Development of Quantum Technologies at SK Telecom
TAEHYUN KIM AND SEAN KWAK
QUANTUM TECH. LAB, SK TELECOM
Since Feynman first proposed the idea of simulating a quantum system using another quantum system in 1981 , substantial progress has been made to control the individual quantum systems; now, many technology companies have become involved in quantum technology. SK Telecom has been developing various quantum technologies for the last five years, and an overview of the progress in the development of a quantum key distribution system, quantum random number generator chips, and a quantum repeater will be given in this article.
The strange phenomena of quantum physics, such as the impossibility of cloning quantum states  or the "spooky action at a distance"  encouraged many physicists to come up with various applications of such unusual behavior of quantum particles toward the resolution of many obstacles in the current framework of information technology. Unfortunately, many of those ideas remain far from implementation with current technologies, but some ideas are now within the reach using existing technology.
The Quantum Tech. Lab at SK telecom (SKT) was formed in October of 2011 to identify potential opportunities and to develop products in the quantum information processing area. Our current interests lie in three different topics, including the commercialization of a quantum key distribution (QKD) system for deployment in commercial networks, the miniaturization of quantum random number generators at the chip scale, and the development of a quantum repeater.
In this article, we will first overview the development of the quantum key distribution system, and the deployment status of our system for field testing. Then we will describe the development status of the quantum random number generator chip, and finally we will provide an overview and present recent progress in the development of a quantum repeater based on ion trap technology.
QUANTUM KEY DISTRIBUTION SYSTEM
The goal of quantum key distribution is to securely generate identical random bit streams (secret keys) at only two remote locations and if there is any attempt to eavesdrop regarding the distribution of the secret keys, the quantum weirdness of the QKD system enables us to detect it. Once the secure key generation is completed, actual data is encrypted and decrypted using these freshly generated keys, and the transmission of the encrypted data still depends on the existing digital communication networks. Therefore, the complete quantum cryptography system is generally composed of two parts, one for key generation (QKD server) and the other for data encryption and decryption (encryptor) as shown in Fig. 1.
Fig. 1: Schematic of a quantum cryptography system composed of encryptors and QKD servers.
The original QKD protocol suggested by Bennett and Brassard (BB84)  relies on the use of single photons to avoid a photon-number-splitting (PNS) attack  by means of a no-cloning theorem . However, usage of a decoy state  can still prevent PNS attack, and therefore, like other commercial QKD implementations, our QKD system also uses a weak coherent state instead of a single-photon state.
Another difference of our system from the original BB84 protocol is that our quantum bit (qubit) is encoded in the relative phase between two wave packets split by an unbalanced Michelson interferometer as shown in Fig. 2 . For each split wave packet pair, Alice (sender) encodes a relative phase chosen randomly out of four possible values (0, π/2, π, 3π/2), and Bob (receiver) applies an additional relative phase chosen randomly between two values (0, π/2). Due to the unbalanced path lengths, two time-multiplexed wave packets can interfere with each other only when the fast wave packet is reflected by a Faraday rotator mirror (FRM) along the long path on Bob's side and the slow wave packet is reflected by a FRM along the short path. The probability of such a coincidence occurring is 50 %, and if the overall relative phase is multiples of π at that coincidence event, then the output from Bob's Michelson interferometer will be in a definite state and Bob's detectors can generate a bit stream which is strongly correlated with Alice's shared bits. However, if the overall relative phase is odd multiples of π/2, the output will be in a superposition state, and a completely uncorrelated detection event will be measured by Bob; therefore, the measurement will be discarded.
Fig. 2: Schematic of time-multiplexed phase-modulation QKD system . OI: optical interferometer, OPM: optical phase modulator, SPD: single photon detector.
Once the raw shared bits are generated, the first step is to calculate the quantum bit error rate (QBER) by comparing some portion of the raw bits. If QBER is above a pre-defined threshold, we conclude that there are some eavesdropping attempts, and discard all the generated shared bits. When QBER is below the threshold, a modified Winnow protocol is used to correct any errors among the remaining bits that were not used during QBER estimation.
