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Abstract
The tolerance of continuous-variable quantum key distribution to co-propagating DWDM channels is investigated. The quantum channel is operated in the S-band or L-band and multiplexed with a commercial C-band DWDM system. The results show that, compared to previously proposed configurations, the number of co-propagating channels can be doubled. At a fiber length of 25 km, 56 DWDM channels with a total launch power of 14.5 dBm are tolerated by the quantum channel.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The majority of today’s cryptosystems is based on public key cryptography. There are many different public key methods, but none of these is known to be secure against quantum computer attacks [1]. Due to that, the long term security of these methods is uncertain. One alternative that is known to be secure against quantum computer attacks, and therefore ensures long term security, is quantum key distribution (QKD). The downside of QKD is that it requires a dedicated quantum communication system. The wide variety of QKD-realizations that have been proposed during the past 20 years can be divided into two main groups: Discrete variable (DV-)QKD and continuous variable (CV-)QKD. In DV-QKD, the quantum signal is detected by single photon counters. These are expensive and exhibit a relatively low quantum efficiency. Additionally, single photon counters detect photons in a wavelength range of several 100 nm. If the QKD system shares a fiber with a classical WDM system, this poses a major challenge since the WDM system induces false counts at the single photon counter. These can be triggered either directly by photons at the WDM system’s operating wavelengths or indirectly through photons generated at a different wavelength by Raman scattering. One way to reduce the impact is to operate the QKD system at a large spectral distance to the WDM system, outside the broadband Raman scattering spectrum [2–5]. This option is not attractive due to the increased fiber loss for the quantum channel and the extremely wide filter specification that are required for multiplexing and demultiplexing the quantum signal with the DWDM channels. Another option is to reduce the launch power of the DWDM system [6], which limits the DWDM system in terms of reach and modulation format. In contrast to DV-QKD, CV-QKD systems employ coherent receivers. Due to the local oscillator (LO), coherent receivers provide a strong wavelength selectivity. Thus, CV-QKD systems promise to be more robust against the wideband Raman scattering and therefore more suitable for an integration into existing fiber-optic networks. Moreover, CV-QKD systems require standard telecom components only [7], which is more practical for a wide implementation.
This motivated the early work that was done on the tolerance of CV-QKD to coexisting WDM channels in the same fiber [8,9]. There, Raman scattering was identified to be the limiting factor for the performance of the QKD system. However, the experiments were not realistic because the WDM system was emulated by only 1–2 unmodulated laser sources. Recently, more realistic experiments with modulated and amplified DWDM channels have been reported [10,11]. In [11], over 10 km, 18 channels at a total launch power of 14 dBm could be tolerated by the quantum channel. In all the previous experiments the DWDM channels and the quantum channel were placed in the C-band. In this configuration, the impact of the DWDM channels on the quantum channel due to Raman scattering can be relatively small if the quantum channel is placed within a spectral distance of 5 nm to all DWDM channels. In a DWDM system, this might not be the best option. One problem is the ASE noise that has to be suppressed heavily before the quantum channel is coupled into the fiber. Also, a part of the C-band would no longer be available for the WDM system. Other options for the integration of the QKD channel would be in the L- or S-band. Fiber-optic filters that combine L-band and C-band or S-band and C-band are cost-effective and readily available. The ASE noise in S-band and L-band is substantially lower than in the C-band and can be suppressed with low technical effort. Additionally, the whole C-band remains available for the DWDM system. In this article, we investigate configurations with the quantum channel in the L-band and in the S-band. In the experiments, the quantum channel is embedded in a commercial C-band DWDM system.
2. Impact of Raman scattering on the quantum channel
In previous experiments [8,9], Raman scattering was identified to be the dominating impairment for the quantum channel. For that reason, we would like to briefly review the important mechanisms of Raman scattering in a CV-QKD system. Raman scattering induces noise at the optical wavelength of the quantum channel λQ. This optical noise is seen as an additional excess noise power in the received signal. For security reasons, the excess noise is attributed to a potential eavesdopper (Eve) and decreases the performance of the CV-QKD system in terms of achievable key rate and distance. Usually, the total excess noise power at the receiver site (Bob) ξBob is given in shot noise units (SNU).
