 Research
 Open Access
 Published:
Field trial of a threestate quantum key distribution scheme in the Florence metropolitan area
EPJ Quantum Technology volume 6, Article number: 5 (2019)
Abstract
Infield demonstrations in realworld scenarios boost the development of a rising technology towards its integration in existing infrastructures. Although quantum key distribution (QKD) devices are already adopted outside the laboratories, current field implementations still suffer from high costs and low performances, preventing this emerging technology from a largescale deployment in telecommunication networks. Here we present a simple, practical and efficient QKD scheme with finitekey analysis, performed over a 21 dBlosses fiber link installed in the metropolitan area of Florence (Italy). Coexistence of quantum and weak classical communication is also demonstrated by transmitting an optical synchronization signal through the same fiber link.
Introduction
In a society based on the continuous exchange of sensitive data and information, the importance of secure and trustful communications is essential. Quantum key distribution (QKD) allows to share data in an informationtheoretical secure way, no longer based on computational assumptions but exploiting the basic principles of quantum mechanics [1,2,3]. During the last 30 years, many QKD protocols have been developed and tested over optical fiber spools in laboratory demonstrations, achieving long transmission distances and key generation rates up to tens of Mbit/s in complete system implementations [4,5,6,7,8,9]. However, this technology is still far from a largescale deployment in existing fiber networks and telecom infrastructures, due to multiple factors: limited distance between users, lack of applications, high costs and high requirements in terms of lownoise fiber links. In order to reveal practical controversies in realworld deployments, several QKD field trials have been implemented by exploiting installed fiber links on a metropolitan scale, with tens of kilometers of typical distance between nodes [10,11,12,13,14,15,16,17,18,19,20,21].
Deployed commercial channels inherently suffer from higher losses and noise (due to splices, connections, bends and interfiber crosstalk), moreover their longterm stability is affected by changes in the environmental conditions and physical stress. Although many field trials were performed on a dark fiber (thus requiring a dedicated link for quantum key transmission), other experiments tested the coexistence between weak quantum signals and classical intense pulses propagated through the same installed fiber [18,19,20,21]. Classical light includes ancillary signals for QKD [18] or highspeed data traffic [19,20,21] and is mixed with quantum signals by means of dense wavelength division multiplexing (DWDM) schemes, often combined with polarization multiplexing [20] and widerange wavelength multiplexing in C and Oband [21]. Recent demonstrations are presented in Fig. 1, where the average secret key rate (SKR) achieved is reported with the corresponding transmission losses and total classical launch power.
In this work we present a field demonstration of a lowcost QKD scheme, performed over an installed fiber link situated in Florence and exhibiting 21 dB of transmission losses. A secret key rate of 3.4 kbit/s is evaluated with a finitekey analysis, in the case of simultaneous transmission of synchronization signal (with −29 dBm launch power) and quantum signal through the same fiber at a different wavelength in the Cband. Time stability of the apparatus is demonstrated as well, by employing a servolocked fiberbased interferometer for security checking.
The fiber link adopted for quantum states exchange is a portion of a darkfiber network connecting the entire Italian peninsula, from Turin National Institute of Metrological Research (INRiM) to Matera Space Center. This installed fiber of about 1700 km in length, currently employed for time standard dissemination, constitutes the proper environment for a future setup of a largescale quantum communication network, referred as the Italian Quantum Backbone [22].
Protocol