Even though small QBER below threshold generally comes from imperfect physical components including fiber noise from the environment rather than eavesdropping, we take the situation conservatively and assume that all the errors came from partial information leakage during an attack. We also estimate the inevitable amount of information exposure during error correction communication. The output of error correction stage goes through privacy amplification  stage which can remove all those potential information leakages.
We use Toeplitz matrix, which distills shorter bit stream from the longer output of error correction, and finally we authenticate each other to make sure that the shared bits are generated by legitimate users.
The generated secure keys are supplied to the corresponding encryptors as shown in Fig. 1, and plain texts can be encrypted using various algorithms including AES256-GCM and ARIA256-GCM at a speed of 40 Gbps per encryptor card (4 channels per card and 10 Gbps per channel).
Another feature of our system is the single photon detector module. We developed proprietary avalanche photodiodes for a QKD system in collaboration with a local company, which can operate at -30 °C with detection efficiency of a minimum 10 % at 1550 nm. The measured dark count probability is less than 6 × 10-6 per gate signal and the after-pulse probability is less than 2 % with 1 μs dead time when it is operating at 125 MHz repetition rate.
Fig. 3 shows a picture of our integrated QKD system, and we consistently obtained final key generation rate of more than 10 kbps at 50 km distance.
Fig. 3: Typical configuration of QKD system using an advanced telecommunications computing architecture (ATCA) form factor. There are three 40 Gbps encryptor cards to achieve total 120 Gbps encryption speed.
To carry out a field test of our systems, we deployed our system in various real networks. The Korean government and SKT set up a testbed to evaluate QKD systems between remote sites and the SKT R&D center in the Bundang area and also inside local network of Korea Institute of Science and Technology Information (KISTI) located at Daejeon as shown in Fig. 4.
Fig. 4: Current status of QKD testbed in South Korea. Left schematic shows the network topology of the testbed. Right maps show the actual locations of the test nodes in South Korea.
Fig. 5 shows another type of field test which exchanges real data over a QKD network in the metropolitan area of Seoul in South Korea.
Fig. 5: One of the Wi-Fi access points (AP) at SKT R&D center in Bundang area is connected to the internet backbone of SKT through a QKD network over a 35km distance.
Finally, we are also operating a QKD system on one of the redundant links in a 4G Long Term Evolution (LTE) commercial network connecting two cities in South Korea from June of 2016 as shown in Fig. 6.
Fig. 6: One of the LTE links in the SK telecom network is being protected by a QKD system. This link is currently delivering real-time traffic including voice and data. The names of cities cannot be released at the time of this writing.
QUANTUM RANDOM NUMBER GENERATOR
One of the well-known properties of quantum mechanics is that it is impossible to know which eigenstate will be measured when a quantum system is in a superposition state. This simple property found a very important application in modern security systems, which heavily depends on random numbers. For example, Alice wants to authenticate Bob at a remote location without explicitly exchanging the shared password over the network. Alice can check whether Bob has the same password as hers by the following protocol (also refer to Fig. 7):
1. Alice encrypts a random number with the shared password and sends the encrypted message.
2. Bob decrypts the encrypted message using the mutually shared password.
3. Bob calculates a new value based on the recovered random number.
4. Bob sends back this new value after encrypted with the same password.
5. Alice decrypts the return message and verify Bob has the same password as well.
Fig. 7: An example of challenge-response authentication protocol.
Unfortunately, the above protocol becomes vulnerable when the random number is predictable. The eavesdropper has much higher chance to find out the shared password once the random numbers and the corresponding encrypted messages are known, and historically there have been many attacks which exploited the lack of entropy in pseudo random number generators. Fortunately, this problem can be trivially solved by quantum mechanics. The simplest implementation we can think of is to split a single photon with 50:50 beam splitter and detect it with single photon detectors (SPD) . Even though it is conceptually simple, it may not be the best way to implement a practical quantum random number generator (QRNG) due to the necessity of SPD and limited generation speed. Therefore, various approaches have been suggested and different types of systems were implemented .
