1. Introduction

Quantum key distribution (QKD) has nowadays been demonstrated as a cryptographic approach to provide absolute security between sender (Alice) and receiver (Bob) [1, 2]. Fiber-based systems have been implemented in prototype QKD experiments, with practical stabilities in long-distance telecom fibers [3–5]. Among those, the so-called “plug and play” QKD system realized in “two-way” fibers is to date the most stable one because its phase-drift balance of Mach-Zehnder (MZ) interferometer can automatically compensate any birefringence effects and polarization-dependent losses in the optical fibers [3]. However, the security to the “twoway” QKD may be threatened by Trojan attacks. In order to overcome this security threat, researchers switched their focus of interest to “one-way” QKD. The “one-way” QKD can be realized with phase encoding in asymmetric MZ interferometers [4], and the influence of polarization fluctuations in long-distance fibers on single-photon interference can be overcome by using Faraday reflection in modified Michelson interferometers [5]. And the practical QKD based on phase-encoding was realized with long-term stability recently [6]. However, precise active modulation and feedback compensation are necessary to avoid the phase shifts that influence the stability and quantum bit error in phase-encoding system. In contrast, polarization encoding can be used for fiber QKD without any active modulation elements at Alice’s or Bob’s sites [7, 8], and thus less lossy elements are used. The key-generation efficiency can be possibly increased with an improved security in practice. Hwang, H. K. Lo and Wang has put forward decoy-state in Refs. [9–11], and the experiments have already been performed by Y. Zhao and C. Peng [12, 13]. Another obvious advantage of the polarization-encoded system comes from its suitability to implement the decoy-state protocol or ideal single-photon sources for QKDs with unconditional securities. Nevertheless, polarization-encoded “one-way” fiber systems are difficult to make practical due to the unpredictable polarization transformation imposed by randomly induced birefringence in installed telecom fibers or polarization-dependent losses of on-line optical elements within the system. At a first glance, polarization-encodedQKD system may rely on standard polarization control schemes widely used in optical telecom, but hardly become applicable in practice as strong feedback control pulses in those schemes unavoidably bring about detrimental scatterings to interfere with single-photon qubits. A practical singlephoton polarization-encoding in long-distance fibers actually requires polarization-control at single-photon level or at least with extremely weak reference pulses for the purpose to minimize the detrimental influence from feedback control pulses. In this paper we demonstrate that polarization transformation in long-distance standard single-mode fibers can be compensated by using on-line fiber-based polarization controllers with negligible losses and detrimental scatterings on single-photon qubits, which supports successfully an experimental implementation of polarization-encoded QKD with a long-term stability in long-distance fibers.

