INTRODUCTION

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ChooseTop of pageABSTRACTINTRODUCTION <<DIRECT GENERATION OF ENCO...RESULTSDISCUSSIONREFERENCESQuantum key distribution (QKD) allows two parties to exchange secret keys with security guaranteed by the fundamental laws of physics.1,21. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002); arXiv:0601207 [quant-ph]. https://doi.org/10.1103/revmodphys.74.1452. C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in IEEE International Conference on Computers, Systems and Signal Processing (IEEE, 1984), Vol. 175. Driven by its potential, tremendous progress has been made in both theoretical and technological developments, such as satellite-based QKD,3,43. S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017); arXiv:1707.00542. https://doi.org/10.1038/nature236554. Y.-A. Chen, Q. Zhang, T.-Y. Chen et al., “An integrated space-to-ground quantum communication network over 4,600 kilometres,” Nature 589, 214–219 (2021). https://doi.org/10.1038/s41586-020-03093-8 QKD networks,5–85. M. Sasaki, M. Fujiwara, H. Ishizuka, W. Klaus, K. Wakui, M. Takeoka, S. Miki, T. Yamashita, Z. Wang, A. Tanaka, K. Yoshino, Y. Nambu, S. Takahashi, A. Tajima, A. Tomita, T. Domeki, T. Hasegawa, Y. Sakai, H. Kobayashi, T. Asai, K. Shimizu, T. Tokura, T. Tsurumaru, M. Matsui, T. Honjo, K. Tamaki, H. Takesue, Y. Tokura, J. F. Dynes, A. R. Dixon, A. W. Sharpe, Z. L. Yuan, A. J. Shields, S. Uchikoga, M. Legré, S. Robyr, P. Trinkler, L. Monat, J.-B. Page, G. Ribordy, A. Poppe, A. Allacher, O. Maurhart, T. Länger, M. Peev, and A. Zeilinger, “Field test of quantum key distribution in the Tokyo QKD Network,” Opt. Express 19, 10387 (2011); arXiv:1008.1508. https://doi.org/10.1364/oe.19.0103876. D. Stucki, M. Legré, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voirol, N. Walenta, and H. Zbinden, “Long-term performance of the SwissQuantum quantum key distribution network in a field environment,” New J. Phys. 13, 123001 (2011). https://doi.org/10.1088/1367-2630/13/12/1230017. J. F. Dynes, A. Wonfor, W. W. Tam, A. W. Sharpe, R. Takahashi, M. Lucamarini, A. Plews, Z. L. Yuan, A. R. Dixon, J. Cho, Y. Tanizawa, J. P. Elbers, H. Greißer, I. H. White, R. V. Penty, and A. J. Shields, “Cambridge quantum network,” Npj Quantum Inf. 5(1), 101 (2019). https://doi.org/10.1038/s41534-019-0221-48. T. Y. Chen, X. Jiang, S. B. Tang, L. Zhou, X. Yuan, H. Zhou, J. Wang, Y. Liu, L. K. Chen, W. Y. Liu, H. F. Zhang, K. Cui, H. Liang, X. G. Li, Y. Mao, L. J. Wang, S. B. Feng, Q. Chen, Q. Zhang, L. Li, N. L. Liu, C. Z. Peng, X. Ma, Y. Zhao, and J. W. Pan, “Implementation of a 46-node quantum metropolitan area network,” Npj Quantum Inf. 7(1), 134 (2021). https://doi.org/10.1038/s41534-021-00474-3 chip-based QKD,9–119. T. K. Paraïso, I. De Marco, T. Roger, D. G. Marangon, J. F. Dynes, M. Lucamarini, Z. Yuan, and A. J. Shields, “A modulator-free quantum key distribution transmitter chip,” Npj Quantum Inf. 5, 42 (2019). https://doi.org/10.1038/s41534-019-0158-710. D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. Derose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018); arXiv:1708.00434. https://doi.org/10.1103/physrevx.8.02100911. P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017); arXiv:1509.00768. https://doi.org/10.1038/ncomms13984 as well as the invention of novel protocols allowing higher secret key capacity.12–1412. M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400 (2018). https://doi.org/10.1038/s41586-018-0066-613. J.