We performed the threestate BB84 protocol with timebin encoding, which has the advantage of being a simple and efficient solution for practical QKD [23]. Quantum states belonging to \(\mathcal{Z}\) basis (adopted for key bits encoding) and \(\mathcal{X}\) basis (implemented for security checking) are portrayed in Fig. 2. In each state of \(\mathcal{Z}\) basis, only one of the two time bins (early and late) is occupied by a photon, while the third state (\(\mathcal{X}\) basis) is the linear superposition of \(\mathcal{Z}\) basis with null relative phase. This relative phase is altered as a result of any attack that is addressed to quantum states, during their trip along the fiber channel. The receiver checks the relative phase of \(\mathcal{X}\) state by monitoring the outputs of a delayline interferometer with two singlephoton detectors, while the projection on \(\mathcal{Z}\) basis is made by another singlephoton detector which measures the photon arrival time. The security of this protocol against general attacks has been proven to be maintained, with finitekey analysis, when only one detector is employed for \(\mathcal {X}\) basis measurements, thus simplifying considerably the experimental resources. In addition, whenever weak coherent pulses (WCPs) are prepared instead of single photons, a very efficient onedecoy state scheme can be implemented in order to detect photon number splitting attacks [24,25,26]. The SKR length (ℓ) per privacy amplification block is given by the following formula:
where \(D_{0}^{\mathcal{Z}}\) and \(D_{1}^{\mathcal{Z}}\) are the lower bounds of vacuum events and singlephoton events in the \(\mathcal{Z}\) basis, \(h(\cdot)\) is the binary entropy function, \(\phi_{1}^{\mathcal{Z}}\) is the upper bound on the phase error rate and \(\lambda_{\mathrm{EC}}\) is the number of bits that are publicly announced during error correction [24]. Finally, \(\epsilon_{\mathrm{sec}}\) and \(\epsilon _{\mathrm{corr}}\) are the secrecy and correctness parameters. In our computations we used a block size of 10^{9} bits and \(\epsilon _{\mathrm{sec}}=\epsilon_{\mathrm{corr}}=10^{9}\).
Experimental setup
As illustrated in Fig. 2, the experimental setup consists of a transmitter (Alice) and a receiver (Bob) connected by a metropolitan darkfiber link in a loopback configuration. A standard optical mirror is installed at the other end of the fiber (situated at the telecom datacenter in Florence) in order to drive light back to the European Laboratory for Nonlinear Spectroscopy (LENS) where Alice and Bob are located. Reflected light coming back from telecom datacenter is collected with an optical circulator, as shown in Fig. 2. The total length of the loopback fiber is about 40 km, with an overall transmission loss of 21 dB. Channel stability in terms of attenuation was monitored for several hours, as reported in Fig. 3a. Figure 3b shows the dark fiber performances in terms of noise at the singlephoton level. No light was injected in the fiber during this test: the count rate reported is acquired with a singlephoton detector monitoring the end of the fiber, after applying a 200 GHz dense wavelength division multiplexing (DWDM) filter, with output wavelengths corresponding to ITUT odd channels from 21 to 51. Detector dark counts, i.e. 2.7 kHz, are subtracted during these measurements. Since the fiber is completely dark, we expect this noise to be mainly due to interfiber crosstalk, coming from other fibers in the same bundle.
To prepare a train of modulated WCPs, Alice carves with an intensity modulator (IMs) the timeencoded pulses from a tunable continuous wave (CW) laser, emitting ITUT channel 21 (1560.61 nm). Repetition rate of quantum states is 595 MHz. A second IM is used to implement the onedecoy state technique with \(\mu_{1}=0.41\) and \(\mu_{2}=0.15\) photons per pulse (only one intensity is reported in Fig. 2 for simplicity). Then, light is sent through a phase modulator (PM) for phase randomization of each state. An alternative solution would be employing a pulsed laser working in gain switching mode: in this way the phase of the weak coherent states is intrinsically random and the setup can be further simplified. Finally, a variable optical attenuator is used to reach the singlephoton regime. In order to test the QKD scheme in a more practical scenario, the synchronization signal between users is carried by classical light copropagated through the same fiber together with quantum pulses, by using a 2x1 beam splitter as shown in Fig. 2. To prepare the optical synchronization signal, we used a second laser working at 1536.61 nm (ITUT channel 51) and modulated by an extra IM with a custom pattern format at 0.145 Mbit/s. Classical light at −29 dBm launch power is then combined together with quantum pulses and sent through the dark fiber link. At Alice’s side, four electrical outputs generated by a field programmable gate array (FPGA) are used to drive the IMs for quantum and synchronization signals. Electrical pulse width is approximately 100 ps, whereas the obtained optical pulse width is around 150 ps. The PM is driven by a digitaltoanalog converter (DAC) which uses 8 bit to obtain \(2^{8}1\) different phase values. Furthermore, a pseudo random binary sequence of \(l=2^{12}1\) bit is used as a key generator, although a quantum random number generator should be used in a real implementation [27,28,29]. (This device can be included in future realization directly on Alice’s FPGA board.) At Bob’s side, a DWDM filter is used to separate classical and quantum light (channel 21 and 51 