Experimental setup

An illustration of our experimental setup is depicted in Fig. 1. The photon source creates pairs of frequency anti-correlated photons by type-0 spontaneous parametric down-conversion. The Sagnac scheme is used to produce the polarisation-entangled quantum state

$$\left|{\Phi }^{-}\right\rangle =\frac{1}{\sqrt{2}}(\left|{{{V}}}_{{\rm{s}}}{{{V}}}_{{\rm{i}}}\right\rangle -\left|{{{H}}}_{{\rm{s}}}{{{H}}}_{{\rm{i}}}\right\rangle ).$$ (1)

Fig. 1: Setup and location of the experiment. We used a fibre optic cable which links the Mediterranean islands of Malta and Sicily. A continuous-wave laser at 775 nm produces, via spontaneous parametric down-conversion, photon pairs which are entangled in polarisation due to the Sagnac geometry. Signal and idler photons are separated by frequency into two different fibres; one photon is detected immediately in Malta in a polarisation analysis module consisting of a half-wave plate in front of a PBS and one superconducting nanowire single-photon detector (SNSPD), and the other detected by a second detector in the same cryostat after transmission through the 192 km submarine fibre loop and a polarisation analysis module. (\(\lambda /4\), \(\lambda /2\): wave-plates; PBS, polarising beam-splitter; YVO\({}_{4}\), yttrium orthovanadate plate; DM, dichroic mirror; PPLN, MgO-doped periodically poled lithium niobate crystal (MgO:ppLN); WDM1: 0.6 nm band-pass filter (centre wavelength 1551.72 nm); WDM2: 0.6 nm band-pass filter (centre wavelength 1548.51 nm); PC, fibre polarisation controllers; LPF, 780 nm long-pass filter; SNSPD, superconducting nanowire single photon detectors; TTM, time-tagging module; FSB, free-space beam. Mirrors and fibre couplers not labelled, lenses omitted.) Image taken from NASA Worldview [https://earthdata.nasa.gov/worldview] which is free to use under public domain. Full size image

Spectral filtering using wavelength-division multiplexers separates the photons into two frequency channels—ITU Grid channels 32 (1551.72 nm) and 36 (1548.51 nm)—with the spacing between adjacent channels being 100 GHz and with each channel having a full-width at half maximum (FWHM) of 0.6 nm (similar to that described in the ref. 20).

One photon from each pair was sent to a polarisation analysis and detection module located in Malta close to the source. Its entangled partner photon was sent to Sicily via a submarine telecommunications optical fibre cable and looped back to Malta. The submarine cable, 96 km long each way, introduced a one-way attenuation of 24 dB and consisted of a bundle of several non-zero dispersion shifted fibres (Corning LEAF21) which comply with the specifications of the International Telecommunication Union (ITU-T G.655). The cable contained some fibres carrying classical data in the C-band around 1550 nm at optical powers in the order of milliwatts, as well as two dark fibres that were used as the quantum channel. In Sicily the two fibre ends were patched together in an underground utility vault on the outskirts of the town of Pozzallo (Italy), resulting in a looped quantum channel 192 km in length, over which the total attenuation was measured at 48 dB. Although the fibres were located inside the same cable, no cross-talk from the classical signals was observed in the quantum channel at our wavelengths. Upon its return to Malta, the photon was detected in close proximity to the source.

Identification of photon pairs

Pairs of photons were identified using timing cross-correlations, an example of which is shown in Fig. 2. The large effective jitter of the system was a primary source of error. In an independent measurement without a long fibre, this peak is 250 ps wide, mainly due to timing uncertainties in the time-tagging unit and the jitter of the detection system. Improved electronics could more than halve this. Chromatic dispersion accounted for a further 760 ps,21 taking into account the shape of the spectrum. This effect can also be mitigated, for example by using narrow band chirped fibre Bragg grating filters.23 Further, separate laboratory experiments have shown that the synchronisation scheme employed using the time taggers introduced a further 500 ps of timing uncertainty when measuring a temporal delay of about 1 ms. This effect could also be compensated by locking the internal clock of the time tagging unit to a more stable external clock. The above techniques should enable us to significantly increase the link distance and key rate.