-P. Chen, C. Zhang, Y. Liu, C. Jiang, W.-J. Zhang, Z.-Y. Han, S.-Z. Ma, X.-L. Hu, Y.-H. Li, H. Liu et al., “Twin-field quantum key distribution over a 511 km optical fibre linking two distant metropolitan areas,” Nat. Photonics 15, 570 (2021). https://doi.org/10.1038/s41566-021-00828-514. M. Pittaluga, M. Minder, M. Lucamarini, M. Sanzaro, R. I. Woodward, M. J. Li, Z. Yuan, and A. J. Shields, “600-km repeater-like quantum communications with dual-band stabilization,” Nat. Photonics 15, 530 (2021); arXiv:2012.15099. https://doi.org/10.1038/s41566-021-00811-0In QKD protocols, time-bin encoding is commonly used,15–1815. A. Boaron, G. Boso, D. Rusca, C. Vulliez, C. Autebert, M. Caloz, M. Perrenoud, G. Gras, F. Bussières, M.-J. Li, D. Nolan, A. Martin, and H. Zbinden, “Secure quantum key distribution over 421 km of optical fiber,” Phys. Rev. Lett. 121, 190502 (2018); arXiv:1807.03222. https://doi.org/10.1103/physrevlett.121.19050216. Z. Yuan, A. Murakami, M. Kujiraoka, M. Lucamarini, Y. Tanizawa, H. Sato, A. J. Shields, A. Plews, R. Takahashi, K. Doi, W. Tam, A. W. Sharpe, A. R. Dixon, E. Lavelle, and J. F. Dynes, “10-Mb/s quantum key distribution,” J. Lightwave Technol. 36, 3427 (2018). https://doi.org/10.1109/jlt.2018.284313617. B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature 501, 69 (2013); arXiv:1309.6431. https://doi.org/10.1038/nature1249318. Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016). https://doi.org/10.1103/physrevx.6.011024 where the temporal modes of a time-bin qubit (early and late time bins) and the phase between them are used to encode the key bits. As practical single photon sources are not yet widely available, QKD systems typically employ lasers to generate weak coherent states to approximate the time-bin qubits. Since the photon number statistics of laser emission follow a Poisson distribution, the emitted pulses have a non-negligible probability of containing more than one photon, making laser-based QKD systems susceptible to a photon-number-splitting (PNS) attack.1919. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330 (2000). https://doi.org/10.1103/physrevlett.85.1330 Although it is still possible to obtain unconditional security, the signal flux has to be heavily attenuated in order to suppress multi-photon emission, thus giving a poor scaling of the secure key rate with transmission distance.2020. D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325 (2004); arXiv:0212066 [quant-ph]. https://doi.org/10.26421/qic4.5-1 Fortunately, this problem can be overcome by employing the decoy state method:21,2221. W.-Y. Hwang, “Quantum key distribution with high loss: Toward global secure communication,” Phys. Rev. Lett. 91, 057901 (2003); arXiv:0211153 [quant-ph]. https://doi.org/10.1103/PhysRevLett.91.05790122. H. K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005); arXiv:0411004 [quant-ph]. https://doi.org/10.1103/PhysRevLett.94.230504 in addition to sending signal states, one also randomly sends a small number of states with reduced intensity, known as decoy states. A potential eavesdropper cannot distinguish between signal states and decoy states; thus, any attempt to perform photon-number-dependent attacks can be detected from the measured photon statistics. As a result, with the decoy state method, single-photon bounds can be reliably estimated, which, therefore, improves the scaling of the secure key rate with distance significantly.

