 Research
 Open access
 Published:
Fully controllable timebin entangled states distributed over 100km singlemode fibers
EPJ Quantum Technology volume 11, Article number: 53 (2024)
Abstract
Quantum networks that can perform userdefined protocols beyond quantum key distribution will require fully controllable entangled quantum states. To expand the available space of generated timebin entangled states, we demonstrate a timebin entangled photon source that produces qubit states \({\psi}\rangle = \alpha {00}\rangle + \beta {11}\rangle \) with fully controllable phase and amplitudes. Eight different twophoton states have been selected and prepared from arbitrary states on the reduced twoqubit Bloch sphere. The photon pairs encoded in the timebin scheme were generated at 2.4 MHz with a visibility of \(V = 0.9475 \pm 0.0016\), with a violation of the CHSH Bell’s inequality by 197 standard deviations. After entanglement distribution over 100 km of singlemode fibers, we obtained a visibility of \(V = 0.9541 \pm 0.0113\) with a violation of the CHSH Bell’s inequality by 6 standard deviations. The prepared states had an average fidelity of \(0.9540 \pm 0.0016\) at the source and an average fidelity of \(0.9353 ^{+0.0100}_{0.0209}\) after entanglement distribution, which shows that the quantum states generated by our timebin entangled photon source can be fully controlled potentially to a level applicable to longdistance advanced quantum network systems.
1 Introduction
Entanglement is an essential resource in the realization of quantum networks [1, 2]. The protocols for longdistance quantum communication [3–6], like quantum teleportation [7–11] and entanglement swapping [12–14] rely on distributed entanglement. Currently, the most popular forms of qubit encodings for entanglement sources are polarization [15–17] and timebin encodings [18–20]. Timebin encoding can be more robust in longdistance transmission through optical fibers [21–23] because timebin encoding inherently exhibits resistance to uncontrollable polarization fluctuations [24, 25] and polarization mode dispersion [23] in deployed fibers, factors that could induce decoherence in polarization qubit states [26]. However, implementing unitary operations and measurements in arbitrary bases is nontrivial for timebin qubits compared to polarization qubits. Previous studies have explored arbitrary entangled polarization qubits [27], timebin to polarization qubits conversions for arbitrary measurement [28, 29], or control of single timebin qubits [30], but not the manipulation or control of two entangled timebin qubits.
Ultimately, users of quantum networks may desire the creation of states beyond a single Bell state, e.g. \({\Phi ^{+}}\rangle \), generated by typical entangled photon source systems for the facilitation of userdefined experiments [31, 32]. For example, with control over phase, protocols such as threepartite quantum secret sharing can be enabled [33]. With additional control over probability amplitudes, partially entangled states can be created for partial teleportation [34] potentially for further optimization of teleportation [35]. The full control over generating entangled states may therefore become an important feature of quantum networks.
However, the statecontrolled distribution of entangled timebin qubits has not been experimentally demonstrated. In typical timebin entangled qubit generation, twoqubit states were prepared by unbalanced MachZehnder interferometers (UMZIs) [21, 36] or by electrooptic intensity modulators [10, 14, 37] with no control over probability amplitudes.
In this work, we aim to provide a more userprogrammable quantum network by expanding the coverage of timebin entangled states on the twoqubit Bloch sphere. Specifically, we prepare twoqubit timebin states \({\psi}\rangle = \alpha {00}\rangle + \beta {11}\rangle \) with fully controllable phase and amplitudes. We generate these entangled photon pairs via spontaneous parametric downconversion (SPDC) at high count rates and fidelity. We evaluate the quality of entanglement by observing twophoton interference in generated Bell pairs with high visibility and a significant degree of violation of the ClauserHorneShimonyHolt (CHSH) inequality [38].
We further demonstrate that the quality of entanglement is maintained even after distributing entangled photons over 100km of optical fibers. While other groups typically used dispersion shifted fibers (DSFs) to distribute entangled photon pairs [10, 22, 23, 39], we distributed our timebin twoqubit states using two 50km standard singlemode fiber (SMF) fiber spools. We compensated for the chromatic dispersion of SMF with dispersion compensating fibers (DCFs). Through quantum state tomography, we show that the fidelities of our prepared states remain consistent before and after distribution, demonstrating a system qualified and stable enough for higher complexity quantum communication protocols.
2 State controlled timebin entanglement generation
A typical process for timebin entanglement generation via SPDC is as follows. Temporally separated double pump pulses are created with a pulsed laser or a CW laser modulated by an intensity modulator. In our setup, the pump wavelength is in the telecom Cband, and the modulated pulses are frequencydoubled via second harmonic generation (SHG) and then converted back into the telecom Cband as entangled photon pairs through SPDC [9, 10, 37, 40]. After SPDC, signal and idler photons are produced at the single photon level with a low mean photon number (\(\mu \ll 1\)). The resulting states of the photons are described by [39]
where \({0}\rangle \) \(({1}\rangle )\) is the early (late) temporal mode, α and β are timebin state amplitudes with \(\alpha ^{2} + \beta ^{2} = 1\), and subscripts s and i indicate signal and idler respectively.