At SK telecom, we are developing affordable QRNG chips composed of light emitting diodes (LED) and complementary metal oxide semiconductor (CMOS) image sensors . The CMOS image sensor is illuminated by weak LED light, and the number of detected photons by each pixel follows the pattern of shot noise because when thermal light is multi-mode or the detector is slower than the coherence time, the photon statistics follows Poisson distribution rather than the Bose-Einstein distribution . Our QRNG chip utilizes this shot noise as a source of entropy.
Fig. 8: Prototype of QRNG chip. (a) Picture of evaluation board and the internal layout. (b) Internal structure of the prototype chip.
Fig. 8 shows the prototype of QRNG chip made in 2015; we obtained 7.9921 minimum entropy with a test unit size of 1 byte when tested with 1Gbit samples. We also ran a NIST SP800-22 test  on the same data with a sample size of 1 Mbit and with the number of queries of 1000, and we passed all the test items except occasional failures in the block frequency test or non-overlapping tests. Based on these results, we are developing a QRNG chip and we are planning to fabricate actual semiconductor devices by 2017. In particular, we expect that the form-factor of our QRNG chip will be less than 5mm × 5mm × 1.5mm so that it can be easily integrated into most computing and network devices in the future.
QUANTUM REPEATER BASED ON ION TRAP TECHNOLOGIES
The physical implementation of a QKD system generally suffers from the attenuation of light inside fibers, and therefore the operating distance of all the current commercial QKD systems is limited to around 100 km. Because superposition states cannot be simply measured and forwarded to the next node, we need quantum repeaters  based on quantum teleportation .
Assume that an arbitrary quantum state is stored in qubit 1 at Alice's node, and we want to regenerate the same quantum state at Bob's node as shown in Fig. 9. To teleport the quantum state, Alice and Bob first create an entangled state between qubit 2 at Alice's node and qubit 3 at Bob's node, and then Alice measures qubit 1 and qubit 2 together in so-called Bell bases. Then Alice transmits her measurement result to Bob over a classical communication channel, and Bob applies one of four possible unitary operations on qubit 3 corresponding to the received digital information. Then the final state in qubit 3 will be identical to qubit 1 up to the global phase .
Fig. 9: Illustration of quantum teleportation. The arbitrary quantum state stored in qubit 1 will be reproduced at qubit 3 at the end of the protocol.
The success of the above procedure requires two key components: deterministic generation of entangled states and deterministic Bell state measurement. Even though it is relatively easy to generate high-quality entangled photon pairs from spontaneous parametric down-conversion (SPDC)  (and consequently, many groups have already demonstrated quantum teleportation with post-processed photons), due to the probabilistic nature of photon-pair generation of the SPDC process and the fundamental limitation of Bell measurement schemes using only linear optics , it is difficult to implement practical quantum repeaters based solely on individual photons.
Trapped ion technology is one of the good candidates for the implementation of a quantum repeater because it is possible to generate entangled states with a herald and long coherence time  in an ultra-high vacuum (UHV) environment allows us to generate entangled pairs in advance and supply them when requested. We are using a single valence electron of an 171Yb+ ion to store quantum information in two hyperfine levels and designate | F=0, mF=0 > as |0 > and | F=1, mF=0 > as |1 >.
Fig. 10 shows how Moehring et al.  first generated entanglement between two remote ions trapped in separate chambers. They first initialized the quantum state of each ion to |0 > by optical pumping, and then excited them with a single pulse of a pico-second laser to generate a single photon emitted from each ion. The emitted photons (flying qubits) can have two different frequencies and the respective ions (stationary qubits) also will be in the corresponding hyperfine states as shown in Fig. 10, but until the qubit is measured, the entire quantum state remains in a superposition of possible combinations. In other words, the flying qubit and the stationary qubits from the same node are entangled. Two flying qubits from two remote chambers interfere at a 50:50 beam splitter, and when the two single photon detectors click simultaneously, two stationary qubits get entangled through entanglement swapping . Even though the success of the entire process is probabilistic, the coincidence heralds the creation of entanglement. Once the entangled qubit pair is created, we need to measure two qubits in the same chamber in Bell bases to implement quantum teleportation. Deterministic Bell measurement can be achieved by a combination of a Hadamard gate and a deterministic controlled-NOT (CNOT) gate which also had been demonstrated with high fidelity by Debnath et al .
Fig. 10: Entanglement generation between two remote trapped ions . At the end of operation, two emitted photonic qubits are destroyed through measurement, and only two ionic qubits are left entangled.
At SK telecom, we are also developing our system to generate entangled states with trapped ions and we will eventually try to implement quantum teleportation with the developed system. To trap atomic ions in a UHV chamber, traditional traps were generally assembled manually using macroscopic components, but to build a scalable quantum system, Kielpinski et al. proposed to use a two-dimensional trap with many microscopic control electrodes . Therefore, we developed a unique micro-fabrication process based on micro-electro-mechanical system (MEMS) technology in collaboration with a research group at Seoul National University . Fig. 11 shows a scanning electron microscope (SEM) image of the fabricated chip, and also the images of actual ions trapped on this chip.
Fig. 11: (a) SEM image of a micro-fabricated ion trap chip. (b) Four 174Yb+ ions trapped on the same chip. The image of the surface trap electrode structure was taken separately and overlaid for clarity. (c) More than 20 174Yb+ ions trapped on the same chip. Compared to (b), the image was magnified by a factor of 10.
There are a few parameters that characterize an ion trap, and it is important to compare the measurement of those parameters with the simulation. When the ions are cooled by Doppler cooling, the remaining motion of those ions can be decomposed into motions along three orthogonal principal axes. Due to the geometry of our linear trap, one of the principal axes is along the axis of the trap, and the other two axes are in radial directions. Along each principal axis, the curvature of the potential at the minimum point decides the trap frequency, and we can predict these frequencies from the simulation. We can also measure those secular frequencies by modulating the trapping potential. At resonant frequency, the amplitude of the secular motion increases and by monitoring the change of the photon scattering rate as we scan the modulating frequency, we can find the secular frequency as shown in Fig. 12 (a). Fig. 12 (b) shows the measured data of secular frequency as we vary the RF amplitude applied to RF electrodes, and the simulation result shows good agreement with the data.
Fig. 12: Measurement of the trap frequencies. (a) Change of fluorescence as we scan the modulation frequency of the potential when RF voltage is fixed at 240 V. (b) Plot of trap frequencies as we vary the RF voltage.
Fig. 13 shows a Rabi oscillation measurement result with a hyperfine qubit of a 171Yb+ ion trapped on our chip. After initialization of the qubit, we applied microwaves at resonant frequency with hyperfine splitting, and measured the qubit value by counting the emitted photons during the cycling transition between the excited state and |1 > state . Even though Fig. 13 (a) shows good agreement between the measured data and sinusoidal curve, visibility gradually decays in Fig. 13 (b) and the measured coherence time was less than 300 ms.
Fig. 13: Measurement of Rabi oscillation. (a) Measured population of |1 > as a function of duration of microwave exposure with different detuning. The only one free parameter used for curve fitting is Rabi frequency. (b) Fitting of Rabi frequency with long-term measurement (> 50 ms).
However, the intrinsic coherence time of the 171Yb+ hyperfine state was supposed to be more than several minutes [18,25], and it is important to have long coherence time in our entanglement generation scheme because we should retain the pre-generated entanglement until it is requested. Therefore, we also verified that the intrinsic coherence time of 171Yb+ is much longer than what we measured in Fig. 13 in the following experiment. Measurement of a long coherence time means that we should be able to measure the quantum state even after we wait for the corresponding amount of time, but generally this is not a trivial task because during the long waiting time, direct cooling methods such as Doppler cooling cannot be used and therefore the trapped ion gets heated over the time, especially in the case of a surface-electrode ion trap due to a phenomenon called anomalous heating . The relatively large depth of the ion trap and the rare collision from background gas in the UHV chamber prevents the ions from escaping from the trap, but the increased amplitude of the secular motion of the heated ion reduces the number of measured photons as shown with black circles and dashed lines in Fig. 14 and eventually increases the detection error. To minimize this problem and recover the original scattering rate, we included sympathetic cooling in our experiment.