Implementing a decoy-state QKD transmitter requires the ability to on-off modulate each time bin within a state, modulate the phase between time bins, as well as vary the intensity level to generate decoy states. To date, this has been achieved by placing intensity modulators after a light source to control the output intensity, and phase modulators are also required in order to encode the phase information. Conventional intensity and phase modulators are based on LiNbO3 crystals. While these modulators are widely available and offer high performance, they are expensive, bulky (centimeter-scale), and require high driving voltage (typically > 4 V), which often necessitates the addition of amplifiers. It is, therefore, highly beneficial to develop an alternative approach that can replace such modulators, as it would significantly reduce the overall complexity, making QKD systems more compact and cost-effective.

Recently, Yuan et al. demonstrated an efficient scheme to perform direct phase modulation without the need for phase modulators.2323. Z. L. Yuan, B. Fröhlich, M. Lucamarini, G. L. Roberts, J. F. Dynes, and A. J. Shields, “Directly phase-modulated light source,” Phys. Rev. X 6, 031044 (2016); arXiv:1605.04594. https://doi.org/10.1103/physrevx.6.031044 Precise phase control is enabled by exploiting optical injection locking (OIL) and gain-switching techniques. Following this work, direct phase modulated laser transmitters for QKD have been studied more widely,2424. T. K. Paraïso, R. I. Woodward, D. G. Marangon, V. Lovic, Z. Yuan, and A. J. Shields, “Advanced laser technology for quantum communications (tutorial review),” Adv. Quantum Technol. 4, 2100062 (2021); arXiv:2108.13642. https://doi.org/10.1002/qute.202100062 bringing the benefits of compact low-drive-voltage phase modulation for chip-based QKD99. T. K. Paraïso, I. De Marco, T. Roger, D. G. Marangon, J. F. Dynes, M. Lucamarini, Z. Yuan, and A. J. Shields, “A modulator-free quantum key distribution transmitter chip,” Npj Quantum Inf. 5, 42 (2019). https://doi.org/10.1038/s41534-019-0158-7 as well as other emerging protocols such as measurement-device-independent QKD.2525. R. I. Woodward, Y. S. Lo, M. Pittaluga, M. Minder, T. K. Paraïso, M. Lucamarini, Z. L. Yuan, and A. J. Shields, “Gigahertz measurement-device-independent quantum key distribution using directly modulated lasers,” Npj Quantum Inf. 7, 58 (2021). https://doi.org/10.1038/s41534-021-00394-2 More recently, the theoretical aspect of the direct phase modulation scheme has also been studied, verifying its favorable features in practical usage.2626. R. Shakhovoy, M. Puplauskis, V. Sharoglazova, A. Duplinskiy, V. Zavodilenko, A. Losev, and Y. Kurochkin, “Direct phase modulation via optical injection: Theoretical study,” Opt. Express 29, 9574 (2021); arXiv:2011.09263. https://doi.org/10.1364/oe.413095 While this scheme allows phase information to be directly encoded, it cannot be used to control the intensity of pulses for decoy state generation. Since a direct intensity modulation scheme is still missing, the use of bulk intensity modulators has been unavoidable.

In this work, we present a novel approach that can directly generate intensity and phase modulated optical pulses. Our scheme only requires two laser diodes and a passive asymmetric Mach–Zehnder interferometer (AMZI). Such a pulse source can generate all the encoding states required for decoy-state QKD, thereby eliminating the need for external modulators and opening a new route for the development of compact, cost-effective, and high-performance QKD systems.