Let us first establish a link between the noise level measured by an optical spectrum analyzer (OSA) and the induced excess noise in the heterodyne quantum system. An optical noise with power PBob(λQ, BQ) at the wavelength λQ within the quantum channel bandwidth BQ that is present at the input of Bob’s receiver induces an excess noise power in SNU of
Here, νQ is the optical center frequency of the quantum signal, η is the receiver efficiency and h is the Planck constant. The optical power measured with an OSA POSA(λQ, ΔλRBW) is usually given in Watt related to the resolution bandwidth ΔλRBW expressed as a wavelength. We assume that the power spectrum of the optical noise is constant within ΔλRBW and BQ. Then, with the optical noise power being measured at Bob’s receiver, we have where ΔνRBW is the resolution bandwidth in Hertz and c0 stands for the vacuum speed of light. With ΔλRBW ≪ λQ, Eq. (2) can be written in terms of ΔλRBW asThe DWDM channels exchange power while propagating through the fiber due to stimulated Raman scattering. However, this effect is relatively small. Even with a fully populated C-band and a total launch power of 20 dBm, the maximum power difference between the DWDM channels after transmission over 100 km of standard single mode fiber was shown to be below 1 dB [12]. Therefore, we only consider power changes of the DWDM channels due to fiber loss. Also, we assume an equal launch power for all the DWDM channels and that the fiber loss is equal for the DWDM channels and the quantum channel. In general, the Raman scattering noise at νQ due to a DWDM channel at the frequency νWDM is a result of spontaneous and stimulated Raman scattering. The evolution of the Stokes and anti-Stokes Raman scattering power PS(z) and PAS(z) along the fiber coordinate z in a small bandwidth B around νQ is described by the following differential equations [13]
Here, α is the attenuation coefficient, γR,DWDM is the fiber Raman coefficient depending on the frequencies of the quantum channel and the DWDM channels averaged over all DWDM channels. P0 is the total launch power of the DWDM system and NBE is the Bose-Einstein factor. The third term on the right hand side of Eqs. (4) and (5) describes spontaneous Raman scattering. The second term describes stimulated Raman scattering due to the previously generated total Raman scattering power. This term can be neglected if We can easily check if this would be a reasonable assumption by using Eq. (1) to reformulate Eq. (6) in terms of the resulting excess noise power in SNU. Additionally, we divide by ηe−αz in order to get the equivalent excess noise power for the Stokes and anti-Stokes case at Alice’s site and . The result is At room temperature and for a frequency difference between quantum channel and DWDM channels of less than 7.5 THz, corresponding to a wavelength difference of about 60 nm, the factor NBE is greater than 0.43. At the same time, CV-QKD systems require excess noise levels of ξAlice < 0.2 SNU even for very short distances of L = 15 km [14]. For increasing fiber length L, the maximum acceptable value of ξAlice decreases. Therefore, the conditions Eq. (6) are valid assumptions and the term for stimulated Raman scattering in Eqs. (4) and (5) can be neglected. Thus, we get the solutions In terms of the crucial excess noise in SNU referred to Alice’s site we get in the Stokes and anti-Stokes case The excess noise is proportional to the launch power of the DWDM system and the fiber length. Thus, to investigate the impact of Raman scattering to a CV-QKD system, it is sufficient to measure it just once for the desired wavelength configuration. The expected performance for that configuration can then be scaled to a different launch power and fiber length.3. Choice of quantum channel wavelength
In order to identify suitable wavelengths for the quantum channel we measured spontaneous Raman scattering spectra induced by a pump laser in the C-band. For this, a continuous wave laser with a power of 1.4 dBm was launched into 25 km of SMF-28 fiber. At the fiber output, the spectrum was measured using an optical spectrum analyzer (OSA). Figure 1 shows the resulting spectra for pump wavelengths located at the edges of the C-band. If the quantum channel is operated in the C-band along with the DWDM channels, the best would be to make use of the narrow local minima located at about λch ± 3 nm with λch being the wavelength of a DWDM channel. However, this approach is only possible for DWDM channels within a small fraction of the C-band. The major part of the C-band suffers from a relatively high level of Raman scattering due to the local maxima at about λch ± 15 nm. This limits the number of usable DWDM channels. Another argument against a quantum channel in the C-band is the high level of ASE-noise that has to be suppressed at the quantum channel wavelength before the quantum channel is multiplexed with the DWDM system. A much more appealing alternative seems to be a quantum channel in the S-band where Raman scattering is relatively low over a wide range of wavelengths. In order to fully exploit this with a fully populated C-band, the best would be a quantum channel at 1480 nm. However, fiber attenuation increases with decreasing wavelength in the S-band which also decreases the key rate and achievable distance of the CV-QKD system. Also, at long distances a fully populated C-band might not be tolerated by the quantum channel. As a compromise, we chose a wavelength of λQ,S = 1504.98 nm on the S-band ITU channel grid. In addition to λQ,S, we chose a wavelength λQ,L for experiments with a quantum channel in the L-band. Here, the goal was to exploit the local Raman scattering minimum at about λch + 47 nm. Similarly to the line of thought for choosing λQ,S, we chose λQ,L = 1580.35 nm to avoid the increasing loss at longer wavelengths in the L-band.