2. Principle of single-photon polarization stabilization and polarization-encoded QKD

In optical fibers, a linearly polarized beam at the input will transform randomly polarized at the output after a long-distance propagation, mainly due to the birefringence induced by the unavoidable stress or asymmetry of the fiber. In fiber based QKD systems, the linear polarized single photons sent out by Alice will arrive at Bob with arbitrary state of polarization (SOP) after a long-distance optical fiber. In order to get accurate polarization decoding in the presence of unpredictable polarization transformation, Bob needs a polarization feedback control to rotate his random SOPs back to the original ones. This can be realized with electronic polarization controllers (EPC) consisting of properly aligned piezoelectronic actuators to stress on fiber along different directions, which induce desired birefringence in fiber to adjust the SOP in a controllable way [14, 15]. Each EPC consists of two electronically controlled piezoelectronic actuators X₁ and X₂ to stress the fiber along 45°and 0°, respectively. According to the visualized representation of polarizations in the Poincare sphere [see the inset of Fig. 1(a)], an applied piezoelectronic voltage on X₁ brings about a clockwise rotation of the SOP along the QR axis, corresponding to a phase retarder between the eigenmodes (i.e., linear polarizations along ±45°) of the induced birefringence, while an applied piezoelectronic voltage on X 2 causes the SOP to rotate along the HV axis clockwise, corresponding to a phase retarder between the eigenmodes polarizations (along 0°and 90°) of the induced birefringence. A proper combination of piezoelectronic voltages on X₁ and X₂ can compensate for the arbitrary SOP changes of orthogonal polarizations, corresponding to rotations along QR and HV axes in a proper series. Polarization-encoded QKD involves at least two nonorthogonal SOPs to ensure its security [16]. In the standard BB84 protocol, Alice sends single photons randomly polarized in either HV or QR base. After a long-distance propagation in fiber, those nonorthogonal SOPs are changed into arbitrary polarizations P_H, P_V, P_Q or P_R, respectively. One may apply proper piezoelectronic voltages on X₁ and X₂ to rotate P_H (P_V) back to H(V), or P_Q (P_R) back to Q(R). At Bob, two EPCs are used to collect feedback signals to control the SOPs in the HV and QR bases, respectively. As Bob tries to decode polarization information, he actually randomly chooses a HV or QR base to measure the SOPs. Once the decoding base is selected, Bob then only focuses on feedback control of orthogonal polarizations in the selected base, disregarding polarization changes induced in the other base since only orthogonal polarizations in the selected base give useful decoding. The polarization decoding base can be selected with a 50/50 beam splitter followed by polarization measurement in HV and QR bases, respectively. After the beam splitter, Bob sets polarization controlling, and polarization decoding in HV and QR bases. Feedback control cycles are interrupted within QKD cycles with proper durations to ensure sufficient polarization stability.

3. Experimental realization of polarization stabilization and QKD demonstration

The above-mentioned scheme offers a promising advantage of very low loss in the whole setup from Alice to Bob since the modulation elements in the experiment consist of single-mode fiber, and the main inserted loss before detectors are introduced by the electronic polarization controllers, which are commercially available with negligible inserted loss. Negligible losses in Bob’s decoding setup are of critical significance in long-distance fiber QKD system as far as absolute security is concerned. As Alice uses passive modulation elements without any loss, the polarization-encoded QKD is promisingly applicable to ideal single-photon sources.

For the feedback control in HV and QR bases, Alice should send H and Q polarizations as reference SOPs, respectively. In the feedback control cycles, Bob’s decoding part functions actually as a polarimeter at single-photon level.With sufficient photons incident on the detectors, the signals of four detectors can form two Stokes parameters S₁ and S₂. For a typical elliptic polarization state at Bob’s site, their normalized values are given by

 

Fig. 1. (a) The schematic single-photon polarization stabilization based on the BB84 protocol. Single-photon detectors D_H, D_V, D_Q, D_R are used to detect H, V, Q and R polarized photons, respectively. EPC_0>~1 is the electronic polarization controllers corresponding to the control of the polarization HV and QR bases; WP: quarter-waveplates; PBS: polarization beam splitters. Inset: the polarization direction of the single-photon pulses at Alice with+45°, -45°, 0° or 90° along the optical axis of the system represented respectively by the point Q, R, H or V in the equator of the Poincare sphere. Polarization direction of the photons arriving at Bob represented by the point P on the Poincare sphere. (b) The schematic setup of stable polarization-encode quantum key distribution; LD_0~4: 1550 nm DFB laser diodes with the pulse width about 2 ns; Attn_0~6: variable optical attenuators; PC_0~6: fiber polarization controllers; OSW_1~2: optical switcher; D_0~3: single-photon detectors; PCI6251: data acquisition card (National Instruments); AMP: voltage amplifier.

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where I(H), I(V), I(Q) and I(R) are photon intensity recorded by the H, V, Q and R detectors, respectively, 2ε and 2θ are the longitude and latitude of a point on the Poincare sphere, which represent the double azimuth and elliptcity angles, respectively. Due to the birefringence induced randomly in the fiber, the linearly polarized pulses sent by Alice as a reference change to be elliptically polarized with random ε and θ at Bob’s site.