Fig. 2: Cross-Correlation. The cross-correlation function between the time tags from the two detectors shows a peak at a relative delay of \(0.945\) ms, which corresponds exactly to the total loop distance of (192,820.538 \(\pm\) 0.004) m, assuming that the latency of the two detectors is identical. The full-width at half-maximum is \(1\) ns. The three main factors that contribute to the peak width are the chromatic dispersion of the fibre link of \(760\) ps for our signal spectrum, the timing jitter of the detectors and of the time-tagging units — \({\sim}{250}\) ps and the clock accuracy estimated from a separate measurement (using a 1 ms delay in the lab) of about 500 ps. The data shown here was measured over \(100\) s, while the rate of coincident clicks was \(3.8\pm 0.2\) s−1. The orange graph is a fit to a measurement using the same detectors without the long fibre link. It has been normalised to the same height as the measured counts from the link experiment. The FWHM is here \(250\) ps in this case. Full size image

The number of coincident pairs of photons was calculated by integrating the correlation function over a region of \(823\) ps, equivalent to \(10\) time-bins of the time tagging unit. The local count rates were \(2.1\,\times\,1{0}^{6}\) s−1 in the first detector and \(55\) s−1 \(\pm\) \(2\) s−1 in the detector after the link, with \(20\) s−1 of these being dark counts. The average rate of coincidence counts for the \(100\) s-long measurements was \(4.3\,\pm\,0.3\) s−1 for the measurements that were supposed to be correlated, horizontal-horizontal (H-H), vertical-vertical (V-V), diagonal-antidiagonal (D-A) and antidiagonal-diagonal (A-D). During the remaining combinations, where no correlation was expected, the average observed coincidence rate was \(0.3\,\pm\,0.2\) s−1.

Measurements of the fidelity of the quantum state

To quantify the quality of the entangled state after transmission through both fibres used in the submarine cable, we performed a series of two-photon correlation measurements. The polarisation-analysis modules were used to measure the coincidence visibility in the H–V or D–A bases, with four measurements required for each basis setting. The fidelity of the two-photon state with respect to Bell state (Eq. (1)) is lower-bounded by the arithmetic mean of the two visibilities.24,25 The highest fidelity measured was \(88\,\pm\,2\)%. Locally, the fidelity was characterised to be \(98\,\pm\,0.2\)%. This apparent deterioration of the quantum state is attributed mainly to the rather large coincidence window of 823 ps (which was a compromise between the optimum pair rate and least error rate) as well as the high local count rate of \(2.1\,\times\,1{0}^{6}\) s−1. This, together with the dark counts, increases the accidental coincidence count rate and deteriorates the detected quantum state. At the given count rate and local visibility, the best fidelity that can be achieved with this current system and coincidence window is approximately \(93.5\)%, since accidental coincidence clicks deteriorate the quality of the measured quantum state. The discrepancy of roughly \(5\)% between this value and our measured results is attributed to the imperfect fibre birefringence compensation and other systematic effects such as offsets in the calibration of the polarisation analysis modules. Previous studies concerning polarisation-mode-dispersion suggest that a deterioration in fidelity by only a few tenths of a percent26,27 is expected for situations such as ours, where about \(0.6\) ps of polarisation-mode-dispersion is expected;21 however, this is clearly not the dominant effect in our case.

Stability of the fidelity

In order to measure the stability of our setup, including the submarine fibre link, we performed a long-duration measurement of the visibility over a period of about \(6.5\) h. Throughout this period, the visibilities in the H–V and D–A bases were measured alternately. Imperfect compensation of the quantum channel and other systematic issues mean that the visibilities of the two bases were quite different. In the H–V basis, the visibility ranged from \(74\,\pm\,2\)% to \(86\,\pm\,2\)%, which corresponds to a maximum polarisation rotation on the Poincare sphere of \(1{2}^{\circ }\). The visibility in the D–A basis was slightly more stable, as it ranged from \(87\pm 2\) to \(94\,\pm\,2\)%, corresponding to a maximum polarisation rotation of \({9}^{\circ }\). Nevertheless, our results show that the lower bound to the fidelity hardly changes over the course of the 6 h. The measured average fidelity was \(85\,\pm\,2\)%, well above \(1/\sqrt{2}\approx 70.7\)%, which is the minimum fidelity required to violate a CHSH inequality and therefore certify entanglement, for the duration of the experiment. For entanglement-based QKD protocols, a fidelity of \(81\)% is required to yield a positive secret key rate.28 This more stringent bound is also surpassed in our data.