The control and preparation of timebin states can be done classically before SPDC using an intensity modulator and a phase modulator. The intensity modulator controls \(\alpha \) and \(\beta \) by modulating the intensity of the double pump peaks to different initial levels, and the phase modulator controls the phase difference between α and β by acting on only one pulse.
Experimentally, the temporal states \({0}\rangle \) and \({1}\rangle \) have specific pulse widths and a time delay between the two timebin pulses. A requirement for choosing these timebin pulse parameters is that the generated states \({0}\rangle \) and \({1}\rangle \) must be orthogonal.
The temporal states \({0}\rangle \) and \({1}\rangle \) can be represented by Gaussian timebin pulses [41]:
where τ is the time delay between timebin pulses, and σ is the standard deviation of the timebin pulse width. From this definition we can derive that the orthogonality between states \({0}\rangle \) and \({1}\rangle \) depends on the ratio of τ to σ [41]:
Lower τ are desired to maximize the generation of quantum states. However, dispersion applies a unitary operation that widens σ upon transmission through optical fiber. This may lead to higher \(\langle{01}\rangle \) upon measurement, resulting in higher error rates due to overlap in temporal modes [20]. To compensate for dispersion and to reduce error rates, linear optics can be employed before or after distribution through optical fiber [15, 18, 19, 42].
3 Experimental scheme
Our entanglement generation and distribution setup is shown in Fig. 1. We use a CW laser pump centered to channel 34 (1550.12 nm) on the dense wavelengthdivision multiplexing International Telecommunication Union (ITU) grid. We carve two pulses (\(\sigma = 42.5\text{ ps}\), \(\tau = 500\text{ ps}\)) with a repetition rate of 200 MHz with an arbitrary waveform generator (AWG) and a lithium niobate intensity modulator. Both intensity and phase modulators (Thorlabs) act on the pump before SHG, monitored by an oscilloscope prior to SPDC. Our chosen values of τ and σ results in a pulse overlap \(\langle{01}\rangle \) of ∼10^{−15}, minimizing errors due to nonorthogonal bases.
The pulses are amplified by an erbiumdoped fiber amplifier (EDFA), and the noise spectrum generated from the EDFA is filtered by a fiber Bragg grating filter (EXFO XTM50) with a 32pm bandwidth. The filtered pulses undergo frequencydoubling by SHG on a type0 periodically poled lithium niobate (PPLN) waveguide (HCP WG Mixer) with a length of 10mm and a normalized conversion efficiency of ∼80%/W/cm^{2}. SPDC generates signal and idler photons by using another type0 PPLN waveguide (Covesion, WGPM155040) with a 40mm length and an 18.5μm poling period. The fundamental 1550 nm and secondharmonic (SH) 775 nm pumps are filtered out by shortpass (filter 1) and longpass (filter 2) filters, respectively. A dense wavelengthdivision multiplexer (DWDM, General Photonics) with 200 GHz spacings separates the generated signal and idler photons based on the ITU grid.
The SPDC spectrum was observed via an optical spectrum analyzer as depicted in Fig. 1 (b). Operating at 54.5^{∘}C for our SPDC process resulted in a spectral FWHM of ∼70 nm. This wide bandwidth is fully able to accommodate the simultaneous distribution of entangled photon pairs across the Cband and supports more complex wavelength division multiplexing schemes [43, 44]. In our experiments, we confirmed entanglement generation across ITU channels 20 through 48, covering wavelengths 1538 nm through 1562 nm. In this work, we select signal and idler photons on the ITU channels 44 (1542.14 nm) and 24 (1558.17 nm) to prepare and separate entangled photon pairs.
Each channel utilizes 50km SMF spools for entanglement distribution. After distribution, DCF spools are employed for channels 24 and 44 with negative dispersion values of \(1080 \text{ ps}\,\text{nm}^{1}\) was applied for DCF 1 and \(720 \text{ ps}\,\text{nm}^{1}\), respectively. While the dispersion values differ for each arm, the main importance of dispersion compensation is to regain the ability to distinguish timebins after entanglement distribution. Once past the threshold for full distinguishability between time slots, any further negative dispersion neither hinders nor improves the quality of qubits as long as the coincidence window can encapsulate and distinguish photons measured in each timebin. As we show later, both DCFs reduced the nonorthogonality of measurement in timebin bases due to dispersion such that high visibility was recovered.
Characterization of timebin entangled qubits requires a precise knowledge of fiber lengths. Measurement of SMFs and DCFs lengths involved comparing the crosscorrelation peak times in a setup with and without fiber spools. As the crosscorrelation peak time indicates the moment when the signal and idler photons are simultaneously generated, a difference in path length of the signal or idler is reflected as a change in timing of the crosscorrelation peak center by the extra time taken for the signal or idler to be transmitted through path length difference.
The measurement setup for timebin encoded photons is shown in Fig. 2. Signal and idler photons are inserted into UMZI planar lightwave circuits (PLCs). The PLCs are fabricated such that the long arm has a time delay of \(\tau = 500 \text{ ps}\) relative to the short arm. The timebin states are characterized by postselection after passing through a UMZI. The UMZIs divide the photons into three distinct time slots. The first and third time slots correspond to early and late qubits, respectively, where the early (late) pulse passes through the short (long) arm of the UMZI and is therefore temporally distinguishable. This is a measurement in the time basis. The second time slot is a projection measurement in the energy basis \(({0}\rangle + e^{i\phi} {1}\rangle )/\sqrt{2}\), observed when an early (late) pulse passes through the long (short) arm of the UMZI and becomes temporally indistinguishable [45].