As an experimental demonstration, the reference SOP was set at the horizontal direction (H) and the polarization stability of single-photon pulses in a long-distance fiber was monitored. The schematic experimental configuration is shown in Fig. 1(b). The whole communication system was synchronized by repetitive pulses from the laser diode LD₀. A separate fiber channel was used for the synchronous pulses in order to avoid influence of intense clock laser and its Raman scattering. Pulses from two laser diodes LD₁ and LD₂ were linearly polarized at vertical and horizontal directions, respectively. Pulses from LD₁ were attenuated to 0.1 photons per pulse after Attn₀ and Attn₆. The light pulses from LD₂ could be switched by an optical switcher (OSW₁) either from Attn₂ to Attn₆ which attenuated the light to 0.1 photons per pulse, or from Attn₃ to Attn₆ which attenuated it to several photons per pulse as reference pulses to monitor SOP. LD₀~LD₄ and OSW₁~OSW₂ were controlled by a computer at Alice’s site. At Bob’s part, the H, V, Q and R SOP photons were detected by D₁, D₀, D₂ and D₃, respectively. The SOPs of photons were adjusted by EPCs (PolaRITE III, General Photonics) to compensate for the random birefringence in the long-distance fiber. Bob used a data acquisition card to collect signals from single-photon detectors, and generate two analog signals V₁ and V₂ to the drivers of the polarization controllers X₁ and X₂, respectively.

The random variation of SOP depended on the fiber distance and environment. For a typical condition, the SOP could maintain relatively stable within a few minutes in 50 km fiber in laboratory. In the stable polarization-encoded QKD system, the communication was suspended from time to time, and the photon pluses were used to optimize the polarization in the fiber. The suspension duration was set according to the fiber length and the mean photon numbers in the system. Note that the signals were divergent clicks on single-photon detectors, which exhibited unavoidable fluctuations mainly due to the dark-noise of single-photon detection. The fluctuation of the dark-counts was estimated as ±3% in our experiment. To minimize influence from such fluctuations, the system was operated with a repetition rate of 1 MHz and an accumulation time of one second (10⁶ counts) for each sampling signal used for feedback control. The feedback-control programs working for HV and QR polarization were similar but independent from each other and operated by turns corresponding to the reference SOP sent by Alice (H or Q polarization). Take HV-base for example to show the process of stabilization control. At first, Bob sent a polarization-control request to Alice through Ethernet and waited for sampling the SOP signals. Having received the request, Alice would send reference photons of H-polarization instead of random H/V and Q/R SOP. After sampling and calculating S 1, the program judged the SOP change by comparing S₁ with thresholds T₁ (close to 1). If S₁>T₁, the program approximated the SOP at Bob as H-polarization. Only if Bob had approximately H-polarization, did the program send order to stop the feedback control cycles and restart the QKD cycles. If S₁<T₁, the program produced two proper analog voltages V₁ and V₂ for EPC₀ to drive piezoelectronic actuators X₁ and X₂, respectively. In the beginning, the value of V₁ and V₂ was set at the mean value of the EPC operation voltage range. There were four possible combinations of the changes for the value of V₁ and V₂ (V₁+/V₂+, V₁+/V₂-, V₁-/V₂-, V₁-/V₂+), (“+” for increase and “-” for decrease). The four possibilities were scanned in turn. If the changes on the V₁ and V₂ didn’t optimize the SOP, the values of V₁ and V₂ were reset and the other combinations were attempted until the combination that could rotate the SOP back to its initial state was found out. V₁ and V₂ could be adjusted according to the change of S₁ which was monitored synchronously to judge whether the polarization was optimized (the target is S₁>T₁). Once polarization control finished, the system would switched back to QKD operation in which V₁ and V₂ values were maintained and saved as initial value for the next optimization cycle.

 

Fig. 2. Feedback signals S₁ and their corresponding controlling voltages V₁ and V₂ for the 50 km (a, b) and 100 km (c,d) fiber systems.

