiber splitter, seven of the optical modes will be directed to SNSPDs measuring in the Z-basis and one detector will measure in the X-basis (see Fig. 4.4).
One of the most important parameters for a QKD system is the classical-post-processing block size (nz) [114]. In Fig. 4.6 the SKR is calculated for different block sizes, at two different distances. It is clear that it is beneficial to use as large a block size as possible, however, a limitation will be enforced by the computation power needed to complete the privacy amplification stage of the post-processing, which envolves large matrix manipulation. Most importantly, the throughput of the privacy amplification should be fast enough to cope with the raw-key-rate of the QKD sytem. Using our FPGA based method (see App. A.2, Sec. 2.6), it is difficult to go beyond a block size of 106with a throughput greater than 48 Mbps. An efficient alternative privacy amplification algorithm is based on the Fast-Fourier Transform (FFT) [115, 116], which can be efficiently implemented in GPUs. We implemented this algorithm in Matlab and ran it on an NVIDIA Tesla K40 GPU. The maximum computable block size was 1.3×108 with a throughput of 235 Mbps, which is sufficiently fast for the target SKR. Henceforth, this will be the block size assumed for the following optimization. The error correction algorithm is assumed to be based on LDPC based codes, implemented in an FPGA, which provides a throughput which matches the privacy amplification, at 235 Mbps (see App. A.2, Sec. 2.5).
Table 4.1 summarizes the parameters chosen for the system to achieve a high SKR. The detection efficiency was set to 80%, as this is seen as a realistic goal in the next-generation in-house SNSPDs. Figure 4.5 shows the resulting SKR as a function of transmission distance.
At zero distance, it would be possible to distill 50 Mbps of secret key, whilst at 50 km and 100 km, the SKR would be around 15 Mbps and 2 Mbps, respectively. These values are around an order of magnitude higher compared to the current state of the art demonstrations [112], which demonstrates the potential of an SNSPD based system.
Table 4.1: Simulation parameters for QKD system optimized for high SKR operation.
Detector efficiency 0.8
Detector DCR 100 cps
Detector deadtime 30 ns
Number of detectors for Z-basis 7 System clock frequency 2.5 GHz Post-processing block size 1.34×108 Optical error rate in Z-basis 0.02 Optical error rate in Z-basis 0.02 Error correction efficiency 1.4
Chapter 4. Long-distance and high-rate quantum key distribution
(a) 0 km. (b) 100 km.
Figure 4.6: Secret key rate as a function of the classical post-processing block size at two different distances.
4.3.2 Long distance optimization
This section is dedicated analyzing the possibility of increasing the maximum achievable distance beyond what was discussed in Sec. 4.1. Long distance QKD demonstrations have typically opted to use SNSPDs (see App. A.6, Tab. 1), mainly due to the fact that very low DCR is achievable. Since the intrinsic DCR can be very low, with the implementation of sufficient filtering of the blackbody radiation, it is possible to arrive at a DCR of less than 1 cps [54]. One aspect that is often overlooked, is the finite key length effects, which can lead to misleading results. For example, in Ref. [117], QKD in presence of 72 dB loss (336 km of dispersion-shifted fiber) is claimed, however, the raw key size in this case was only 50 bits, in which case no secret key could be distilled in reality. As discussed in App. A.6, an important consideration is the stability of the system during the collection period of the classical-post-processing block, which started to impact the performance of the system at the longest distances. We have shown that at 307 km it is possible to distill a key whilst taking into account the finite-key effects, in which case the collection time was around 3 hours. In order to provide a fair comparison in this section, we shall fix the maximum allowed collection time, to similar values.
Given this constraint, an increase of the maximum transmission distance can be facilitated by the increase in the average number of photons per pulse, through the use of the decoy state BB84 protocol, the higher clock-rate, as well as the superior detection efficiency of the SNSPDs, compared to the InGaAs/InP NFADs.