Fig. 1 Measured Raman scattering spectra at the output of a 25 km SMF-28 fiber. The peak power normalized spectra are shown when a CW laser at 1530 nm (left) respectively 1565 nm (right) was launched with a power of 1.4 dBm and recorded with a resolution bandwidth of 1 nm.
4. Experimental setup
4.1. DWDM system
Figure 2 shows the setup for combining the quantum channel with the DWDM-system as well as the investigated channel configurations. To generate the DWDM channels, a frequency comb consisting of 96 continuous wave sources on the C-band 50 GHz ITU channel grid is multiplexed and amplified. A commercial Infinera transponder is used to modulate all 96 channels with 32 GBd DP-QPSK at the same time. The modulated DWDM comb is amplified again to compensate for losses. Then, the 96 signals are decorrelated with a setup consisting of a demultiplexer, several fibers of different lengths and a multiplexer with an amplifier at the end. The signal is launched into a wavelength selective switch (WSS) which allows to activate only the desired DWDM channel wavelengths for the QKD experiment.
Fig. 2 Experimental setups for multiplexing the DWDM system with the quantum channel and schematic representations of the corresponding spectra at the fiber input. Setup A is for a quantum channel in the S-band and Setup B for a quantum channel in the L-band. The number of DWDM channels Nch is varied in two different configurations: Either “Blue WDM” or “Red WDM”. The OSA is used to measure the optical noise at the quantum channel wavelength before each transmission experiment. During the transmission experiments the OSA is not connected.
The DWDM wavelengths are allocated in two different configurations. With the “Blue WDM” configuration, channels are added with increasing wavelength starting from the blue edge of the C-band. With the “Red WDM” configuration, channels are added with decreasing wavelength starting from the red edge of the C-band. The DWDM signal is fed into the booster. It incorporates an erbium doped fiber amplifier (EDFA) to set the launch power at the fiber input to either 0 dBm or −3 dBm per channel.
Additionally, the booster generates the optical supervisory channel (OSC), which is a low baud rate channel used for controlling and monitoring the network. In a real network, the quantum channel has to tolerate the OSC. That is why it is also transmitted in all experiments even though it is not processed at the receiver. The OSC is transmitted at a wavelength of 1509 nm and comes with a noise floor covering the entire S-band.
In the S-band configuration the launch power of the OSC is −27.6 dBm. At this launch power the OSC noise floor induces an additional excess noise of 0.01 SNU at the quantum channel wavelength λQ,S. In order to mitigate this impact, the OSC is separated from the DWDM channels using an S/C-band splitter before a narrow bandpass filter is applied to it. Like this, the noise floor of the OSC at λQ,S is suppressed by at least 10 dB. After that, the quantum channel is combined with the OSC via a 50/50 coupler. The subsequent S/C-band combiner multiplexes quantum channel, DWDM channels and OSC. Then, the total signal is propagated over 25 km or 50 km of Corning SMF-28 ULL fiber. At the fiber output, an S/C-band splitter is applied. Before the quantum signal is detected, the OSC is suppressed using a band-pass filter.
In the L-band configuration, two cascaded SC/L-band combiners are used to multiplex the quantum signal with the DWDM system. This cascade is required to achieve sufficient suppression of the ASE-noise at the quantum channel wavelength λQ,L.
For each transmission experiment, the optical spectrum is measured at the receiver site. The measured noise level at the quantum channel wavelength serves as an estimate for the excess noise power due to Raman scattering.
At the Receiver site of the DWDM system the BER of one DWDM channel is continuously monitored. During the experiments, no performance degradation occurred.