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We experimentally tested the feasibility and long-term stability of the above-mentioned polarization feedback control at single-photon level in 50, 75 and 100 km fiber systems. For different fiber lengths between Alice and Bob, we intentionally adjusted the intensity of the reference pulses to have approximately the same mean photon number I(H)+I(V) arriving at Bob. The mean photon numbers of reference pulses at Alice were about 0.5, 1.6 and 5.1 per pulse for the 50, 75 and 100 km systems, respectively, corresponding to I(H)+I(V)~3200 counts per second at Bob for all three cases. In the experiments, the single-photon polarization control was limited by the different polarization extinction of polarization beam splitters used in the setup. Taking into account the limited polarization extinctions and dark-count probabilities of single-photon detection, we set the thresholds T₁ as 0.96, 0.95, 0.93 for the 50, 75 and 100 km fiber systems under test, respectively. And the intervals of periodically interrupted communication were adjusted according to the fiber lengths. In order to guarantee satisfactory polarization stability in the long-term operation, any possible random degenerations of the reference SOP (from H to PH) were regularly tracked with the preset interruption cycles within sufficiently short intervals. In our experiment, we selected 4.7, 3.1, and 1.6 minutes for the 50, 75 and 100 km fiber lengths, respectively. Figure 2 shows typical experimental situation in the 50 and 100 km fiber systems where the controlling voltages V₁ and V₂ applied on X₁ and X₂ established stable feedback polarization controls. Due to random fluctuation, the stabilization might go beyond controlling at some points as those spikes in Figs. 2(b) and 2(d), the pro-gram could automatically adjust the controlling voltages V₁ and V₂ on X₁ and X₂ according to the measured feedback signals, and eventually made S₁ return to the well-controlled loop. As voltages V₁ and V₂ applied on both X₁ and X₂ were accumulated increase or decrease from the previous counterparts in accordance with feedback signals, continuous increase or decrease might cause the voltages to exceed the available ranges of the X₁ or X₂ drivers (0~150 V). This can be readily avoided by resetting the paranormal controlling voltage with an increase or decrease of a 2π voltage (52.2 and 49.0 V for X₁ and X₂, respectively). Figure 3 compares the polarization stabilities with and without feedback polarization control in 50, 75, 100 km fiber systems by monitoring the S₁ of single-photon pulses at Bob, from which we can conclude that Bob could actively maintain polarization-stabilized single-photon pulses of the same SOPs with Alice’s reference for very long durations. Table 1 shows the duration of polarization adjustment in the tested case, the long-term stability was maintained up to 630, 587, and 400 minutes for the 50, 75, 100 km fiber systems, respectively.The SOP at Bob’s site was feedback-controlled to Alice’s reference polarization H with about 9% of the communication duration interrupted for feedback control. The test could in principle operate for longer duration. The current limited factors came from somewhat unstable operation of single-photon detectors, which required a little fine adjustment of the coincidence detection after continuous operation about tens of hours.

 

Fig. 3. The comparison of the single-photon polarization variation with (dark lines) and without active feedback controls (grey lines) for S₁ monitored in long-term operations of 50 km (a), 75 km (b), and 100 km (c) fiber systems.

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Table 1. Duration of polarization adjustment in the test