respectively). Classical pulses at 0.145 Mbit/s serve as reference signals for a time tagging unit, which collects also the electrical outputs from the two InGaAs singlephoton avalanche detectors (SPADs) that are employed for quantum state measurements [30]. Bob’s choice of measurement basis is made passively by a 10 dB beam splitter. In the \(\mathcal{Z}\) basis, one SPAD is used for collecting photons and detecting their arrival time, while pulses measured in the \(\mathcal{X}\) basis are sent to a fiberbased delayline interferometer (DLI). A second SPAD monitors one of the two outputs of the DLI, in order to check for potential eavesdropping disturbances. Additionally, to phasestabilize Bob’s DLI, a feedback scheme involving a counterpropagating CW laser (emitting ITUT channel 35, 1549.32 nm) is employed. The optical power monitored at the other DLI input allows a piezoelectric system to lock the phase, thus autostabilizing \(\mathcal{X}\) basis measurements.
Results and discussion
In Fig. 4 we present the infield performances of our QKD scheme in terms of quantum bit error rate (QBER) achieved in both measurement bases and final secret key rate (SKR) evaluated with a finitekey analysis [24]. We started testing states exchange with the fiber completely dark, i.e. with only quantum pulses propagated and electric synchronization between the two stations (Fig. 4a). Electric synchronization is provided by Alice’s FPGA, which is connected directly to Bob’s time tagger during this acquisition. Our setup (including both states preparation and measurement as well as fiber channel) exhibits good stability for more than 10 hours, that is the reason why we fixed a block size of 10^{9} for all our SKR evaluations. Then we performed a 4 hours continuous acquisition with simultaneous transmission of optical clock signals and quantum pulses (Fig. 4b). Our scheme is less stable in this case, because of the bias instability of the IM used for carving classical clock pulses. In addition, the average SKR evaluated with optical synchronization (3.40 kbit/s) is slightly lower than the one obtained with electric synchronization (4.53 kbit/s), because of background noise generated by classical pulses that results in higher QBER in both measurement bases. Another wavelength filter was added at the receiver in order to limit QBERs deterioration, but this also increased Bob’s overall losses, thus resulting in a lower raw key rate (as shown in Fig. 4b). A different and more efficient filter can be employed in order to maximize the secret key parameter. As already mentioned, both of these longterm acquisitions are achieved without manual stabilization of the experimental setup, thanks to our servolocking fiberbased interferometer.
As it is shown in Fig. 5, our SKR values are compatible with the expected rate achievable by this protocol when singlephoton detectors operate in saturation regime, due to their dead time (20 μs) which limits the maximum detection rate achievable at the receiver. Furthermore, the simulations show the performances of our scheme in case of shorter (longer) fiber link with the same intrinsic optical attenuation. Our setup can generate a positive key rate up to 28 dB channel losses, which corresponds to 175 km of ultralow loss single mode fiber.
Figure 6 shows the performances of our QKD scheme (evaluated with electric synchronization only) with increasing launch power of a CW laser emitting at ITUT channel 51 and sent into the fiber channel together with quantum signals (ITUT channel 21), by means of a DWDM scheme. As expected, the increasing classical power degrades both \(\mathcal{Z}\) basis QBER and visibility of the interferometer (related to \(\mathcal{X}\) basis QBER), in a way that at −27 dBm launch power the overall error exceeds the threshold value that prevents a secret key to be shared. At this power level, more advanced multiplexing schemes (including widerange wavelength multiplexing and polarization multiplexing) are required for secret key exchange with this protocol and detectors. We set a launch power of −29 dBm for our longterm acquisition (Fig. 4b) in order to keep the QBERs low and, at the same time, to preserve a good signal to noise ratio for clock detection at the receiver. Indeed, a lower power level would increase the occurrence of zero detection for synchronization pulses, resulting in a decreasing raw key rate.
Conclusions
In conclusion, we demonstrated a simple and lowcost quantum key distribution scheme over a metropolitan fiber link. Quantum and weak classical light have been copropagated along the installed fiber, proving the stability of the entire setup for more than 4 hours. This work acts as a milestone for the future Italian quantum network, proving how the already installed fibers can be pursued for quantum communication over the whole country.
Abbreviations
 QKD:

Quantum Key Distribution
 DWDM:

Dense Wavelenght Division Multiplexing
 InGaAs:

Indium Gallium Arsenide
 SNSPD:

Superconducting Nanowire Single Photon Detector
 bps:

bit per second or bit/s
 WCPs:

weak coherent pulses
 BB84:

Bennett and Brassard 1984 QKD protocol
 IM:

Intensity Modulator
 CW:

continuous wave
 PM:

Phase Modulator
 BS:

beam splitter
 VOA:

variable optical attenuator
 ITUT:

International Telecommunication UnionTelecommunication Standardization Bureau
 Cband:

1530–1565 nm
 Oband:

1260–1360 nm
 FPGA:

Field Programmable Gate Array
 DAC:

DigitaltoAnalog converter
 SPAD:

Single Photon Avalanche Detectors
 DLI:

delayline interferometer
 QBER:

Quantum Bit Error Rate
 SKR:

Secret Key Rate
 APD:

avalanche photodiode
 LENS:

European Laboratory for Nonlinear Spectroscopy
 INRiM:

National Institute of Metrological Research
References
 1.
Bennett CH, Brassard G. Quantum cryptography: publickey distribution and coin tossing. In: Proceedings of IEEE international conference on computers systems and signal processing. 1984. p. 175–9.
 2.
Scarani V, BechmannPasquinucci H, Cerf NJ, Dušek M, Lütkenhaus N, Peev M. The security of practical quantum key distribution. Rev Mod Phys. 2009;81(3):1301–50.
 3.
Diamanti E, Lo HK, Qi B, Yuan Z. Practical challenges in quantum key distribution. npj Quantum Inf. 2016;2:16025.
 4.
Boaron A, Boso G, Rusca D, Vulliez C, Autebert C, Caloz M, Perrenoud M, Gras G, Bussières F, Li MJ, et al.. Secure quantum key distribution over 421 km of optical fiber. Phys Rev Lett. 2018;121(19):190502.
 5.
Hwang WY. Quantum key distribution with high loss: toward global secure communication. Phys Rev Lett. 2003;91(5):057901.
 6.
Minder M, Pittaluga M, Roberts GL, Lucamarini M, Dynes JF, Yuan ZL, Shields AJ. Experimental quantum key distribution beyond the repeaterless secret key capacity. Nat Photonics. 2019;13:334–8.
 7.
Yin HL, Chen TY, Yu ZW, Liu H, You LX, Zhou YH, Chen SJ, Mao Y, Huang MQ, Zhang WJ, et al.. Measurementdeviceindependent quantum key distribution over a 404 km optical fiber. Phys Rev Lett. 2016;117(19):190501.
 8.
Da Lio B, Bacco D, Cozzolino D, Da Ros F, Guo X, Ding Y, Sasaki Y, Aikawa K, Miki S, Terai H, et al.. Recordhigh secret key rate for joint classical and quantum transmission over a 37core fiber. In: 2018 IEEE photonics conference (IPC); 2018. p. 1–2.
 9.
Dynes JF, Tam WW, Plews A, Fröhlich B, Sharpe AW, Lucamarini M, Yuan Z, Radig C, Straw A, Edwards T, et al.. Ultrahigh bandwidth quantum secured data transmission. Sci Rep. 2016;6:35149.
 10.
Qiu J. Quantum communications leap out of the lab. Nat News. 2014;508(7497):441–2.
 11.
Peev M, Pacher C, Alléaume R, Barreiro C, Bouda J, Boxleitner W, Debuisschert T, Diamanti E, Dianati M, Dynes JF, et al.. The SECOQC quantum key distribution network in Vienna. New J Phys. 2009;11(7):075001.
 12.
Yuan ZL, Shields AJ. Continuous operation of a oneway quantum key distribution system over installed telecom fibre. Opt Express. 2005;13(2):660–5.
 13.
Shimizu K, Honjo T, Fujiwara M, Ito T, Tamaki K, Miki S, Yamashita T, Terai H, Wang Z, Sasaki M. Performance of longdistance quantum key distribution over 90km optical links installed in a field environment of Tokyo metropolitan area. J Lightwave Technol. 2014;32(1):141–51.
 14.
Tang YL, Yin HL, Zhao Q, Liu H, Sun XX, Huang MQ, Zhang WJ, Chen SJ, Zhang L, You LX, et al.. Measurementdeviceindependent quantum key distribution over untrustful metropolitan network. Phys Rev X. 2016;6(1):011024.
 15.
Bunandar D, Lentine A, Lee C, Cai H, Long CM, Boynton N, Martinez N, DeRose C, Chen C, Grein M, et al.. Metropolitan quantum key distribution with silicon photonics. Phys Rev X. 2018;8(2):021009.
 16.
Collins RJ, Amiri R, Fujiwara M, Honjo T, Shimizu K, Tamaki K, Takeoka M, Andersson E, Buller GS, Sasaki M. Experimental transmission of quantum digital signatures over 90 km of installed optical fiber using a differential phase shift quantum key distribution system. Opt Lett. 2016;41(21):4883–6.