DIRECT GENERATION OF ENCODING STATES

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ChooseTop of pageABSTRACTINTRODUCTIONDIRECT GENERATION OF ENCO... <<RESULTSDISCUSSIONREFERENCESOur scheme further extends direct phase modulation techniques2323. Z. L. Yuan, B. Fröhlich, M. Lucamarini, G. L. Roberts, J. F. Dynes, and A. J. Shields, “Directly phase-modulated light source,” Phys. Rev. X 6, 031044 (2016); arXiv:1605.04594. https://doi.org/10.1103/physrevx.6.031044 by generating and interfering with three intermediate pulses with carefully crafted relative phases in order to accurately control both the relative phase and intensity of the final output pulses. The experimental setup is shown in Fig. 1(a). The two laser diodes (referred to as “master” and “slave” following standard nomenclature) are connected in an OIL configuration. The master laser is gain-switched such that the laser produces long pulses (i.e., with a high duty cycle) when it is driven above the threshold and switched off between the pulses. As a result, each pulse is produced with a random phase as they are seeded by spontaneous emission photons.2727. Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014); arXiv:1501.01900. https://doi.org/10.1103/physrevapplied.2.064006 Subsequently, these pulses are injected through a circulator into the slave laser, which is gain-switched to produce three short pulses within each long master pulse [see Figs. 1(b-i) and 1(b-ii)]. Because the stimulated emission of the slave laser is seeded by the injected photons, the three slave pulses inherit the phase of the corresponding injected master pulse. The relative phases between these pulses are well defined as they are seeded by the same master pulse; however, collectively, their global phase is random.In order to prepare the slave pulses for interference to achieve the desired outputs, their relative phases need to be carefully controlled. This is achieved by manipulating the phase evolution of the master pulse , which can be realized by introducing an amplitude perturbation to the electrical driving signal of the master laser2323. Z. L. Yuan, B. Fröhlich, M. Lucamarini, G. L. Roberts, J. F. Dynes, and A. J. Shields, “Directly phase-modulated light source,” Phys. Rev. X 6, 031044 (2016); arXiv:1605.04594. https://doi.org/10.1103/physrevx.6.031044 [Fig. 1(b-i)]. This electrical modulation, with a temporal width of Δtm, changes the carrier density in the laser cavity, which in turn alters the cavity refractive index and causes a temporary optical frequency shift of Δν, thus the photons produced after the modulation experience a phase shift of Δϕ = 2πΔνΔtm.2323. Z. L. Yuan, B. Fröhlich, M. Lucamarini, G. L. Roberts, J. F. Dynes, and A. J. Shields, “Directly phase-modulated light source,” Phys. Rev. X 6, 031044 (2016); arXiv:1605.04594. https://doi.org/10.1103/physrevx.6.031044 By locating the modulation in the interval between the onsets of two slave pulses, this phase difference can be transferred to the slave pulses. As shown in Fig. 1(b), the relative phases between the three slave pulses, ϕ12 and ϕ23, can be implemented independently by adding two small electrical perturbations to the master laser.The prepared slave pulses then pass through an AMZI with one of its arms having a delay line that matches the temporal separation of the slave pulses, resulting in interferences between consecutive slave pulses. As shown in Fig. 1(b-iv), at the outputs of the AMZI, three pulses are formed within a single logical bit: two of them with their intensities and the relative phase completely determined by ϕ12 and ϕ23, whereas the third pulse has a random intensity due to the interference of two slave pulses originating from different master pulses with random phase relation (indicated in gray shading). As a result, the first two pulses could be used to represent the early and late bins for time-bin encoding.To express the relative phase between the early and late time bins and their intensities in terms of ϕ12 and ϕ23, we consider the pulses generated by the slave laser as three coherent states α1, α2, and α3, with amplitude A,α1=Aei(ωt+ϕ1),α2=Aei(ωt+ϕ1+ϕ12),α3=Aei(ωt+ϕ1+ϕ12+ϕ23),(1)where the phase of the first coherent state, ϕ1, is uniformly distributed over [0, 2π).In the AMZI, the interference between α1 and α2 (α2 and α3) gives rise to the early (late) time bin αE (αL), which can be expressed asαE=A2eiωt+ϕ11+eiϕ12,αL=A2eiωt+ϕ1+ϕ121+eiϕ23,(2)and their corresponding intensities and phases are given byrE=Acosϕ122,ϕE=ωt+ϕ1+ϕ122,rL=Acosϕ232,ϕL=ωt+ϕ1+ϕ12+ϕ232,(3)respectively. The relative phase between the early and late time bins ϕEL and their intensities are simulated based on Eq. (3) and shown in Fig. 2. This scheme could, therefore, be applied to time-bin based BB84 decoy-state QKD with Z and Y basis encoding. For Z-basis encoding, a pulse is located in either the early time bin (representing bit 0) or the late time bin (representing bit 1). To encode bit 0, ϕ12 is set to 0 to produce a pulse with maximum intensity in the early time bin, and ϕ23 is set to π to suppress any light in the late time bin. Similarly, bit 1 can be encoded by choosing ϕ12 = π and ϕ23 = 0.A decoy state in the Z basis can be generated in a similar way as described earlier. Instead of using zero relative phase , which results in a pulse with maximum intensity, a decoy state with a lower intensity can be generated by choosing a relative phase close to π, according to Fig. 2(a). For example, a decoy bit-0 state with an intensity of 0.1 can be generated by choosing ϕ12 = 0.9π and ϕ23 = π. Therefore, the flexibility to adjust the intensity level of the decoy state is enabled simply by implementing the appropriate relative phases, which itself is controlled by simple modulation of the electrical drive signal applied to the master laser.In the Y-basis, a single bit comprises both the early and late time bins with a relative phase of π/2 (bit 0) or 3π/2 (bit 1). Each time bin has half the intensity of the signal state in the Z basis. From Eq. (2), the relative phase between the early and late time bins is simply ϕEL = (ϕ12 + ϕ23)/2. Since the intensities of the early and late time bins must be equal, it is necessary that ϕ12 = ϕ23. As a result, to encode bit 0 with ϕEL = π/2, ϕ12 = ϕ23 = π/2. Similarly, to encode bit 1 with ϕEL = 3π/2, ϕ12 = ϕ23 = 3π/2. A summary of the phase settings for various potential encoding states, including an example of a decoy state, is illustrated in Fig. 3.