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Such a single-photon polarization control was checked in the real QKD test to make sure that it was sufficient for polarization-encoding protocol. The experimental setup is shown in Fig. 1(b) and the stability and QBER of the polarization-encoded QKD was checked in a longterm operation. Alice randomly selected HV or QR base to encode qubits, and the weak pulses were attenuated to 0.1 photons per pulse in our experiment. Figure 4 shows the experimental tests of the 75 km fiber systems within a long-term operation of 620 minutes, giving the QBER as (3.9±1.5)%. The key generation rate was ~210 bps. The attenuated single-photon pulses contained 0.002 photon per pulse after 75 km fiber propagation (including 2 dB loss from on-line optical elements), respectively. The single-photon detectors we used were based on InGaAs/InP avalanche photodiodes (APD) working in the gated Geiger mode. The APDs were placed in the bottle of liquid nitrogen and the temperature was set-95°C. The singlephoton detectors were designed and fabricated in our research group [17]. The dark counts of the single-photon detectors used in the experiments were 6×10^-7 (detector D₀), 8×10^-7 (detector D₁), 3.1×10^-6 (detector D₂) and 2.9×10^-6 (detector D₃), and the quantum efficiency reached ~15%. The dark-count noise produced ~1.6% QBER in the 75 km system. The measured QBER, which was still larger than that merely caused by dark noises, could be ascribed to the incompletely compensated single-photon polarization transformations. A QBER of (3.9±1.5)% in 75 km fiber implied that single-photon polarization control could guarantee stable polarization encoding and decoding for BB84 QKD. The 0.1 averaged photon number was chosen according to the Poissonian distribution to decrease the possibility of multi-photon signals which could be utilized by Eve to implement the so-called photon number splitting attacks (PNS). As known, the PNS attack threatens the present QKD experimental schemes using weak coherent pulse as light source. Therefore, the transmission distance is highly limited due to the possibility of multi-photon signals of the source and loss in the fiber channel [18, 19], a longer transmission distance can be realized providing that decoy-state QKD is implemented. And it should be noticed that the polarization-encoded system is quite suitable to implement the decoy-state protocol, and our feedback control system is a powerful tool for long-term polarization stability in decoy-state QKD. It has been pointed out that random polarization changes in long-distance fiber was dependent on the central wavelengths of the carrier pulses [20]. While the laser diodes (LD_0~4) used in our experiments were DFB lasers without temperature control, and accordingly, the central wavelengths of the laser diodes are 1548 ~1551 nm and the linewidth of each laser is about 2.5 nm, thus the photon source couldn’t be distinguished by wavelength analysis and it wouldn’t be a security loophole for the experiment. However, the different wavelengths might produce polarization transformation slightly dependent on the laser diodes, leading to some instable origins for polarization feedback controlling. Using dense wavelength division multiplexing laser diodes can solve these problems, since the linewidth of these lasers is less than 0.02 nm, and the central wavelength can be tuned precisely by changing the temperature of the laser diode.

Our experimentwas achieved in the laboratory environment. The temperaturewas constant at 20°C (±0.5°C). The influences of outside environment will make this scheme a little difficult to operate because in installed fiber the polarization is more instable, causing the degenerations of the SOP. Then the system has to spend more time working in “polarization control” cycle and the key generation efficiency will be decreased. But the SOP is not as sensitive as thought [21]. Moreover this problem can be solved if we make the system working at higher repetition rate. Because the feedback control is based on the accumulation of photon counts to judge if the SOP is suitable for QKD, higher repetition rate will reduce the time of “polarization control” state and make the system fit for installed fiber.

 

Fig. 4. QBERs of polarization-encoded QKD in 75 km fiber system.

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4. Conclusion

In conclusion, we have achieved polarization feedback control in long-distance fiber at singlephoton level, which facilitated polarization-encoded QKD with long-term stabilities. Experimental test of polarization encoding with negligible loss elements demonstrated that the singlephoton polarization transformation in long-distance fibers could be controlled to provide QBER below the security threshold for polarization-encoded “one-way” QKD in fiber. Furthermore, the polarization-encoded scheme is suitable to utilize decoy-state for enhanced security and extended transmission distance. Our experimental tests were based on single-photon polarization stabilization and encoding on BB84 protocol. Furthermore, the polarization feedback control could stabilize the orthogonal SOPs simultaneously by EPC, which could be directly used in the protocol of entangled photons with Wigner’s inequality [22]. Polarization-encoded “oneway” QKD is not only promisingly applicable to ideal single-photons and entangled photons, but also possesses an enhanced security due to its low losses in the whole setup from Alice to the detectors at Bob’s site.