4.2. Heterodyne quantum communication system
Figure 3 shows the experimental heterodyne quantum communication system. Alice uses a nested Mach-Zehnder modulator (NMZM) driven by an arbitrary waveform generator to perform single sideband (SSB) modulation. The electrical modulation signal m(t) contains the quantum signal at an intermediate frequency of fs = 120 MHz as well as a sinusoidal pilot signal at a frequency of fP2 = 40 MHz. Thus, it has the form
Here, s(t) is the pulse-shaped baseband quantum signal. It contains Alice’s symbols a(n) pulse-shaped by a root raised cosine filter with a roll-off factor of r = 0.5. The bandwidth of the shaping filter is set to be equal to the symbol rate of the quantum signal, which is 40 MBd. The system supports an arbitrary choice of modulation format. Here, Alice’s symbols a(n) are complex numbers where the real and imaginary part are independent Gaussian distributed random variables, which is a common modulation format in CV-QKD. The bias voltages of the NMZM are tuned to a small offset with respect to the zero transmission point in order to transmit a part of the optical carrier such that its optical power is equal to that of the pilot in m(t). The peak voltages of the real and the imaginary part of m(t) are lower than 10% of the Vπ of the NMZM. Thus, the modulation is approximately linear. The optical carrier and the electrical pilot are denoted as pilot 1 and pilot 2 respectively. The desired launch power at the output of the multiplexer is set by a variable optical attenuator. Then, the optical signal is multiplexed with the DWDM system and propagated through the fiber, before it is demultiplexed again and fed into Bob’s balanced receiver.Fig. 3 Heterodyne quantum communication system with free-running LO and ADC. Two frequency-multiplexed pilots are used to support Bob’s quantum signal demodulation. A detailed description of the DSP can be found in [15]. Alice applies a bivariate Gaussian modulation to the quantum signal. Multiplexer and demultiplexer are as shown in Fig. 2.
Bob tunes his LO to have a frequency difference δνAB compared to Alice’s laser. It is set to 20 MHz < δνAB < 50 MHz. Thus, the quantum signal is converted to the electrical intermediate frequency fQ = δνAB + fs > 140 MHz which is higher than the full base-band quantum signal bandwidth BQ(1 + r)/2 = 30 MHz. This allows Bob to perform a heterodyne measurement of the quantum signal [16]. Bob’s local oscillator (LO) and the analog to digital converter (ADC) are free running. The polarization of the LO is manually aligned to the one of the incoming quantum signal using a polarization controller (PC). The pilots enable Bob to perform clock recovery and carrier phase estimation without direct evaluation of the quantum signal, which is necessary to successfully demodulate the quantum signal at a typical quantum signal SNR of much lower than 0 dB.
In the DSP routine, phase and frequency estimation are performed based on an extended Kalman smoother. A detailed description of the full DSP routine can be found in [15]. The output of the DSP is the noisy quantum symbol sequence b(n). In each transmission experiment 15 quantum signal blocks are received and processed, where each block consists of 107 symbols. After each block, the demultiplexer is disconnected from the receiver for a short period during which a noise signal of the same block length is recorded. Additionally, before each transmission experiment, an electronic noise signal is recorded by also switching off the LO. The noise signals are processed in the same way as the quantum signal. Like this, the total noise sequence bN,tot(n) and the electronic noise sequence bN,el(n) are obtained. Based on the processed sequences, estimates for the total power, the total noise power and the electronic noise power are calculated as
Here, 〈·〉 stands for the arithmetic mean. The shot noise power per quadrature is estimated by N̂0 = (P̂N,tot − P̂N,el)/2. Usually in CV-QKD, in order to enable Bob to estimate the received quantum signal power PQ within b(n), Alice reveals a randomly selected subset of her symbols a(n). Here, the complete sequence a(n) is used to calculate the estimate Finally, the excess noise power in SNU for each transmission experiment is estimated as Using the security analysis in [14], the excess noise power can be translated to an achievable key rate. For that, a reconciliation efficiency of 95% is assumed. The key rate calculation based on [14] is also used to optimize the optical launch power of the quantum signal for each experimental scenario. This optimization is performed with respect to a maximum level of tolerable excess noise.5. Results & discussion
Figure 4 shows the results for a fiber length of 25 km and a launch power of 0 dBm per channel. From the good match between solid and hollow data points it can be seen that the excess noise corresponding to the noise level measured with an OSA predicts very well the actual excess noise that is measured in the transmission experiments. This indicates that Raman scattering is the dominant impairment caused by the DWDM system and that it is the limiting factor for the embedded quantum channel. In accordance to the discussion in section 3, the “Red WDM” configuration induces the lowest noise level in the S-band. It corresponds to the best case for the quantum channel’s performance. In this case, the average additional excess noise per channel up to the 16th channel, is only 3.7 × 10−3 SNU. For a practical scenario in which all C-band DWDM channels should be available for use, it is also interesting to look at the results for the “Blue WDM” channel allocation. This corresponds to the worst case for the quantum channel wavelength λQ,S. In this case, the average excess noise is 7.5 × 10−3 SNU per channel. This is twice as much as with the “Red WDM” allocation. For the quantum channel wavelength λQ,L, the “Blue WDM” allocation is the best case in terms of Raman scattering. It shows an average additional excess noise of 1.1 × 10−2 SNU per channel. Thus, it can be concluded that the S-band configuration that is preferable over the L-band configuration. For comparison, the results for 25 km of reference [9] are also shown. There, only one CW laser source was transmitted which was located at 1550.12 nm while the quantum channel was at 1531.12 nm. This scenario is similar to the worst case channel map of the S-band configuration in the present work. However, the additional excess noise per channel in ref [9] is still higher.