Figure 4.7 shows the resulting collection time required as a function of distance for different sizes of the classical-post-processing block. The effect on the SKR is also plotted. It is possible to maintain a collection time of around 4 hours at 400 km if the block size is reduced to around 105, with a positive SKR. Taking this into account, Tab. 4.2 summarizes the simulation parame-ters for a long distance implementation, whilst Fig. 4.8 plots the predicted SKR versus distance including the optimum parameters. This proposed system is capable of maintaining the same SKR as with the COW system (a few bps), whilst increasing the distance by nearly 100 km.
Another change in this scenario would be the use of a more efficient error reconciliation 48
4.4. Summary
protocol [118], since the throughput is no longer a large constraint.
Table 4.2: Simulation parameters for QKD system optimized for long distance operation.
Detector efficiency 0.8
Detector DCR 3 cps
Detector deadtime 30 ns
Number of detectors for Z-basis 1 System clock frequency 2.5 GHz Post-processing block size 2.5×105 Optical error rate in Z-basis 0.01 Optical error rate in Z-basis 0.01 Error correction efficiency 1.05
(a) Secret key rate. (b) Collection time.
Figure 4.7: Secret key rate as a function of the classical-post-processing block size at two different distances.
4.4 Summary
In this chapter I have discussed the application of single-photon detectors to QKD, which is a demanding application since it is sensitive to all of the main characteristic of the detectors, including efficiency, noise, temporal resolution and recovery time. Since these parameters are often inter-linked, it is important to find the optimum trade-offs in order to optimize the system performance. Indeed the QKD system performance is usually limited by the detectors.
It has been shown how InGaAs/InP NFAD detectors can be used to enable record distance QKD operation, which paves the way to compact systems which can operate over distance greater than 300 km. Moreover an important step has been taken in considering the finite-key effects, which has has so far been a major oversight for long distance experiments.
In terms of the ultimate detector performance, SNSPDs still provide the state-of-the-art and they may well be a viable detector solution for specialized QKD installations. The final part of this chapter looked at how these detectors could be used in the future to increase the state-of-the-art SKR by over an order of magnitude as well as increasing the maximum operating
Chapter 4. Long-distance and high-rate quantum key distribution
Figure 4.8: Secret key rate for the decoy-state BB84 protocol, optimized for operation over very long distances. The optimum parameters for each distance are also included. The red star signifies the current state-of-the-art maximum distance of 307 km, as discussed in Sec. 4.1.
of security, since it would be secure against the most general attacks. This work takes an important step towards ever more versatile QKD systems which are gradualy coming in line with the stringent demands of classical-communication systems, which QKD must support in order to ensure the longevity of information security.
50
5 Conclusion and outlook
During this thesis two approaches to single-photon detection have been studied, using semi-conductor and supersemi-conductor technologies. Although there are many applications to for single-photon detectors, the focal technology studied here was quantum key distribution (QKD), since this is a relatively young field which relies heavily on developments in single-photon detectors.
In the first part of the thesis I discussed the operation of free-running InGaAs/InP negative-feedback avalanche diodes (NFADs). Through extensive study of the low-temperature behavior of these detectors, insights into the fundamental characteristics such as the efficiency, dark count rate (DCR), afterpulsing and jitter, were found. One of the main achievements was the ability to reduce the DCR to record low values of a few counts per second at moderate efficiencies.
The second part of the thesis concentrated on the development, fabrication and characteriza-tion of superconducting nanowire single-photon detectors. The idea for such a detector was first published in 2001 [45], hence it is a very new field, but an exciting one fueled by important breakthroughs in the last few years [46]. These detectors are highly attractive because they can achieve excellent attributes simultaneously, such as high efficiency, low noise, good temporal resolution, no afterpulsing and high count rates. Although we have shown in this thesis that NFADs can match some of the characteristics of SNSPDs, especially DCR and jitter (at least for the time being), it comes at a cost of the other parameters since there are many trade-offs.
Therefore, SNSPDs are more versatile detectors, although less practical due to the cryogenic temperatures required. The main achievement of this section was the demonstration of a system detection efficiency as high as 65%, at 1550 nm, for an in-house fabricated SNSPD.