RESULTS

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ChooseTop of pageABSTRACTINTRODUCTIONDIRECT GENERATION OF ENCO...RESULTS <<DISCUSSIONREFERENCESA key element to implement our proposed scheme is precise control of the relative phases between slave laser pulses, ϕ12 and ϕ23, as they completely determine the final output states. This can be achieved by carefully adjusting the amplitude of the modulation applied to the master laser’s electrical signal. The master laser is operated at 667 MHz and the slave laser at 2 GHz so that every master pulse is long enough to seed three slave pulses. A modulation with a fixed temporal width of 150 ps is applied to the electrical signal between the onsets of two slave pulses, and its voltage amplitude is varied. The amplitude of the pulse at the output of the AMZI is measured as a function of modulation voltage, as shown in Fig. 4(a), confirming the ability to continuously tune the transmitter output pulse intensity. Figure 4(b) shows that the half-wave voltage, Vπ is around 0.8 V, which is significantly lower than that of common LiNbO3 phase modulators. The minor deviation from the theoretical values can be attributed to the imperfections in experimental equipment (e.g., phase noise in lasers).To demonstrate the potential of our scheme for QKD, we implement the BB84 protocol with two decoy states.2828. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005); arXiv:0503005 [quant-ph]. https://doi.org/10.1103/physreva.72.012326 The experimental setup is shown in Fig. 5. The outputs of Alice (the transmitter) (Fig. 6) consist of a random mixture of the signal states with intensity μ prepared in the Z and Y bases and the decoy states with intensities ν and ω prepared in the Z basis, where μ > ν > ω. The intensity levels of the decoy states can be accurately adjusted to maximize the key rate performance. A variable optical attenuator is placed before the output of Alice in order to attenuate the signals to the desired mean photon number level. Bob (the receiver) adopts a passive basis of choice using a beamsplitter. In the Z basis, the photons are directly detected by a single-photon detector (SPD), where the bit value can be retrieved from their arrival time using a time-tagger. In the Y basis, the photons pass through an AMZI , which results in three interfering pulses within a bit. Only the first interfering pulse is measured, as it originated from the interference between the early and late time bins. The phase basis of the AMZI is adjusted such that bits 0 and 1 correspond to the detections in different detectors. The other two interfering pulses involve the interference of photons with no deterministic phase difference, and they are not processed to be used for key generation (similar to the traditional processing scheme for detecting phase-encoded time bins using an AMZI at Bob2323. Z. L. Yuan, B. Fröhlich, M. Lucamarini, G. L. Roberts, J. F. Dynes, and A. J. Shields, “Directly phase-modulated light source,” Phys. Rev. X 6, 031044 (2016); arXiv:1605.04594. https://doi.org/10.1103/physrevx.6.031044). The very slight variation in pulse heights in Fig. 6 is related to the finite bandwidth of real-world high-speed components. This has been observed in other QKD transmitter designs too, but not related to our new approach introduced here. The study of such real-world encoding imperfections is a topic in itself, and various solutions have been proposed, including variations to the security proofs and post-processing.29,3029. X. Sixto, V. Zapatero, and M. Curty, “Security of decoy-state quantum key distribution with correlated intensity fluctuations,” Phys. Rev. Appl. 18, 044069 (2022). https://doi.org/10.1103/physrevapplied.18.04406930. K.-i. Yoshino, M. Fujiwara, K. Nakata, T. Sumiya, T. Sasaki, M. Takeoka, M. Sasaki, A. Tajima, M. Koashi, and A. Tomita, “Quantum key distribution with an efficient countermeasure against correlated intensity fluctuations in optical pulses,” Npj Quantum Inf. 4, 8 (2018). https://doi.org/10.1038/s41534-017-0057-8In our proof-of-principle QKD experiment, we implement a standard, asymptotic, decoy-state BB84 analysis,2828. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005); arXiv:0503005 [quant-ph]. https://doi.org/10.1103/physreva.72.012326 which does not explicitly consider the presence of the extra pulses inherent to our modulation scheme. A full security proof is beyond the scope of this work, but we provide some arguments as to why this should not represent an issue in the discussion section. The quantum bit error rate (QBER) is measured and used to compute the secure key rate (SKR), as shown in Fig. 7. Positive key rates can extend up to a channel loss of 48 dB (equivalent to 240 km of standard fiber with an attenuation of 0.2 dB/km). A secure key rate of 2.21 Mbps is measured at 15 dB (75 km), demonstrating the suitability of our system for metro-scale QKD networks. The QBER can be maintained at a base level of 3.3% before the detector noise becomes comparable to the signal counts at high channel losses. This is comparable to the performance achieved by QKD systems using conventional phase and intensity modulators.16,3116. Z. Yuan, A. Murakami, M. Kujiraoka, M. Lucamarini, Y. Tanizawa, H. Sato, A. J. Shields, A. Plews, R. Takahashi, K. Doi, W. Tam, A. W. Sharpe, A. R. Dixon, E. Lavelle, and J. F. Dynes, “10-Mb/s quantum key distribution,” J. Lightwave Technol. 36, 3427 (2018). https://doi.org/10.1109/jlt.2018.284313631. M. Lucamarini, K. A. Patel, J. F. Dynes, B. Fröhlich, A. W. Sharpe, A. R. Dixon, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Efficient decoy-state quantum key distribution with quantified security,” Opt. Express 21, 024550 (2013); arXiv:1302.4139. https://doi.org/10.1364/oe.21.024550

