Experimental Demonstration of High Key Rate and Low Complexity CVQKD System with Local Local Oscillator

We experimentally demonstrate a 250MHz repetition rate Gaussian-modulated coherent-state CVQKD with local local oscillator implementation which is capable of realizing record 14.2 Mbps key generation in the asymptotic regime over 15km of optical fiber.


Experimental setup
shows the experimental setup of our GMCS-LLO-CVQKD system realized using COTS optical communication components. In a commercial system it is clear that two laser sources will be used in Alice and Bob, however, for convenience in this laboratory demonstration we use a single laser (center wavelength of 1549.73nm and a linewidth ∆ of 50 kHz) both in the transmitter and local oscillator in the receiver. The transmission distance of the CVQKD signals is significantly greater than the coherence length of the source laser, therefore the noise performance of the system is equivalent to one with a second laser at Bob, whose wavelength is controlled by a feedback loop. We note that the system has also been tested with a second laser at Bob and the experimental results are equivalent to those presented here. The output of the source laser is split by a 50:50 beam splitter (BS) and each arm contains an optical isolator to prevent back reflections. At Alice, a LiNbO3 intensity modulator (AM1, iXblue) with high extinction ratio is used to transform the continuous wave (CW) light into 0.2ns pulses at a rate of 500MHz. This pulse train is modulated as interleaved signal and reference pulse trains, one delayed by 2ns relative to the other. In this setup, the signal amplitude is modulated by a second LiNbO3 intensity modulator (AM2) and the phase is modulated by a cascaded pair of electro-optic phase modulators (PM1,PM2, iXbule). All modulation and synchronization signals originate from an arbitrary-waveform generator (AWG, Tektronix) and are then amplified by wideband RF amplifiers (AMP, iXblue). These amplified signals are then shifted to the appropriate bias voltage levels by bias-tees. In GMCS, the phase needs to be modulated between 0 to 2 . As the high modulation voltage swing required to provide a 0 -2 modulation range [10] is not available from the available broadband amplifiers, two PMs (PM1 and PM2) are cascaded to provide the required phase modulation. The amplitude and phase of the signal pulses are randomly modulated with a two-dimensional zero-centered Gaussian distribution with an adjustable modulation variance where is the shot noise variance. The variance is tuned by a variable optical attenuator (VOA). Reference pulses are modulated with a fixed intensity 2 and a constant zero phase. This enables the phase sharing scheme described in [8] to be used to correct for fast phase drift through reference pulses. A 50:50 BS placed at the output of Alice is used to monitor and optimize the in real time. After that, the signal and reference pulses propagate through a 15km standard single mode fiber spool (3.0dB loss).
At Bob, the LO with a power of 13.5dBm provides a large shot to electronics noise ratio of 10. A polarization controller (PC) is applied to compensate the polarization drift during transmission and from environmental perturbations. In order to measure both X and P quadrature through heterodyne detection, both signal and reference pulses are fed into a 90-degree optical hybrid (Kylia) and detected by two shot-noise limited balanced homodyne detectors (BHD, Thorlabs). An oscilloscope (Keysight, DOSO254A) with a bandwidth of 2.5GHz is used to collect the quadrature information and the results are sent to a computer for √ normalization. The real-time shot noise is determined by measuring the variance between the signal and reference pulses. Consequently, the effect of the photon leakage can be tracked and corrected correspondingly. Such a system configuration has significant advantages of low complexity and adjustment-flexibility.

Noise model analysis
Optimal performance requires a comprehensive noise analysis, especially for the excess noise that arises from the experimental imperfections and noise introduced by Eve's manipulation. All values are normalized to . One of the most critical contributions to the excess noise in the LLO-CVQKD system is the phase noise, which contains two main contributions [11]: 1. the phase estimation error noise originating from the quantum uncertainty of the reference pulse at the detector as = ( + 1)/ 2 where is the total noise; and 2. the drift noise resulting from the relative phase drift between the lasers at Alice and Bob; this can be calculated as , where ∆ , ∆ are the lasers' linewidths and =250 MHz is the data repetition rate. In addition to the phase noise, several other excess noise sources also cause a degradation in system performance. Firstly, the modulation noise due to the amplitude leakage on each optical pulses caused by amplitude modulator's (AM) finite dynamic range, which is approximated as = 2 10 − /10 where is the AM extinction ratio. Secondly, the ADC quantization noise appears in Bob's output measurements and its value is given by ≥ 2 /(12 * 2 ). Other noise contributions, in our experimental setup, are deemed small enough to be included within the original system excess noise =0.01. The overall excess noise model can be described as: =

Experimental results
From the above expressions, we find both and 2 critically influence the excess noise, and hence the system performance. Therefore, instead of optimizing system parameters individually, the combined-optimization method evaluates and 2 together and to validate our proposed method by experiment. The other parameters are identical to the values used in our experiment, shown in Fig. 2(a). Following the secret key rate derivation with heterodyne detection in [12], the theoretical key rate performance for varying and 2 is compared in Fig. 2(b). The peak key rate of 14.6Mbps occurs in simulation when =3.1 and 2 =622. Any other parameter value choice away from the peak point reduces the key rate performance. In order to validate the theoretical optimization method, the simulation and experimental data for a range of reference pulse intensities with 15km optical fiber at =3.1 are shown in Fig.  2(c). The excess noise (grey circles) measured using a block size of 10 7 data is a good fit to the derived noise model (blue line). The minimum excess noise in simulation is 0.0802 at 2 / =221. Experimental characterization and secure key rate estimation are shown in Fig.3. Here the excess noise measurements (red stars) are shown in Fig. 3(a), where each block has a size of 10 7 data and the measurement follows the standard procedures mentioned in [5,9].
, the average excess noise when a 15km fiber is used was 0.0823 (red dashed line) in an asymptotic regime. According to the excess noise, thresholds shown as the solid lines in Fig. 3(a), a stable secret key rate generation in the asymptotic regime of greater than 10Mbps is predicted to be achieved. Fig. 3 (b) presents the simulation predictions of secret key rate with respect to transmission distances, together with that estimated from our experiment. The asymptotic theoretical key rate of our optimized model (blue dashed line) and excess noise thresholds (solid lines) shown in Fig. 3(a) are plotted respectively. For our system, the key rate is experimentally investigated under both a 15km optical fiber where a key rate of 14.2Mbps (red star) is predicted. For a 3dB equivalent attenuation loss an excess noise of = 0.0806 is achieved and a key rate of 14.5Mbps (grey circle) predicted. Considering the environmental perturbation, it is reasonable that the attenuation-only case gives a slightly better result. Although the performance is degraded if finite-size effects are considered, we have verified the feasibility of implementing a 10Mbps, low complexity LLO-CVQKD system over metropolitan area length scales.

Conclusion
In this paper, a 250MHz, low complexity LLO-CVQKD system is proposed and a record asymptotic key rate of 14.2Mbpsover 15km optical fiber has been predicted. The real-time shot noise calibration and combined-optimization scheme are integrated through noise model analysis to achieve a stable low excess noise performance. It is expected that a higher repetition rate can be achieved or the transmission distance extended to 65km before the link fails. The excess noise also can be additionally reduced at the expense of additional system complexity.