This is already higher than what is currently possible with InGaAs/InP based detectors, hence opens up a host of exciting applications.
Both detector technologies have their place in various applications, since it is not always necessary to have every single state-of-the-art attribute simultaneously. The final part of the thesis looks at the application of these detectors to QKD. It was demonstrated that the
Chapter 5. Conclusion and outlook
use of NFADs can enable record distance QKD over 307 km of optical fiber. The final part of this section proposed an experiment which can further improve the performance of QKD through the use of SNSPDs. In particular two scenarios are analyzed and simulated, namely long-distance operation which could extend the record distance by an additional 100 km and high-rate operation which could increase the record secret key rate by over an order of magnitude.
There are many unfinished developments, open questions and new directions which are left to be explored upon reaching the end of this thesis, in all three of the main topics studied.
These shall now be briefly explored.
5.1 The future of semiconductor single-photon detectors
Looking at InGaAs/InP NFADs, now that it’s clear that low temperature operation can be very favorable, there might be opportunity to optimize the device structure especially for this temperature range. For example, the absorption region thickness could be increased in order to increase the quantum efficiency. This would be facilitated by the fact that at low temperatures, thermally generated dark counts are negligible. Another interesting direction is to try to utilize part-passive and part-active quenching of such devices, which would lead to increased count rates [119].
One of the main drawbacks of the InP based avalanche diodes is the significant amount of afterpulsing. Efforts should be made to improve the material quality to minimize the quantity of defects leading to the trapping sites. An interesting experiment would be to try to empty these traps actively, possibly by excitation from a long wavelength light source.
One of the main methods for afterpulse limitation is the restriction of the charge generation during an avalanche, which limits the probability that an a trap gets populated. This is done by quenching the avalanche as fast a possible, typically by gating with ultra-short gates [28].
Ironically, this actually leads to a near linear-mode operation, since the avalanche is not allowed to reach the saturation. This points towards a push to develop linear-mode avalanche diodes based InP which can reach single-photon sensitivity. This is quite difficult, since the excess noise factor in InP is quite high, prohibiting high gain.
An interesting idea is to use a multiplication region with multiple discrete sections, with each region limited in gain to a fixed value, thanks to a feedback element, which prohibits a runaway avalanche[120, 121]. This is essentially like having multiple NFADs in the same device. Such devices are known as discrete-avalanche photon detectors (DAPD) and could be an interesting approach to achieving very high count rates.
As mentioned before, the ultimate APD would operate in the linear mode with a sufficiently large gain in order to provide single-photon sensitivity. In order to have such performance, the multiplication region should have an excess noise factor near 1, which means that ionization
52
5.2. Superconducting nanowire single-photon detectors
should take place exclusively for either electrons or holes, but not both [23]. A material which ionizes almost exclusively electrons is HgCdTe and has shown promise for linear-mode photon counting [122, 123]. This technology could have an important role in the single-photon detector community in the future.
Finally, other internal amplification processes could be utilized. One recent proposal is a phonon-assisted cycling-excitation process, which also achieves very low excess noise factor and high gain [124]. This idea is in the very early stages and it is still not clear if it’s feasible for single-photon detection.
5.2 Superconducting nanowire single-photon detectors
Superconducting nanowire detectors still have a bright future ahead, in terms of research opportunities. As far as the work related directly to this thesis, there is still a lot of short- to mid-term developments which can be implemented in order to improve the system performance, such as detection efficiency and temperature dependence. The main future directions were already discussed at the end of Chapter 3 and mainly focused on improving the fabrication process, such as etching of dielectric layer deposition.
A logical direction would be to start optimizing the SNSPD optical stack for different wave-lengths, since the internal detection process is extremely broadband. This could make SNSPD the detectors of choice for certain applications where other detector technologies may not be optimum, for example the gap at around 900 nm, where neither Si on InGaAs based APDs have very high quantum efficiency, could be filled in nicely by SNSPDs. Indeed it would be interesting to see how far it’s possible to push the spectral response, both into the UV/X-Ray and IR ranges.