 17.
Zhang YC, Li Z, Chen Z, Weedbrook C, Zhao Y, Wang X, Xu C, Zhang X, Wang Z, Li M, et al. Continuousvariable QKD over 50km commercial fiber. arXiv:1709.04618 (2017).
 18.
Tanaka A, Fujiwara M, Nam SW, Nambu Y, Takahashi S, Maeda W, Yoshino K, Miki S, Baek B, Wang Z, et al.. Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization. Opt Express. 2008;16(15):11354–60.
 19.
Choi I, Zhou YR, Dynes JF, Yuan Z, Klar A, Sharpe A, Plews A, Lucamarini M, Radig C, Neubert J, et al.. Field trial of a quantum secured 10 Gb/s DWDM transmission system over a single installed fiber. Opt Express. 2014;22(19):23121–8.
 20.
Wonfor A, Dynes JF, Kumar R, Qin H, Tam WWS, Plews A, Sharpe AW, Lucamarini M, Yuan ZL, Penty RV, et al.. High performance field trials of QKD over a metropolitan network. In: Quantum cryptography (QCrypt); 2017.
 21.
Mao Y, Wang BX, Zhao C, Wang G, Wang R, Wang H, Zhou F, Nie J, Chen Q, Zhao Y, et al.. Integrating quantum key distribution with classical communications in backbone fiber network. Opt Express. 2018;26(5):6010–20.
 22.
Calonico D. A fibre backbone in Italy for precise time and quantum key distribution. In: 4th ETSI/IQC workshop on quantumsafe cryptography; 2016.
 23.
Boaron A, Korzh B, Houlmann R, Boso G, Rusca D, Gray S, Li MJ, Nolan D, Martin A, Zbinden H. Simple 2.5 GHz timebin quantum key distribution. Appl Phys Lett. 2018;112(17):171108.
 24.
Rusca D, Boaron A, Curty M, Martin A, Zbinden H. Security proof for a simplified Bennett–Brassard 1984 quantumkeydistribution protocol. Phys Rev A. 2018;98(5):052336.
 25.
Rusca D, Boaron A, Grünenfelder F, Martin A, Zbinden H. Finitekey analysis for the 1decoy state QKD protocol. Appl Phys Lett. 2018;112(17):171104.
 26.
Lo HK, Ma X, Chen K. Decoy state quantum key distribution. Phys Rev Lett. 2005;94(23):230504.
 27.
Avesani M, Marangon DG, Vallone G, Villoresi P. Sourcedeviceindependent heterodynebased quantum random number generator at 17 Gbps. Nat Commun. 2018;9(1):5365.
 28.
Stefanov A, Gisin N, Guinnard O, Guinnard L, Zbinden H. Optical quantum random number generator. J Mod Opt. 2000;47(4):595–8.
 29.
Jennewein T, Achleitner U, Weihs G, Weinfurter H, Zeilinger A. A fast and compact quantum random number generator. Rev Sci Instrum. 2000;71(4):1675–80.
 30.
Tosi A, Della Frera A, Bahgat Shehata A, Scarcella C. Fully programmable singlephoton detection module for InGaAs/InP singlephoton avalanche diodes with clean and subnanosecond gating transitions. Rev Sci Instrum. 2012;83(1):013104.
Acknowledgements
D. Bacco acknowledges financial support from the COST action MP 1403.
Availability of data and materials
Not applicable. For all requests relating to the paper, please contact the first author.
Funding
This work is supported by the Center of Excellence, SPOCSilicon Photonics for Optical Communications (ref DNRF123), by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/20072013) under REA grant agreement n^{∘} 609405 (COFUNDPostdocDTU). This research was sponsored by the NATO Science for Peace and Security program under grant G5485.
Author information
Affiliations
Contributions
DB and AZ conceived the experiment. DB, IV, NB carried out the experimental work. DB and BDL carried out the theoretical analysis on the protocol. All authors discussed the results and contributed to the writing of the manuscript. All authors read and approved the final manuscript.
Corresponding author
Correspondence to Davide Bacco.
Ethics declarations
Competing interests
The authors declare that they have no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bacco, D., Vagniluca, I., Da Lio, B. et al. Field trial of a threestate quantum key distribution scheme in the Florence metropolitan area. EPJ Quantum Technol. 6, 5 (2019) doi:10.1140/epjqt/s405070190075x
Received:
Accepted:
Published: