Telecom quantum photonic interface for a 40Ca+ single-ion quantum memory

Entanglement-based quantum networks require quantum photonic interfaces between stationary quantum memories and photons, enabling entanglement distribution. Here we present such a photonic interface, designed for connecting a 40Ca+ single-ion quantum memory to the telecom C-band. The interface combines a memory-resonant, cavity-enhanced spontaneous parametric down-conversion photon pair source with bi-directional polarization-conserving quantum frequency conversion. We demonstrate preservation of high-fidelity entanglement during conversion, fiber transmission over up to 40 km and back-conversion to the memory wavelength. Even for the longest distance and bi-directional conversion the entanglement fidelity remains larger than 95% (98%) without (with) background correction.


I. INTRODUCTION
Entanglement-based quantum networks are the backbone for many quantum technology applications connecting remote partners, such as distributed quantum computing [1], quantum repeaters [2], quantum key distribution (QKD) with entangled photons [3] or networks of quantum sensors [4].Here we consider networks involving matter-based quantum memories communicating via optical photons.To realize such networks, several requirements have to be fulfilled simultaneously: (i) a source of high-rate and high-fidelity entanglement is essential [5,6]; (ii) the spectral characteristics of photonic information carriers and matter-based quantum memories have to match; and (iii) the communication wavelength has to be in a low-loss band of optical fibers.Requirement (i) may be addressed by photon pair sources based on spontaneous parametric down-conversion (SPDC) that have shown immense potential as highfidelity sources of entanglement since their introduction [7].For their interfacing with atom-based quantum memories, requirement (ii) [8][9][10], a narrow spectrum of the photon pairs is required.This can be attained by spectral filtering [11] or by placing the nonlinear crystal inside a cavity that is tuned to be resonant with the desired atomic transition [12,13].The latter scheme also enables very high pair rates, but it may suffer from reduced state purity due to distinguishability induced by the birefringence of both crystal and resonator.An alternative approach with higher-quality entanglement but with a much lower pair rate is to use single-pass conversion in an interferometric configuration, which eliminates all distinguishability and eliminates the 50% background of unsplit photon pairs [14][15][16].Ideally, resonator-enhanced generation and interferometric configuration would be combined.
For the distribution of entangled photon pairs over long distances in fiber networks, requirement (iii), transmission loss is a crucial issue, limiting the entanglement rate and thereby the secret key rate of QKD.Thus it is advantageous to use wavelengths in the telecom bands (1260 nm -1625 nm), where fiber absorption is minimal.Most of the relevant transitions in atomic or ionic quantum memories, however, are in the visible or near IR regime [17][18][19][20].One possible approach to address quantum memory transitions and at the same time minimize fiber loss is to use non-degenerate SPDC entangled-pair sources.In this case one photon is resonant to the memory transition while the other has a wavelength in the telecom regime [8,[21][22][23][24].Alternatively, non-degenerate photon pairs may be generated from degenerate pairs by quantum frequency conversion (QFC) of one of the photons [25] which shifts the photon wavelength while preserving all other properties.Here, an efficient conversion process is three-wave mixing in χ (2) -nonlinear media [26], but its strong polarization dependence is adverse to the conversion of polarization qubits.To overcome this limitation, several schemes for polarization-preserving conversion have been developed [27][28][29][30][31][32][33] and employed to demonstrate photon-photon [28,32] and light-matter entanglement over short distances [30,31] as well as over km-long fibers [33][34][35][36].
In this paper we present a photonic interface designed to connect a single-ion quantum memory with the arXiv:2211.08841v1[quant-ph] 16 Nov 2022 telecom C-band.Our interface combines a 40 Ca +resonant, cavity-enhanced SPDC photon-pair source at 854 nm in interferometric configuration with highly efficient polarization-preserving QFC to 1550 nm and backconversion to the atomic wavelength.It thereby facilitates bi-directional sender and receiver operations between atomic and photonic quantum bits [17,37], as needed for a quantum network environment involving atom-based memories.We present four different setups and verify entanglement for each case by quantum state tomography: First, we characterize the source operation, then the combined system with QFC to generate polarization entanglement between a 40 Ca + -resonant photon and a telecom photon.In the third step we show entanglement distribution over 20 km of fiber.Finally we demonstrate the preservation of high-quality entanglement after transmission over 40 km of fiber and consecutive back-conversion of the telecom photon to the 40 Ca + -wavelength.We thus show for the first time the simultaneous conversion and back-conversion by a single bi-directional frequency converter.Even for the longest distance and bi-directional conversion the entanglement fidelity remains larger than 95% (98%) without (with) background correction.

A. SPDC Photon Pair Source
Our SPDC photon pair source combines the interferometric configuration of [14,38] with cavity enhancement, enabling the generation of photons with very high pair rate, narrow linewidth and high-fidelity, offset-free entanglement simultaneously.Compared to an earlier version of the source [39,40], we also optimised the locking stability and the output mode structure.The experimental setup is shown in Fig. 1 and will be discussed in the following.
In order to address the D 5/2 -P 3/2 transition in 40 Ca + at 854 nm, we use a frequency-stable laser at 427 nm to pump the SPDC process in a periodically poled KTP crystal with type-II phase-matching.The polarized pump light is split on a non-polarizing 50:50 beam splitter (BS), and the two beams are coupled into the non-linear crystal in opposite directions.The crystal is placed inside a signal-and idler-resonant 3-mirror ring resonator (FSR H = 2π • 1.85 GHz, FSR V = 2π • 1.83 GHz).Downconverted photons from both pump directions leave the resonator at the same outcoupling mirror, M out , under different angles.The polarizations of the signal and idler photons in one of the output arms are interchanged by a half-wave plate.Then, the photons of both output arms FIG.1: Schematic of the photon pair source including filtering and detection.SPDC source in interferometic configuration with PDH locking beams.Stabilization of the resonator and the interferometer is achieved by piezo driven mirrors (PM).During the stabilization runs, the photons are switched off by an optial chopper in order to protect the APDs.HWP/QWP: half-/quarter-wave plate, PBS: polarizing beamsplitter, BS: non-polarizing beamsplitter, DM: dichroic mirror, Pol: polarizer, WP: Wollaston prism, GP: glass plate, PM: piezo driven mirror, FPI: frequency filter are overlapped on a polarizing beam splitter (PBS).This arrangement erases all distinguishability between the two photons of a pair.Moreover, it avoids the background of unsplit pairs that is inherent in single-direction SPDC generation.The photonic 2-qubit state at 854 nm produced by the source is a polarization Bell state [41] where A and B refer to the output ports of the PBS.
As shown in Fig. 1  out the ion-resonant mode and its partner mode is effected by two monolithic Fabry-Pérot filters (FPI), one in each output.The filters are described in more detail in the Methods section.
The SHG light that is produced by the locking beam is detected at the BS that splits the pump beam and is used for the stabilization of the Mach-Zehnder-type interferometer formed between this BS and the PBS that combines the SPDC output arms.By tuning the phase of this interferometer, we tailor the phase ϕ of the photonic 2-qubit state, Eq. (1).For the experiments described below, we set this phase to ϕ = 270 • .A more detailed account of the relation between ϕ and the interferometer phase is given in the Supplement.
With the described setup we reach a generated photon pair rate of R pair = 4.7 • 10 4 pairs s mW × P pump .In the experiments below, we used a maximum pump power of P pump = 20 mW.The SPDC photons are available, after spectral filtering and fiber coupling, with 31% (21.4%) efficiency in port A (B).
For analysis of the photonic polarization state, we use a projection setup consisting of half-wave plate, quarterwave plate, and polarizer (film polarizer or Wollaston prism) in each output arm.As single-photon detectors we use two APDs (Excelitas Technologies) with approximately 10 s −1 dark counts.Detected photons are timetagged, and time-resolved coincidence functions between the two arms are evaluated for various combinations of polarization settings.
For the characterization of the temporal shape of the photon wavepacket, we measure the polarizationindiscriminate coincidence function between the photons of the two output arms [42].Fig. 2 shows the result, measured by summing the coincidences for the four settings HV, VH, HH, and VV.The decay times (or wave packet widths) of the two photons differ slightly because of different loss of the two polarization modes in the cavity: we get values of τ H = 15.78 ns for the H-polarized photons and τ V = 12.94 ns for the V-polarized photons.
An important figure of merit is the signal-to-background ratio (SBR) of the coincidence functions.The greyshaded area in Fig. 2, representing the coincidences in the time-window ∆t around zero, is taken as the signal (S).The background (B) is determined using the same time window size but at a delay τ > 150 ns (red shaded area).For our setup the background is dominated by accidental coincidences, originating from the temporal overlap of the generated photons.
Theoretically, the number of polarization-indiscriminate coincidence counts in a time interval T and for a given pair rate R pair is given by where η 1 and η 2 are the detection efficiencies for the two outputs, and is the mean wavepacket width of the photons.The theoretical value for the background is Hence the SBR of the source is expected to be given by [40] Fig. 3 shows a comparison between this theoretical expression and our measurement, for fixed pump power of 20 mW and variable coincidence window ∆t.When ∆t is similar to the 1/e width of the photon wavepacket, we reach an SBR of ∼30, whereas for a coincidence window that covers 99.97% of the photon, we find an SBR of ∼10.

Fig. 3 also shows how the coincidence rate varies with ∆t.
From fitting Eq. ( 2) to the data, with η 1,2 independently measured, we derive the pair rate R pair as mentioned before.
The SBR enters into the maximally reachable fidelity of the photon pair state to the ideal Bell state of eq. ( 1).The fidelity of a measured (i.e., reconstructed) density matrix ρ to a given state |Ψ is calculated as where F w/o BG corresponds to the fidelity of the photonic state when the entire background is subtracted [40].This formula is used below for the theoretical curves in Fig. 6.  4) for the SBR and and Eq. ( 2) for the coincidence rate, with Rpair the only fit parameter.

B. Polarization Preserving Frequency Conversion
The setup for the polarization-preserving frequency conversion (Fig. 4a) is located in a second lab and is connected to the photon-pair source via 90 m of fiber.We use difference frequency generation (DFG) in a nonlinear PPLN waveguide to convert the 854 nm photons to the telecom C-band at 1550 nm [29].As the DFG efficiency in the waveguide is strongly polarization dependent, the setup is realized in a Sagnac configuration [31,33].First, the 854 nm signal is filtered by an input bandpass filter to prevent background photons being coupled back into the source setup and overlapped with the strong, diagonally polarized pump field at 1904 nm on a dichroic mirror.Both fields are then split into their H-and V-polarization component on a PBS.To achieve polarization preserving operation, the H-components are rotated to V by an achromatic waveplate inside the Sagnac loop (HWP).All beams are now V-polarized for optimum conversion and are coupled in a counterpropagating way into the waveguide.After exiting the waveguide, the converted 1550nm light from the original V-component also passes the achromatic waveplate and is thereby rotated to H. Finally, the two converted polarization components are coherently overlapped on the PBS, which closes the Sagnac loop.The light then passes the dichroic mirror a sec-ond time where unconverted (or back-converted) light at 854 nm is split off.The same happens to SHG light from the pump that is parasitically generated in the waveguide; it is then blocked by the input bandpass filter.The converted light that is transmitted through the first DM together with the pump light is separated with a second DM and coupled into a telecom fiber, directing it to the detection setup.
Apart from enabling polarization-independent conversion, an additional advantage of the Sagnac configuration is that all fields have the same optical path, such that no phase difference between the split polarization components occurs, and hence no active phase stabilization is needed.At the same time, the configuration facilitates bi-directional conversion without compromising the conversion efficiency.An experimental demonstration of bi-directional operation will be presented below.
The conversion-induced background in this process mainly originates from anti-Stokes Raman scattering of the pump field [29,43,44].As this is spectrally very broad compared to the converted signal, we can significantly reduce the background count rate with a narrowband filtering stage.By combination of a bandpass filter (transmission bandwidth ∆ν BPF = 1500 GHz), a volume Bragg grating (VBG, ∆ν VBG = 25 GHz) and a Fabry-Pérot etalon (FSR = 12.5 GHz, ∆ν FPE = 250 MHz) we achieve broadband suppression outside a 250 MHz transmission bandwidth.To ensure high transmission through VBG and Etalon, a clean gaussian spatial mode is needed.That is why these filters are included in the detection setup, which is separated from the conversion setup by 10 m of fiber (or later the fiber link) acting as spatial filter.With this filtering stage, the total conversion-induced background count rate is 24 s −1 .
The device efficiency including all losses in optical components and spectral filtering for H and V input polarizations and different pump powers in the corresponding converter arm is shown in Fig. 4b.The measurement agrees well with the theoretical curve given by η ext (P ) = η ext,max sin 2 ( √ η nor P L) with the normalized power efficiency η nor and waveguide length L [45].
We achieve a maximum external conversion efficiency of η ext,max = 60.1% (57.2%) for H(V)-polarized input at 660 mW (630 mW) pump power.The difference is explained by slightly different mode overlaps between signal and pump field in the two arms.Since for polarizationpreserving operation both efficiencies need to be equal, the pump power in the H-arm is reduced via the two HWPs in the pump laser arm to 485 mW to match 57.2% conversion efficiency.To verify equal conversion efficiency for arbitrary polarized input, the process matrix [46] was measured with attenuated laser light, resulting in a value for the process fidelity of 99.947(2)%.Thus the preservation of the input polarization state is confirmed with very high fidelity.Note that in fact the converter rotates the input state by a constant factor π/2 due to the achromatic waveplate.This could be compensated by an additional waveplate at the output, however the polarization also gets arbitrarily rotated in the input and output fibers, so we compensate for all rotations together by rotating the projection bases in all measurements as described in the Methods section.Further details on the conversion setup as well as the background and process fidelity measurements are found in the supplement.

C. Experimental results
To assess the performance of our quantum photonic interface we analyze the photon pair states via quantum state tomography [47] for four different configurations, as sketched in Fig. 5a-d.
In the first configuration (Fig. 5a) and for calibration purposes, we measure the output state of the photon pair source itself, i.e., without conversion.In the next configuration (Fig. 5b), we include the frequency converter in the detuned output arm of the photon pair source (arm A in Fig. 1).Tomography is then performed on the pairs of converted and unconverted photons.
In the third configuration (Fig. 5c), we extend the fiber link between converter and detection setup to 20 km in order to evaluate the influence of fiber transmission.We emphasize that the transmission of photons at a wavelength of 854 nm via a suitable single mode fiber would suffer about -70 dB fiber attenuation [48] whereas conversion to 1550 nm and using a low-loss telecom fiber results in a total fiber attenuation of -3.4 dB [49].
Finally, in the fourth configuration (Fig. 5d) bidirectional conversion is implemented by terminating the 20 km fiber with a retroreflector.Thus, the telecom photons are converted back to 854 nm at the second passage of the converter, after 40 km of fiber transmission.
To separate the returning back-converted photons from the outgoing ones in the source lab, we use a 50:50 fiber beamsplitter that reflects 50% of the back-converted photons to the second tomography setup.Note that in this configuration the converter filter stage is not used, but the FPI filter in the 854 nm tomography setup, as explained in the supplement.
In all four configurations, we use source pump powers of 5 mW, 10 mW, 15 mW and 20 mW.The detected coincidence rates at 20 mW pump power are: 4168 s −1 for setup a), 974 s −1 for setup b), 428 s −1 for setup c) and 40 s −1 for setup d) (also see Supplement).From the timeresolved coincidences in the different detection bases, the density matrix is reconstructed by applying an iterative maximum likelihood estimation (MLE) algorithm [51].
From the density matrix, we then calculate all measures that characterize the quantum state, such as fidelity and purity.For each configuration we show a representative density matrix in the supplement.Before performing the tomography, the polarization rotations in both arms, including the converter and the fiber link, were calibrated; details on the procedure are found in the methods part.
The results of the four configurations are summarized in Fig. 6.For all configurations and source pump powers, the fidelities with respect to the maximally entangled state (1) are above 95% with and without background correction, for a detection window of ∆t = 1.5 τ mean (subfigure a).Thus the entanglement is well-preserved for every scenario of Fig. 5.For fixed source pump power, the fidelities of the individual configurations differ only slightly outside the error bars, which confirms the high process fidelity of the converter and the low detrimental effect of the fiber link.With increasing source pump power, the fidelity decreases, which is expected according to eq. ( 5).The black dashed line shows the theoretically achievable fidelity for the given SBR, considering only accidental coincidences.This line is expected to be an upper bound to the measured values, as additional effects lead to further reductions: (i) errors in the calibration of the polarisation rotation compensation; (ii) drifts in the polarization rotation of the setup away from the calibration point during the measurements; (iii) fluctuations of the photonic state phase resulting from power fluctuations of the locking signal.
The SBR for each individual measurement is shown in Fig. 6b.Here the error bars are calculated by taking Poissonian noise into account.As expected from eq. ( 4), the SBR decreases for increasing pump power of the pair source.Again we only see minor differences between the four configurations, as the conversion-induced background rate is negligible compared to the pair rate and source background rate in the relevant time window.For the back-conversion part, the SBR is consistently lower, which is explained by the use of the FPI filter instead of the converter filtering stage.
When choosing a larger detection window, fidelities and SBR decrease due to the temporal overlap of the photons.
The results for a detection window of ∆t = 5 τ mean , corresponding to 91% of the photon, are shown in Fig. 6c-d.Due to the lower SBR, here the fidelities are lower by a few percent, while the detected pair rate is increased by a factor of 1.7.

III. DISCUSSION
In summary, we have presented and characterized a combined system of entangled photon pair source and bidirectional quantum frequency converter and use it for entanglement distribution over a fiber link.Pair rate and entanglement fidelity of the source are near the theoretical optimum, while efficiency, polarization fidelity and noise performance of the converter are among the best reported values [29,31,32].The system is tailored as interface to the 40 Ca + single-ion quantum memory.
The presented measurements demonstrate the preservation of photon entanglement with high fidelity through up to 2 conversion steps and distribution over up to 40 km of fiber.The high-efficiency bi-directional quantum frequency conversion adds low background to the photon pair source and thus enables a proof-of-principle demonstration of a quantum photonic interface suitable to connect remote quantum network nodes based on 40 Ca + single-ion memories.
Several future improvements are readily identified.The FIG. 6: Fidelity and SBR vs. SPDC pump power for the four configurations of Fig. 5. a) and b) show the measurement results for a detection time window of 1.5τmean which corresponds to 78% of the photon temporal shape.In a) the MLE results are represented by the data points, the dot-dashed line shows the mean background corrected fidelity, while the dashed line shows the theoretical expectation according to eq. ( 5).The uncertainties are derived from a simulation; see Method section for further details.b) shows the comparison of the SBR for the four different measurement settings.The dashed line is calculated for the given pair rate according to eq. ( 4).The error bars are calculated by including the √ N -noise of the measured coincidences [50].c) and d) show the results when choosing a larger detection window of 5τmean for the evaluation.
coincidence rates can be enhanced by replacing lossy fiber-fiber couplings by direct splices and by replacing the fiber beam splitter by an optical circulator.Given the low unconditional background rate of the QFC process, we can further increase photon count rates by lowering the finesse of the monolithic Fabry-Pérot filters, which results in higher transmission.The conversion fidelity can be improved near the theoretical maximum by repeating the polarization calibration more frequently in a fully automated procedure.Furthermore, a redesign of the source-cavity itself would make it possible to shorten the photons to 8 ns, which corresponds to the transition linewidth of 23 MHz between the D 5/2 and P 3/2 state.Due to less overlap between two subsequent photons, the SBR and the fidelity would improve as well.
Recent developments in quantum networking operations with single ions [52][53][54], together with progress in iontrap quantum processors [55,56] confirm the importance and the potential of quantum photonic interfaces for quantum information technologies.The interface we demonstrate here enables extension towards further fundamental operations in trapped-ion-based quantum networks.In particular, bi-directional QFC allows for teleportation between remote quantum memories, or for their entanglement via direct exchange of a photon (see e.g.[57]), employing heralded absorption [17,40] of a back-converted telecom photon.

State characterization
We perform full state tomography to reconstruct the photonic two-qubit state.We project each photon to one of the six polarization basis states (horizontal, vertical, diagonal, anti diagonal, left circular, or right circular), which results in 36 possible measurement combinations.In order to reconstruct the 2-qubit density matrix, 16 combinations are sufficient.We therefore measure twophoton correlations in 16 independent polarization settings [58] and reconstruct the density matrix by applying a maximum likelihood algorithm to the count rates inside the detection window [51].We infer from the density matrix all characteristic measures such as purity and fidelity.For calculating the error bars, we use a Monte Carlo simulation [50] where we run the algorithm repeatedly on randomly generated, Poisson-distributed coincidence rates based on the measured rates.From the distribution of the resulting fidelities, we estimate the error bars.

Polarization bases calibration
Polarization rotation due to the birefringence of optical components in the setup, in particular the fibers, has to be accounted for to ensure projection onto the correct basis states.We model the rotation in each arm by a unitary rotation matrix M that transforms the input polarization λ in to an output polarisation λ out = M λ in .Non-unitary effects such as polarization-dependent loss play only a negligible role on the final state fidelity.By blocking one pump direction of the source, we deterministically generate photons with linear (H) polarization.Additionally, we can insert a quarter-wave plate directly behind the source to rotate the polarization to R. We then perform single-qubit tomography with the de-tection setups to measure the rotated polarization states.From this we calculate the rotation matrix M , and the projection bases are rotated accordingly.
Depending on the experimental configuration (Fig. 5), we measure the rotation matrix less or more frequently during the experiments: for the first two configurations, short fibers are used, thus the polarization is very stable over time and is measured only at the beginning of the experiment.In the last two configurations, although the fiber spool is actively temperature stabilized to minimize polarization drifts, the rotation matrix is measured every 60 minutes.

Fabry-Pérot filter
The Fabry-Pérot filters which we use for filtering the 854 nm photons to a single frequency mode are built from single 2 mm thick NBK-7 lenses.Both sides have a highreflectivity coating (R = 0.9935).This results in a finesse of 481, a FSR of ∼ 50 GHz and a FWHM of ∆ν ≈ 104 MHz, which is sufficient for filtering a single mode of the SPDC cavity (FSR ∼ 1.84 GHz).Frequency tuning over a whole FSR is possible by changing the temperature in the range between 20°C and 70°C.The stabilization of the temperature with a precision of 1 mK (corresponding to 3 MHz) is sufficient for stable operation; no further active stabilization is needed.

V. DATA AVAILABILITY
The underlying data for this manuscript is openly available in Zenodo at https://doi.org/10.5281/zenodo.7313581.The evaluation algorithms are available from the corresponding author upon reasonable request.The interferometer is stabilized in the following manner: the light used for the PDH-lock also generates a small amount of SHG light in both pump directions such that a Mach-Zehnder interferometer is formed between the red PBS and the blue BS.An APD in current mode is attached to the free port of the BS to detect the fringes.
Feedback is applied to a pair of piezo-movable mirrors in one of the pump arms.The measured relation between the interferometer phase and the reconstructed photonic state phase ϕ (eq.( The total device efficiency of the converter is composed of the internal efficiency of the conversion process, coupling efficiencies, and losses induced by all optical elements.A detailed list of transmissions and efficiencies of all components is shown in Supplementary Table I.The 854 nm signal passes the aspheric fiber coupling lens, a dielectric mirror, a dichroic mirror, the PBS and two silver mirrors.In total, the setup transmission up to the WG coupling lens is 92.3%(93%) for the H(V)-arm.Although the WG coupling lens is custom AR-coated for all three wavelengths, it shows a transmission of only 93% for 854 nm.
It was not possible to also measure the total setup transmission for the converted 1550 nm light.As the converted light is overlapped with the strong pump laser behind the WG either a dichroic mirror to reflect the pump light out of the 1550 nm path or a seperate 1550 nm laser would be needed which weren't available.Only the aspheric lens transmission could be measured for 1550 nm.The total transmission through all 3 lenses in the 1550 nm path (WG coupling lens and fiber in and out coupling lenses) is 94.4%.The bandpass filter shows a transmission of 96%.The fiber between conversion and detection setup is ARcoated only on the input side, the combined in and out coupling efficieny is 93.5%.For the VBG and Etalon we get transmissions of 98.5% and 93.4% respectively.From these numbers and the device efficiency we can now infer the combined internal efficiency and 1550 nm setup transmission which is 93.3%(87.4%)for the H(V)-arm.
It is apparent, that the device efficiency is not limited by a single element with low transmission, but rather the sum of many components with already low individual loss.For a significant improvement of the device efficiency we therefore need to replace several components.
For future experiments we will therefore use custom di-electric mirrors with reflectivities > 99.5% for the single photon wavelengths instead of the currently used silver mirrors for WG coupling.The WG coupling lens will be replaced by one with transmission > 99% for 854 nm and 1550 nm.For connecting converter and detection setup, we will use a fiber with AR coating on both ends.Thus, a device efficiency of up to 70% is within reach.

Laser Process Tomography
To characterize the converter polarization preservation for arbitrary polarized light, quantum process tomography with attenuated laser light is used.For that, first the polarization rotation matrix of the conversion and detection setup is measured and compensated as described in the Methods section.Here we prepare 37 polarization states at the converter input with a linear polarizer and two waveplates and measure the corresponding output polarization with the single photon detectors.We then prepare the polarizations H,V,D,A,R and L at the converter input and perform quantum state tomography on the output states.From the resulting photon count rates in the different detection basis settings, the process matrix in the Pauli-basis (σ 0 ,σ 1 ,σ 2 , σ 3 ) is reconstructed with a maximum likelihood algorithm [1].The result is shown in Supplementary Figure 4. We only get a significant contribution from the first matrix entry, which corresponds to the process fidelity of 99.947(2)% where the error is calculated with a Monte Carlo simulation assuming Poissonian photon statistics.

Conversion Induced Background
For our DFG-process, the dominant noise source is Anti-Stokes Raman noise [2][3][4].To reduce the noise, we chose a waveguide with a comparably low phase-matching temperature of 19°C and the narrowband filtering stage.For quantifying the conversion induced noise, the 854 nm input light was blocked.The remaining count rate was integrated over 15 minutes for different pump powers.The dark-count corrected count rates measured on both SNSPD channels are shown in Supplementary Figure 5.The actually generated noise rate is inferred from these numbers by dividing by the detection efficiencies of the detectors (31%/35%, here the detection efficiency was set to a different value than in the main experiment), the transmission through the waveplates and the Wollaston prism (98%) and the coupling efficiency to the detector fibers (90%).The larger error bars for the total noise rate stem from the uncertainty in the detection efficiency of 3%.The theoretical curve assumes backconversion of

FIG. 3 :
FIG.3: Signal-to-background ratio and coincidence rate of the photon pair source.The SBR and the coincidence rate are plotted in dependence of the coincidence time window ∆t, for a pump power of 20 mW.The error bars are calculated from the Poissonian noise of the measured coincidences.The dashed lines show the theoretical calculations according to Eq. (4) for the SBR and and Eq.(2) for the coincidence rate, with Rpair the only fit parameter.
FIG. 4: a) Schematic quantum frequency conversion setup.Details are found in the main text.TDFL: Thulium-doped fiber laser, LPF: low-pass filter, BPF: band-pass filter, VBG: volume-Bragg grating, DM: dichroic mirror, HWP: half-wave plate, SNSPD: superconducting nanowire single photon detector; b) Device efficiency of the converter for different pump powers and input polarizations.The maximum efficiencies of the H-and V-polarizations are slightly different.

FIG. 5 :
FIG. 5: Overview of the different experimental configurations.a) The output state is measured directly at the source.b) One of the photons is frequency-converted before its detection.c) 20 km of fiber is inserted between conversion and detection.d) The 20 km fiber gets terminated with a retro-reflector.The back reflected photons get backconverted after 40 km of fiber and are extracted with a 50:50 fiber beamsplitter before their detection.The background colors correspond to the colors of the data points in Fig. 6.
SBR for a detection window ∆t = 5τmean

Supplementary Figure 2 :
Relation between interferometer phase and state phase.The plot shows the measured state phase for different interferometer phases.In the upper plot the theoretical interferometer fringe is displayed.The grey shaded areas indicate regions where no locking is possible.
)) is shown in Supplementary Figure2.At the turning points of the fringe, i.e. the gray shaded areas, no stabilization is possible.This is the reason why we use a phase of 270 • instead of 0 • or 180 • which would result in the conventional Ψ + or Ψ − Bell state.The offset between the state phase and the interferometer phase depends mainly on the path length difference of the two interferometer paths.For the case of equal paths the resulting phase is around 270 • .