The ultimate limits of SNSPD operation have still not been reached, for example it would be interesting to see how far it’s possible to push the system detection efficiency and the temporal resolution. Technological advances in the fabrication proceedures and the readout schemes will still bear fruitful in the near future, however, reaching the fundamental limits will require progress in the theoretical understanding of the detection mechanism, which is a very open and challenging field [57]. This is an exciting area since it and requires ongoing collaboration between experimentalists and theorists.
Fundamentally new directions might enable new types of devices. One attribute of SNSPDs which would be interesting to alter is the maximum count rate. Currently, this is limited by the thermal properties of the structure, since the large resistive hotspot resulting from the current-driven self-heating has to be dissipated before the current can be redirected into the nanowire. It would be preferable to try and detect only the first perturbation caused by the photon detection, which generates a cloud of quasiparticles, without driving the device into the regime where the resistive domain expands over a large area of the nanowire.
Chapter 5. Conclusion and outlook
5.3 Quantum key distribution
As it has been discussed throughout this thesis, breakthroughs in experimental QKD are most often related to advancement in detector technology. There is no reason to think that Gbps secret key rates should not be achievable in the future. This is a key goal for the technology in order to enable the use of the one-time pad encryption for high-rate communication, which is the only information-theoretically-secure encryption protocol.
As discussed in at the end of Chapter 4, the next steps required for the an increase of an order of magnitude (to 10-100 Mbps ) has already been outlined and is within reach with current technology. Alternative protocol approaches should also be expolored, which might open up an alternative route to Gbps, through the use of homodyne detection [125, 126, 127]. The key aim for all of these directions, should be to maintain the highest level of security, namely against the most general coherent attacks.
In terms of increasing the maximum operating distance of QKD, some short- to mid-term advancements could see an increase of up to 400 km, as discussed at the end of Chapter 4 and pushing this to 500 km could be imagined. Improvements in fiber technology, as discussed in App. A.6.1 Sec. III, could decrease the fiber attenuation down to about 0.1 dB/km which would prove crucial for QKD. Unftunatelly there will be an eventual limit of how far a single QKD link can reach, due to a rate-loss relationship [113]. To go beyond the 1000 km distance, one would need to implement trusted node relays, which is already underway in several projects. Beyond that, ground-to-space QKD demonstrations could provide a method for inter-continental QKD. In order to avoid the use of trusted nodes, quantum repeaters will be required [128].
54
A Peer-reviewed articles
A selection of the peer-reviewed articles, which are refereed to in the main text of the thesis, is included in this appendix.
A.1 A high-speed multi-protocol quantum key distribution
trans-mitter based on a dual-drive modulator
A high-speed multi-protocol quantum key distribution transmitter based on a
dual-drive modulator
Boris Korzh,∗Nino Walenta, Raphael Houlmann, and Hugo Zbinden
GAP-Optique, University of Geneva, CH-1211 Geneva 4, Switzerland
∗boris.korzh@unige.ch
Abstract: We propose a novel source based on a dual-drive modulator that is adaptable and allows Alice to choose between various practical quantum key distribution (QKD) protocols depending on what receiver she is communicating with. Experimental results show that the proposed transmitter is suitable for implementation of the Bennett and Brassard 1984 (BB84), coherent one-way (COW) and differential phase shift (DPS) protocols with stable and low quantum bit error rate. This could become a useful component in network QKD, where multi-protocol capability is
Abstract: We propose a novel source based on a dual-drive modulator that is adaptable and allows Alice to choose between various practical quantum key distribution (QKD) protocols depending on what receiver she is communicating with. Experimental results show that the proposed transmitter is suitable for implementation of the Bennett and Brassard 1984 (BB84), coherent one-way (COW) and differential phase shift (DPS) protocols with stable and low quantum bit error rate. This could become a useful component in network QKD, where multi-protocol capability is