Each UMZIs features a total insertion loss of 4.6 dB and 4.7 dB, which includes a 3 dB loss from the 50:50 split. For balanced optical power splitting, transmission loss is specifically engineered into the short arm to compensate for additional loss on the long arm. This adjustment resulted in an intensity ratio of 93.1 % and 93.7% for the early pulse to late pulse in UMZI 1 and UMZI 2, respectively. Phase differences between both arms are controlled by a temperature controller (Meerstetter Engineering TEC1091) with \(\pm 0.01 ^{\circ}\text{C}\) precision and stability of \(\pm 0.0005 ^{\circ}\text{C}\). The full period of 2π was approximately 2^{∘}C for each UMZI. Each UMZI output port is connected to superconducting nanowire singlephoton detectors (SNSPDs, Single Quantum) with detector efficiencies of 0.80 and 0.84, ∼400 Hz dark count, \(\sim 30\text{ ps}\) jitter at FWHM, and \(\sim 20 \text{ ns}\) dead time. Photon counts from the SNSPDs are analyzed using a timecorrelated singlephoton counter (TCSPC, HydraHarp 400), and the coincidence counts are recorded within a 200 ps coincidence time window.
4 Results
4.1 Entanglement characterization
Before distributing entanglement, we conducted measurements of twophoton interference fringes to characterize the degree of entanglement of timebin entangled photons generated by SPDC. At an incident SH pump power of 89 μW, we observed a coincidence count rate of 11.3 kHz at a coincidencetoaccidental count ratio (CAR) 309. This corresponds to a pair generation rate of \(R = 2.4\text{ MHz}\) and an average photon number per qubit \(\mu = 0.012\). The total detection efficiency for both signal and idler respectively, including the SNSPD detector efficiencies, SPDC output coupling loss, DWDM insertion loss, and other fiber losses, was \(\eta _{s} \, (\eta _{i}) \simeq 0.0670\) (\(11.74\text{ dB}\) loss) respectively (see Appendix A for details). To measure each interference fringe in Fig. 3, the phase of UMZI1 was held at a constant temperature, while the phase of UMZI2 was adjusted in steps of \(\pi /8\) by changing the temperature incrementally at 0.125^{∘}C per measurement. We note that there is a drop in detected coincidence counts to a maximum of \(\sim 1500\text{ Hz}\) as shown on Fig. 3 due to an inherent loss in postselection for measuring in the energybasis [23] as well as the added insertion loss from the UMZI chips. Each data point was acquired for 1 minute, and the visibility of the fitted curves was \(V = 0.9475 \pm 0.0016 \) without subtracting accidental coincidences, exceeding the value of 0.7071 needed to confirm entanglement [38]. The visibility deviates from unity due to both multiple photonpair generation and fabrication imperfections in the UMZIs [46, 47]. Theoretically, we expect that our visibility should give values according to [23, 48]:
In this equation, \(\mu ' = \mu /2\) is the average number of photons per pulse. For our values \(\mu = 0.012\), \(\eta _{s} \, (\eta _{i}) \simeq 0.0464 \, (0.0453)\) including extra loss from fabricated UMZIs, and dark counts per pulse \(d_{s} = d_{i} \simeq 2 \times 10^{6}\), we calculate that the theoretical visibility should be \(V = 0.988\). The deviation in theoretical and experimental visibility arose due to a difference in optical loss between the short and long arm of our UMZI PLC chips.
The degree of Bell’s inequality violation S can be measured via the CHSH inequality given by [38, 49]. From the twophoton interference fringes in Fig. 3, we extracted a CHSH violation of \(S = 2.684 \pm 0.003\), a value above the classical threshold \(S = 2\) by 197 standard deviations. This value indicates an extremely high degree of entanglement and confidence that our entangled photons exhibit a significantly quantum nature.
4.2 State control
Figure 4 demonstrates full controllability of entangled twoqubit states. States A through D were generated as \(({0}\rangle _{s}{0}\rangle _{i} + e^{i\phi} {1}\rangle _{s}{1}\rangle _{i})/\sqrt{2}\) with \(\phi = \pi /2, 0, \pi /2, \pi \), respectively. This control was achieved by applying voltages \(V_{\pi /2} = 3.3 \text{ V}\), \(V_{0} = 4.5 \text{ V}\), \(V_{\pi /2} = 5.7 \text{ V}\), \(V_{\pi} = 6.9 \text{ V}\) to the phase modulator, respectively. Similarly, the probability amplitude of the twoqubit timebin states was controlled for states E through H by adjusting the voltage applied to the intensity modulator. The pulse amplitudes were monitored by measuring the SH pump’s early and late pulse powers using the SH pump’s early and late pulse powers used for states A through D as reference points.
To measure and confirm the control of quantum bits, quantum state tomography was conducted as outlined in [50, 51] and as shown explicitly for timebin states in [37]. Our UMZIs were set in 4 combinations of temperatures of \(T_{1}, T_{2} = (26.070^{\circ}\text{C}, 29.130^{\circ}\text{C})\), \((26.070^{\circ}\text{C}, 29.630^{\circ}\text{C})\), \((26.570^{\circ}\text{C}, 29.130^{\circ}\text{C})\), \((26.570^{\circ}\text{C}, 29.630^{\circ}\text{C})\), which correspond to projection measurements in \({++}\rangle \), \({+L}\rangle \), \({L+}\rangle \), \({LL}\rangle \) states respectively, with states \({+}\rangle \), \({L}\rangle \) corresponding to \({+}\rangle = ({0}\rangle + {1}\rangle )/\sqrt{2}\) and \({L}\rangle = ({0}\rangle + i {1}\rangle )/\sqrt{2}\). Overall, the set of states {\({0}\rangle \), \({1}\rangle \), \({+}\rangle \), \({L}\rangle \)} was used to uniquely determine a density matrix ρ. The density matrix obtained in this manner was further optimized using maximum likelihood estimation (MLE) [52] by maximizing \(P(\mathcal{M\rho )}\), the probability that a dataset \(\mathcal{M}\) would have been measured given that the quantum state was set as ρ before measurement. MLE was implemented as described in [51] to obtain a final density matrix.
The fidelities of all the measured states are shown in Fig. 5. The average fidelity measured at the source for all eight states was \(0.9540 \pm 0.0016\). See Appendix B for further details on fidelity data and error calculations. When measuring our timebin qubits, counts for state \({00}\rangle \) was 12.7% lower than \({11}\rangle \), which is reflected in the calculated density matrices. This is due to a difference in optical transmission ratio of \({0}\rangle \) and \({1}\rangle \) while passing through UMZIs, with each UMZI exhibiting 93.1% and 93.7% transmission loss ratio of \({0}\rangle \) to \({1}\rangle \) respectively. The effect of different transmission loss ratios was also reflected in the state fidelity, resulting in deviations from unity. We note that the states \({00}\rangle \) (E) and \({11}\rangle \) (H) are inherently less affected because no interference is needed for measurement. This results in higher fidelity for states \({00}\rangle \) and \({11}\rangle \) than other states.
4.3 Entanglement distribution
We distributed the entangled photon pairs across two 50km SMF spools and observed twophoton interference patterns after dispersion compensation using DCFs. All other measurement settings remained unchanged before entanglement distribution. Figure 6 displays the 3fold coincidence counts of the distributed entangled photon pairs, with each data point representing a measurement acquired for 2 minutes. The threefold coincidence rate decreased from approximately 1500 Hz to ∼ 1 Hz postdistribution due to losses in the SMFs (0.22 dB/km) and DCFs (3.0 dB for DCF 1, 4.5 dB for DCF 2).
Without DCFs, the visibility dropped significantly below the quantum boundary of 0.7071 due to chromatic dispersion in the SMFs. Each timebin pulse expanded to \(\sigma = 382.2\text{ ps}\). The increased pulse width resulted in \(\langle{01}\rangle = 0.651\), indicating a high nonorthogonality between timebin states. With DCFs reducing dispersion, pulses were restored to \(\sigma = 93.4\text{ ps}\) and \(\sigma = 72.2\text{ ps}\) for signal and idler channels, respectively. This led to a reduction in nonorthogonality to \(\langle{01}\rangle \sim 10^{3}\) and 10^{−5} for signal and idler channels, respectively. The reduction in nonorthogonality also restored the visibility of the interference fringes to \(V = 0.9541 \pm 0.0113\). The visibility of the fringes mainly depends on the SH pump power (via the probability of multiple photonpair emission in SPDC), the inherent interference quality of the UMZIs, detector noise, and dispersion [42]. As the pump power was maintained such that \(\mu = 0.012\), consistent visibility was observed before and after entanglement distribution once dispersion was accounted for, as expected. CHSH calculations yielded \(S = 2.667 \pm 0.109\), showing that a high degree of entanglement is maintained even after entanglement distribution, with a violation of the CHSH Bell’s inequality by 6 standard deviations.
The eight different twoqubit states depicted in Fig. 4 with different θ and ϕ on the Bloch sphere have also been transmitted through the two 50km SMF spools. Fidelity comparisons are shown in Fig. 5. The average fidelity measured after entanglement distribution for all 8 generated states was \(0.9353 ^{+0.0100}_{0.0209}\).
When the measured count rate is low, error calculations show that the fidelity can have asymmetrical errors (see Appendix B). This is particularly true for the case after entanglement distribution, as shown in Fig. 5. Therefore, for states such as F or H, the fidelity derived from measured counts may be higher after entanglement distribution. However, MonteCarlo simulations show that the average simulated fidelity is actually lower after entanglement distribution as expected (see Appendix B).
Furthermore, fidelity may not always be the most accurate method of measuring the degree of decoherence upon transmission. Another way to measure the degree of entanglement is by measuring the concurrence [51]. The concurrence was measured for each state and is shown in Fig. 7.
Concurrence measurements show that the degree of entanglement is controllable in generated states \({\psi}\rangle = \alpha {00}\rangle + \beta {11}\rangle \). Concurrence is minimal for completely separable states \({00}\rangle \) and \({11}\rangle \), and the concurrence is maximal for Bell states as expected. Upon transmission through fiber channels, the decrease in concurrence shows a degradation in the degree of entanglement for all states.
5 Conclusions
We have experimentally demonstrated full controllability in both phase and amplitude of twophoton timebin entangled qubits with an average fidelity of \(0.9540 \pm 0.0016\) at the source and \(0.9353 ^{+0.0100}_{0.0209}\) after 100km distribution over SMFs. Our system generates controllable entangled timebin quantum states with a pair generation rate of 2.4 MHz. We successfully distributed eight different twoqubit states over 100km SMFs while maintaining high visibility and state fidelity. Using this system, we detected 11.3 kHz coincidence counts with a CAR value of 309. We obtained a high degree of entanglement with \(S = 2.684 \pm 0.003\) before entanglement distribution and \(S = 2.667 \pm 0.109\) after entanglement distribution. To further increase coincidence count rates, the repetition rate can easily be increased by fully utilizing the high sampling rates of commercially available AWGs to improve the generation rate of entangled photon pairs vastly. Additional improvements can be made to the DWDM to not only decrease optical loss but to also fully exploit the 70 nm bandwidth of the SPDC source for multipartite communication protocols. Overall, we provide an important tool to improve the flexibility of available quantum communication protocols by increasing controllability over entangled timebin qubit states at high count rates and fidelities. The increased degree of freedom makes our system an ideal candidate for laying the foundation to create reconfigurable quantum networks in the future.
Data availability
The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
 UMZI:

unbalanced MachZehnder interferometer
 SPDC:

spontaneous parametric down conversion
 CHSH:

ClauserHorneShimonyHolt inequality
 DSF:

dispersion shifted fiber
 SMF:

singlemode fiber
 DCF:

dispersion compensating fiber
 CW:

continuous wave
 SHG:

second harmonic generation
 IM:

intensity modulator
 AWG:

arbitrary waveform generator
 PM:

phase modulator
 EDFA:

erbiumdoped fiber amplifier
 FBG:

fiber Bragg gratings
 PPLN:

periodically poled lithium niobate
 DWDM:

dense wavelengthdivision multiplexer
 OSA:

optical spectrum analyzer
 ITU grid:

International Telecommunication Union grid
 EPS:

entangled photon source
 FWHM:

fullwidth half maximum
 SNSPD:

superconducting nanowire singlephoton detector
 TCSPC:

timecorrelated singlephoton counting device
 CAR:

coincidencetoaccidental count ratio
 MLE:

maximum likelihood estimation
References
Kimble HJ. The quantum internet. Nature. 2008;453:1023–30. https://doi.org/10.1038/nature07127.
Wehner S, Elkouss D, Hanson R. Quantum internet: a vision for the road ahead. Science. 2018;362(6412):9288. https://www.science.org/doi/pdf/10.1126/science.aam9288. https://doi.org/10.1126/science.aam9288.
Cacciapuoti AS, Caleffi M, Tafuri F, Cataliotti FS, Gherardini S, Bianchi G. Quantum internet: networking challenges in distributed quantum computing. IEEE Netw. 2020;34(1):137–43. https://doi.org/10.1109/MNET.001.1900092.
Alshowkan M, et al.. Reconfigurable quantum local area network over deployed fiber. PRX Quantum. 2021;2:040304. https://doi.org/10.1103/PRXQuantum.2.040304.
Chung J, et al.. Illinois Express Quantum Network (IEQNET): metropolitanscale experimental quantum networking over deployed optical fiber. In: Donkor E, Hayduk M, editors. Quantum information science, sensing, and computation XIII. vol. 11726. SPIE; 2021. p. 1172602. https://doi.org/10.1117/12.2588007.
Briegel HJ, Dür W, Cirac JI, Zoller P. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys Rev Lett. 1998;81:5932–5. https://doi.org/10.1103/PhysRevLett.81.5932.
Ren JG, Xu P, Yong HL, et al.. Groundtosatellite quantum teleportation. Nature. 2017;549:70–3.
Bouwmeester D, Pan JW, Mattle K, et al.. Experimental quantum teleportation. Nature. 1997;390:575–9. https://doi.org/10.1038/37539.
Valivarthi R, Puigibert MG, Zhou Q, Aguilar GH, Verma VB, Marsili F, Shaw MD, Nam SW, Oblak D, Tittel W. Quantum teleportation across a metropolitan fibre network. Nat Photonics. 2016;10:676–80.
Valivarthi R, et al.. Teleportation systems toward a quantum internet. PRX Quantum. 2020;1:020317. https://doi.org/10.1103/PRXQuantum.1.020317.
Bennett CH, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters WK. Teleporting an unknown quantum state via dual classical and EinsteinPodolskyRosen channels. Phys Rev Lett. 1993;70:1895–9. https://doi.org/10.1103/PhysRevLett.70.1895.
Zukowski M, Zeilinger A, Horne MA, Ekert AK. “Eventreadydetectors” Bell experiment via entanglement swapping. Phys Rev Lett. 1993;71:4287–90. https://doi.org/10.1103/PhysRevLett.71.4287.
Pan JW, Bouwmeester D, Weinfurter H, Zeilinger A. Experimental entanglement swapping: entangling photons that never interacted. Phys Rev Lett. 1998;80:3891–4. https://doi.org/10.1103/PhysRevLett.80.3891.
Sun QC, et al.. Entanglement swapping over 100 km optical fiber with independent entangled photonpair sources. Optica. 2017;4(10):1214–8. https://doi.org/10.1364/OPTICA.4.001214.
Neumann SP, Buchner A, Bulla L, et al.. Continuous entanglement distribution over a transnational 248 km fiber link. Nat Commun. 2022;13:6134. https://doi.org/10.1038/s41467022339190.
Wengerowsky S, et al.. Entanglement distribution over a 96kmlong submarine optical fiber. Proc Natl Acad Sci USA. 2019;116(14):6684–8. https://doi.org/10.1073/pnas.1818752116.
Wengerowsky S, et al.. Passively stable distribution of polarisation entanglement over 192 km of deployed optical fibre. npj Quantum Inf. 2020;6:5. https://doi.org/10.1038/s4153401902388.
Pelet Y, Sauder G, Cohen M, Labonté L, Alibart O, Martin A, Tanzilli S. Operational entanglementbased quantum key distribution over 50 km of fielddeployed optical fibers. Phys Rev Appl. 2023;20:044006. https://doi.org/10.1103/PhysRevApplied.20.044006.
Liu J, Lin Z, Liu D, Feng X, Liu F, Cui K, Huang Y, Zhang W. Highdimensional quantum key distribution using energytime entanglement over 242 km partially deployed fiber. Quantum Sci Technol. 2024;9:015003. https://doi.org/10.1088/20589565/acfe37.
Fitzke E, Bialowons L, Dolejsky T, Tippmann M, Nikiforov O, Walther T, Wissel F, Gunkel M. Scalable network for simultaneous pairwise quantum key distribution via entanglementbased timebin coding. PRX Quantum. 2022;3:020341. https://doi.org/10.1103/PRXQuantum.3.020341.
Brendel J, Gisin N, Tittel W, Zbinden H. Pulsed energytime entangled twinphoton source for quantum communication. Phys Rev Lett. 1999;82:2594–7. https://doi.org/10.1103/PhysRevLett.82.2594.
Inagaki T, Matsuda N, Tadanaga O, Asobe M, Takesue H. Entanglement distribution over 300 km of fiber. Opt Express. 2013;21(20):23241–9. https://doi.org/10.1364/OE.21.023241.
Honjo T, et al.. Longdistance entanglementbased quantum key distribution over optical fiber. Opt Express. 2008;16(23):19118–26. https://doi.org/10.1364/OE.16.019118.
Li DD, et al.. Field implementation of longdistance quantum key distribution over aerial fiber with fast polarization feedback. Opt Express. 2018;26(18):22793–800. https://doi.org/10.1364/OE.26.022793.
Fitzke E, Bialowons L, Dolejsky T, Tippmann M, Nikiforov O, Walther T, Wissel F, Gunkel M. Scalable network for simultaneous pairwise quantum key distribution via entanglementbased timebin coding. PRX Quantum. 2022;3:020341. https://doi.org/10.1103/PRXQuantum.3.020341.
Hübel H, Vanner MR, Lederer T, Blauensteiner B, Lorünser T, Poppe A, Zeilinger A. Highfidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber. Opt Express. 2007;15(12):7853–62. https://doi.org/10.1364/OE.15.007853.
Wei TC, Altepeter JB, Branning D, Goldbart PM, James DFV, Jeffrey E, Kwiat PG, Mukhopadhyay S, Peters NA. Synthesizing arbitrary twophoton polarization mixed states. Phys Rev A. 2005;71:032329. https://doi.org/10.1103/PhysRevA.71.032329.
Bussières F, Slater JA, Jin J, Godbout N, Tittel W. Testing nonlocality over 12.4 km of underground fiber with universal timebin qubit analyzers. Phys Rev A. 2010;81:052106. https://doi.org/10.1103/PhysRevA.81.052106.
Kupchak C, Bustard PJ, Heshami K, Erskine J, Spanner M, England DG, Sussman BJ. Timebintopolarization conversion of ultrafast photonic qubits. Phys Rev A. 2017;96:053812. https://doi.org/10.1103/PhysRevA.96.053812.
Valivarthi R, et al.. Efficient bell state analyzer for timebin qubits with fastrecovery WSi superconducting single photon detectors. Opt Express. 2014;22(20):24497–506. https://doi.org/10.1364/OE.22.024497.
CabrejoPonce M, Spiess C, Muniz ALM, Ancsin P, Steinlechner F. Ghzpulsed source of entangled photons for reconfigurable quantum networks. Quantum Sci Technol. 2022;7(4):045022. https://doi.org/10.1088/20589565/ac86f0.
Grice WP, Beck M, Earl D, Mulkey D, Schaake J. Reconfigurable entangled photon source (conference presentation). In: Gruneisen MT, Dusek M, Alsing PM, Rarity JG, editors. Quantum technologies and quantum information science V. vol. 11167. SPIE; 2019. p. 111670. https://doi.org/10.1117/12.2536266.
Williams BP, Lukens JM, Peters NA, Qi B, Grice WP. Quantum secret sharing with polarizationentangled photon pairs. Phys Rev A. 2019;99:062311. https://doi.org/10.1103/PhysRevA.99.062311.
Agrawal P, Pati AK. Probabilistic quantum teleportation. Phys Lett A. 2002;305(1):12–7. https://doi.org/10.1016/S03759601(02)01383X.
Modławska J, Grudka A. Nonmaximally entangled states can be better for multiple linear optical teleportation. Phys Rev Lett. 2008;100:110503. https://doi.org/10.1103/PhysRevLett.100.110503.
Marcikic I, Riedmatten H, Tittel W, Scarani V, Zbinden H, Gisin N. Timebin entangled qubits for quantum communication created by femtosecond pulses. Phys Rev A. 2002;66:062308. https://doi.org/10.1103/PhysRevA.66.062308.
Takesue H, Noguchi Y. Implementation of quantum state tomography for timebin entangled photon pairs. Opt Express. 2009;17(13):10976–89. https://doi.org/10.1364/OE.17.010976.
Clauser JF, Horne MA, Shimony A, Holt RA. Proposed experiment to test local hiddenvariable theories. Phys Rev Lett. 1969;23:880–4. https://doi.org/10.1103/PhysRevLett.23.880.
Kim JH, Chae JW, Jeong YC, Kim YH. Longrange distribution of highquality timebin entangled photons for quantum communication. J Korean Phys Soc. 2022;80:203–13. https://doi.org/10.1007/s40042021003425.
Zhao J, Ma C, Rüsing M, Mookherjea S. High quality entangled photon pair generation in periodically poled thinfilm lithium niobate waveguides. Phys Rev Lett. 2020;124:163603. https://doi.org/10.1103/PhysRevLett.124.163603.