DISCUSSION

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ChooseTop of pageABSTRACTINTRODUCTIONDIRECT GENERATION OF ENCO...RESULTSDISCUSSION <<REFERENCESWe have demonstrated a simple scheme to generate phase- and intensity-tunable pulses at GHz clock speeds, which can implement the BB84 protocol without the need for any phase or intensity modulators. As shown earlier, the performance of QKD based on our scheme approaches that of conventional LiNbO3 modulators. We attribute this feature to the adoption of OIL , which significantly reduces the timing jitter and the frequency chirp in the output pulse27,3227. Z. L. Yuan, M. Lucamarini, J. F. Dynes, B. Fröhlich, M. B. Ward, and A. J. Shields, “Interference of short optical pulses from independent gain-switched laser diodes for quantum secure communications,” Phys. Rev. Appl. 2, 064006 (2014); arXiv:1501.01900. https://doi.org/10.1103/physrevapplied.2.06400632. E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15, 618 (2009). https://doi.org/10.1109/jstqe.2009.2014779 while maintaining a coherent phase transfer from the master to the slave laser.The presence of additional pulses in this modulation method means it is not completely trivial to apply the security proof for a standard scheme.2828. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005); arXiv:0503005 [quant-ph]. https://doi.org/10.1103/physreva.72.012326 The concern would be that Eve could somehow break security by attacking these extra pulses. However, this is unlikely to be true, as the state in these extra time bins is essentially obfuscated by the phase randomization procedure. Additionally, well known uncertainty relations between phase and photon number further constrain Eve’s ability to extract relevant information. In the Appendix, we describe these arguments in more detail and provide a sketch for how a fully general security proof could be carried out.Compared to the common approach, where dedicated phase and intensity modulators are required in the transmitter to generate the encoding states and the decoy states, our scheme allows all such states to be generated directly from two lasers and an AMZI by exploiting direct phase modulation technique2323. Z. L. Yuan, B. Fröhlich, M. Lucamarini, G. L. Roberts, J. F. Dynes, and A. J. Shields, “Directly phase-modulated light source,” Phys. Rev. X 6, 031044 (2016); arXiv:1605.04594. https://doi.org/10.1103/physrevx.6.031044 and coherent interference. In this way, we not only remove the modulators but also the high-speed RF signals and power supplies necessary to drive the modulators, thereby reducing the complexity and cost of a QKD system significantly.As our transmitter only has two active components (i.e., the lasers), the power consumption is expected to be low. Together with the low Vπ, the design is well-suited for on-chip integration,99. T. K. Paraïso, I. De Marco, T. Roger, D. G. Marangon, J. F. Dynes, M. Lucamarini, Z. Yuan, and A. J. Shields, “A modulator-free quantum key distribution transmitter chip,” Npj Quantum Inf. 5, 42 (2019). https://doi.org/10.1038/s41534-019-0158-7 offering a route to compact, low cost and power efficient quantum transmitters. Beyond QKD, this simple approach to generating intensity- and phase-variable pulses could find other applications in classical optical communications, where the ability to precisely manipulate intensity and phase enables novel high-density encoding schemes for pushing communication bit rates.

In conclusion, we have demonstrated a scheme to directly generate phase- and intensity-tunable pulses at high speed using two gain-switching lasers in an OIL configuration with an AMZI. By applying appropriate electrical driving signals to the lasers, the intensity and phase of the pulses can be simply varied. The design is shown to have strong potential as a QKD transmitter for decoy-state QKD, where all required encoding and decoy states for a BB84 protocol can be directly generated without any bulk modulators. Therefore, our scheme offers a new possibility to perform QKD using compact, low-cost, yet high-performance devices, advancing the development of quantum communications toward larger scale deployments.