Fig. 4 Experimental results for a fiber length of 25 km and a launch power of 0 dBm per DWDM channel. The launch power of the quantum channel was 2.4 ph/sym.
For shorter distances of 50 km and less, a launch power of −3 dBm per channel would be sufficient in many cases. Figure 5 shows the experimental results for a launch power of −3 dBm at fiber lengths of 25 km and 50 km. The quantum channel was in the S-band with a “Red WDM” channel map. The excess noise in the transmission experiments for 50 km exhibit an increased fluctuation compared to the 25 km results. Additionally, at 50 km the measured excess noise is significantly higher than it is predicted from evaluating the Raman scattering spectrum. This behavior is not caused by the DWDM system. It is a result of cross-talk from the pilot tones to the quantum channel due to undesired non-linearities of the receiver. This nonlinear cross-talk increases the total excess noise. Also, the receiver non-linearity is strongly frequency dependent while the differential frequency of the lasers δνAB is fluctuating. This causes an additional variation of the excess noise result. For 50 km, this effect is stronger because the excess noise is referred to Alice’s site, meaning that Bob’s measured excess noise is multiplied by a higher channel attenuation. However, the slope of the measured excess noise is in agreement with the predicted excess noise from the optical spectrum.
Fig. 5 Experimental results for a reduced launch power of −3 dBm per channel in the S-band configuration with a “Red WDM” map. Results are shown for a fiber length of 50 km and 25 km where the quantum channel launch power was 2 ph/sym and 2.4 ph/sym respectively.
At 50 km, about the same excess noise power is measured with the OSA for 16 DWDM channels as at 25 km for 32 channels. This is in excellent agreement with Eq. (9).
Over a distance of 25 km, the integration of a quantum channel into a DWDM systems seems highly feasible. A total of 56 channels can be used in the C-band, still leaving a margin to the zero key rate threshold of about 0.04 SNU. This margin would be available for statistical worst case estimates based on confidence intervals as it is commonly done in CV-QKD.
The 56 channels correspond to a total DWDM power of 28 mW (14.5 dBm) and result in an excess noise of 0.115 SNU. In [9], this level of excess noise is reached at a launch power of about 10.5 mW which corresponds to only 21 channels.
At 50 km, 16 channels can be used, resulting in an additional excess noise of 0.07 SNU. In [9] the same level of excess noise is reached for a DWDM power corresponding to only 8 channels in our experiment. Thus, compared to the C-band configuration of [9], the proposed S-band configuration allows to double the channel count at the same quantum channel performance.
The results show also an improvement compared to [11] where a quantum channel was successfully embedded in a DWDM system with 16 channels at a total launch power of 14 dBm over 10 km. There, all DWDM channels are at less than 6 nm spectral distance to the quantum channel, meaning that the narrow Raman scattering minimum seen in Fig. 1 is exploited. As a result, launch power per channel and number of DWDM channels can not be traded off equally for one another. In contrast to that, our S-band quantum channel allows for such an equal trade-off between channel count and launch power within a large part of the C-band, providing a higher level of flexibility.
6. Conclusion
The tolerance of a CV-QKD system in the S- and L-band to a co-propagating commercial C-band DWDM system was investigated experimentally. The results show that operating the quantum channel in the S-band is always better than in the L-band. The S-band configuration shows also a better performance compared to all C-band configurations that have been reported so far. Compared to the C-band configuration in [9], the DWDM power can be more than doubled. Over 25 km, 56 C-band channels on a 50 GHz grid at a total launch power of 14.5 dBm can be tolerated. The impact is approximately equally distributed between these 56 channels. Being able to use such a large part of the C-band provides a high level of flexibility for DWDM channel allocation.
Funding
German Federal Ministry of Education and Research (BMBF) within the project SENDATE FICUS (FKZ16KIS0490).
Acknowledgments
Special thanks to Ulrich Gaubatz and Bernhard Spinnler from Coriant R&D GmbH for the fruitful discussions and the valuable input for the experiments. Portions of this work have been accepted for presentation at the Optical Fiber Communication Conference in 2019, Experimental Investigation of Heterodyne Quantum Key Distribution in the S-Band Embedded in a Commercial DWDM System, Th1J.3.
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