SedziakKacprowicz K, Czerwinski A, Kolenderski P. Tomography of timebin quantum states using timeresolved detection. Phys Rev A. 2020;102:052420. https://doi.org/10.1103/PhysRevA.102.052420.
Fasel S, Gisin N, Ribordy G, Zbinden H. Quantum key distribution over 30 km of standard fiber using energytime entangled photon pairs: a comparison of two chromatic dispersion reduction methods. Eur Phys J D. 2004;30:143–8. https://doi.org/10.1140/epjd/e2004000808.
Joshi SK, et al.. A trusted node–free eightuser metropolitan quantum communication network. Sci Adv. 2020;6(36):0959. https://www.science.org/doi/pdf/10.1126/sciadv.aba0959. https://doi.org/10.1126/sciadv.aba0959.
Wengerowsky S, Joshi SK, Steinlechner F, Hubel H, Ursin R. An entanglementbased wavelengthmultiplexed quantum communication network. Nature. 2018;564:225–8.
Marcikic I, Riedmatten H, Tittel W, Zbinden H, Legré M, Gisin N. Distribution of timebin entangled qubits over 50 km of optical fiber. Phys Rev Lett. 2004;93:180502. https://doi.org/10.1103/PhysRevLett.93.180502.
Zhong T, Wong FNC, Restelli A, Bienfang JC. Efficient singlespatialmode periodicallypoled ktiopo4 waveguide source for highdimensional entanglementbased quantum key distribution. Opt Express. 2012;20(24):26868–77. https://doi.org/10.1364/OE.20.026868.
Zhong T, Wong FNC. Nonlocal cancellation of dispersion in franson interferometry. Phys Rev A. 2013;88:020103. https://doi.org/10.1103/PhysRevA.88.020103.
Dynes JF, et al.. Efficient entanglement distribution over 200 kilometers. Opt Express. 2009;17(14):11440–9. https://doi.org/10.1364/OE.17.011440.
Aspect A, Dalibard J, Roger G. Experimental test of Bell’s inequalities using timevarying analyzers. Phys Rev Lett. 1982;49:1804–7. https://doi.org/10.1103/PhysRevLett.49.1804.
Altepeter JB, Jeffrey ER, Kwiat PG. Photonic state tomography. In: Advances in atomic, molecular, and optical physics. vol. 52. San Diego: Academic Press; 2005. p. 105–59. https://www.sciencedirect.com/science/article/pii/S1049250X05520032. https://doi.org/10.1016/S1049250X(05)520032.
James DFV, Kwiat PG, Munro WJ, White AG. Measurement of qubits. Phys Rev A. 2001;64:052312. https://doi.org/10.1103/PhysRevA.64.052312.
Banaszek K, D’Ariano GM, Paris MGA, Sacchi MF. Maximumlikelihood estimation of the density matrix. Phys Rev A. 1999;61:010304. https://doi.org/10.1103/PhysRevA.61.010304.
Shen S, Yuan C, Zhang Z, et al.. Hertzrate metropolitan quantum teleportation. Light: Sci Appl. 2023;12:115. https://doi.org/10.1038/s41377023011587.
Acknowledgements
This work is supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) Grant funded by the Korean government (MSIT) (No. 2022000463, Development of a quantum repeater in optical fiber networks for quantum internet), and by the Electronics and Telecommunications Research Institute (ETRI) grant funded by the Korean government (Grant No. 24ZS1220, Proprietary basic research on computing technology for the disruptive innovation of computational performance).
Funding
This work is supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) Grant funded by the Korean government (MSIT) (No. 2022000463, Development of a quantum repeater in optical fiber networks for quantum internet), and by the Electronics and Telecommunications Research Institute (ETRI) grant funded by the Korean government (Grant No. 24ZS1220, Proprietary basic research on computing technology for the disruptive innovation of computational performance).
Author information
Authors and Affiliations
Contributions
J.K. and J.P. acquired experimental data, analyzed the data, and wrote the main manuscript text. H.S.K, G.K., J.K, and J.P. acquired experimental data and interpreted experimental data. S.C.K. acquired experimental data. K.M., M.K., and J.J.J. designed and conceived the experiments in the manuscript. All authors reviewed the manuscript.
Corresponding author
Ethics declarations
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix A: Source characterization details
In Fig. 8, we show the measured coincidence count rate and accidental coincidence count rate in relation to SH pump power, the average power measured with a power meter before the SPDC PPLN. The coincidence to accidental count ratio (CAR) in relation to the SH pump power is also shown in Fig. 9. In this work, we chose our SH pump power to be \(89~\mu\text{W}\), as this gave a high coincidence count rate of 11.3 kHz as well as a reasonable CAR, which is defined as