Estimation of the secure key rate

As shown in Fig. 3a, the measured QBER stays below 9% with the exception of one measurement and therefore facilitates the generation of a secure key. Since only two detectors were available to us, without a fast basis choice, in total eight measurements were needed to estimate the fidelity. We use these results to estimate the sifted key rate. A setup which chooses a random basis with 50% probability would measure all these measurement combinations in the same time interval, together with another eight combinations, in which both users measure in a different basis. Therefore, the fast switching QKD setup would be able to analyse sixteen combinations of polarisation during the time in which a two-detector setup, like ours, can measure only one combination. However, the rate of coincident photons in each basis combination would only be one quarter of the rate of the two-detector setup, since the setups will only measure both in the D–A and both in the H–V for one quarter of the time, respectively. Therefore, the sifted key \({R}_{{\mathrm{s}}}\) which would have been observed in a fast-switching QKD setup is estimated to be one fourth of the sum of coincident clicks of our eight measurements. In Fig. 3b, the red points correspond to an estimate of the secure key rate, based on the observed count rate and fidelity3 in the asymptotic temporal limit, therefore ignoring finite size effects. For this, an error correction efficiency of 1.15 was assumed.29

Fig. 3: Long-term measurements on the entangled photon state over the 192 km fibre link. A measurement over 6.5 h demonstrates excellent passive stability of the system. a QBER, estimated from the visibility measurements. The QBER shown were calculated from eight different combinations of measurement bases each integrated over 100 s (The third and fourth data points correspond to a measurement duration of \(84\) s and \(80\) s long, respectively). b The red points correspond to the estimated secure key rate, based on the observed count rate and fidelity in the asymptotic time limit. c Position of the coincidence peak, as observed from histograms similar to Fig. 2 over an interval of several hours during which no compensation of the fibre birefringence was carried out. The error bars correspond to one standard deviation as derived from the fitting parameters. Full size image

Length changes of the fibre

Another observable that we have access to is the relative delay between the two photons, corresponding to the length of the optical link. We used this data, shown in Fig. 3c, to assess the stability of the net optical length of the fibre by tracking the evolution of the temporal position of the coincidence peaks, which were determined via Gaussian fits similar to the one shown in Fig. 2. The error bars have been obtained from the covariance matrix of the corresponding Gaussian fits. The maximum change of the coincidence delay, \(124\) ps, between hours \(2.28\) and \(6.28\) can be explained by a net change in the average temperature of the fibre, which we consider a proxy for the temperature of the seabed. We estimated the temperature change to be about \(22\) mK using a thermal expansion coefficient of optical fibres of \(\frac{{\rm{d}}L}{{\rm{d}}T}=5.6\times 1{0}^{-7}\ {{\rm{K}}}^{-1}\) and the change of refractive index per kelvin of \(\frac{{\rm{d}}n}{{\rm{d}}T}=8.45\times 1{0}^{-6}\ \,{{\rm{K}}}^{-1}\).30 This agrees roughly with the findings of ref. 31 where the environmentally induced phase noise in submarine fibre cables was investigated in this region. This temperature change corresponds to a length change of approximately \(2.4\) mm, which does not have any significant effect on the transmitted fidelity since slow length changes do not exert sufficient strain to cause significant birefringence. When compared to refs, 32,33 our results show that this submarine environment is very favourable for polarisation-based quantum communication in optical fibres, demonstrating even greater stability than in laboratories with conventional climate control, which often only regulates the temperature with the accuracy of \(1\) or 2 K.