where \(N_{CC}\) is the coincidence counts within the coincidence window, and \(N_{ACC}\) is the accidental coincidence counts. We characterized \(N_{ACC}\) as the average counts in coincidence windows within 5 repetition pulses away from the main coincidence counts window. At a SH pump power of \(89~\mu\text{W}\), CAR had a value of 309. We used the following relations [53]
where \(N_{s}\), \(N_{i}\), \(N_{CC}\), and \(N_{ACC}\) are the measured signal counts, idler counts, coincidence counts, and accidental coincidence counts respectively, \(D_{s}\) and \(D_{i}\) are dark counts measured for signal and idler channels, R is the generation rate of photon pairs and \(\eta _{s}\) and \(\eta _{i}\) are the detection efficiencies of signal and idler photons accounting for the total loss in each detection arm after SPDC. From these relations, we found R to calculate our mean photon number \(\mu = R/R_{Rep}\), where \(R_{Rep}\) is our pump repetition rate of 200 MHz. For our SH pump power of \(89~\mu \text{W}\), we obtained a pair generation rate of 2.4 MHz with an average photon number \(\mu = 0.012\).
Appendix B: Additional notes on fidelity
Table 1 shows all fidelities of prepared states before and after entanglement distribution. The errors for the fidelities were obtained by conducting a MonteCarlo simulation assuming that the measured counts follow a Poissonianlike distribution. For each set of simulated counts, quantum state tomography and MLE is conducted to obtain a distribution of fidelities. An example simulation is shown in Fig. 10 with 10,000 runs for state F to find the distribution of fidelities assuming a Poissonian distribution of counts. The errors are given to reflect the distribution of fidelities. After entanglement distribution, the measured counts are lower. This means that the Poissonian error distribution is wider, thus resulting in a wider fidelity distribution.
Figure 10 also shows that the fidelity of the state is not actually improved upon distribution through the fiber channel for states such as state F. While the fidelity calculated post MLE for state F after entanglement distribution gives 0.9413, the average fidelity from the MonteCarlo simulated distribution is 0.9254. On the other hand, in the 0km case, the fidelity calculated from the density matrix post MLE corresponds to the average fidelity from the MonteCarlo simulation. This is also shown in Table 1, thus showing that the average fidelity after MonteCarlo simulations reflects a lower fidelity after entanglement distribution for all states. The asymmetrical errors are given to reflect these mismatches between the fidelity derived from measured counts and the MonteCarlo distribution.
Table 2 shows the concurrence of each state before and after distribution. Similar to fidelity, the error of each concurrence was found by conducting MonteCarlo simulations using the measured counts assuming Poissonian error. At low counts, the concurrence calculated from the density matrix after MLE also did not always match the average concurrence shown by MonteCarlo simulations. This is also shown in Table 2.
Appendix C: Timing drift
Additionally, longperiod measurements were conducted over 52 hours after entanglement distribution over 100km SMFs to monitor the effect of timing drifts without a feedback system. When measured over 52 hours, we found a total timing drift of each signal and idler counts of approximately 1 ns over 12 hours for each channel depending on the time of day. However, as the lab was well airconditioned, the fluctuations in timing difference had a standard deviation of 246 ps over 52 hours. We anticipate that extended quantum communication protocols involving multiple entanglement distribution systems or Bell state measurements will require feedback systems to mitigate or get around such timing fluctuations as demonstrated by [10, 53].
Rights and permissions
Open Access This article is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License, which permits any noncommercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/byncnd/4.0/.
About this article
Cite this article
Kim, J., Park, J., Kim, HS. et al. Fully controllable timebin entangled states distributed over 100km singlemode fibers. EPJ Quantum Technol. 11, 53 (2024). https://doi.org/10.1140/epjqt/s40507024002675
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjqt/s40507024002675