Sympathetic cooling can be implemented in various ways, but generally the species of the cooling ion is chosen to be different from that of the qubit ion so that the cooling laser won't cause any excitation in the qubit ion due to large detuning . However, this requires additional sets of lasers, optics, and sometimes even a camera due to chromatic aberration of imaging optics . In our experiment, we used a Yb isotope ion so that we could use the same optics and most of the lasers while we still had some detuning from the qubit ion. Generally, the frequency difference between isotopes is on the order of several GHz, so if the cooling laser would reach the qubit ion at its saturation intensity during the long waiting time, the probability of exciting the qubit ion would be still very high. Therefore, a tightly focused cooling laser was used to minimize the crosstalk to the qubit ion . As a cooling isotope, we used a 170Yb+ isotope rather than the most abundant and popular 174Yb+ because it has the largest detuning from the relevant transition frequencies of 171Yb+ among stable isotopes with 0 nuclear spin for a simple cooling scheme. The red circles and solid line in Fig. 14 show that sympathetic cooling can minimize the reduction of the scattering rate of the qubit ion.
Fig. 14: Detected counts of emitted photons from the qubit ion as a function of waiting time. The counts are normalized with respect to the maximum detected count obtained without any waiting time. The black circles and dashed line show the emission without any cooling, and the red circles and solid line show the measurement with sympathetic cooling.
In addition to sympathetic cooling, we applied a dynamical decoupling method  to our qubit to cancel out decoherence caused by any slowly varying environment. Fig. 15 shows the result of the Ramsey interference measurement. To measure the Ramsey interference, we first initialize the qubit to | 0 >, and apply π/2-pulse to make (| 0 > + |1 >)/√2. Then we wait for some fixed time (T) during which we apply dynamical decoupling by periodically flipping the qubit (π-pulse). Finally, we apply π/2-pulse with different phases. If there is no decoherence, a plot of the population of |1 > state as a function of phase should make a perfect sinusoidal curve, but as T gets longer, the decoherence increases and the visibility of the sinusoidal curve decreases as shown in Fig. 15. Our preliminary measurement gave us more than 10 seconds of coherence time, and we are still working to improve our result.
Fig. 15: Visibility measurement of Ramsey interference after (a) T = 1 second and (b) T = 10 seconds, respectively.
Even though all the experimental results shown above were obtained by measuring the quantum state of individual ions, the long wavelength of microwave radiation prevents us from manipulating individual ions when there is more than one ion in the same trap. Therefore, to be able to control individual ions in the same trap, we need to use a focused laser like the one we used for sympathetic cooling. Because our qubit is stored between two hyperfine states (12.6 GHz), the corresponding energy difference is not compatible with any laser, but stimulated Raman transition is still possible with a laser . To generate lasers whose frequencies are separated by exact splitting of hyperfine states, we are using an optical frequency comb centered around 355nm. After splitting a mode-locked laser into two paths (A and B), we shift the frequency of path A so that one comb tooth from A path is separated from another comb tooth from B path by hyperfine splitting. By combining those two lasers at the ion location, we can induce a stimulated Raman transition. Fig. 16 shows our experimental result with our mode-locked laser. In our experiment, we could also resolve the sideband transitions, which is a key component for sideband cooling and two-qubit gate implementation.
Fig. 16: Experimental result of Raman transition with a mode-locked laser with (a) weak focus and (b) tight focus.
In terms of the generation of entangled states between two trapped ions, we are working to build a system shown in Fig. 10 by the next year. We are also developing two-qubit gate capability, which is a critical component for the Bell-state measurement. With the combination of all of these components, we are hoping to demonstrate quantum teleportation in the near future.
At SK Telecom, the first generation of QKD systems is already operating in a commercial network and is going through various stages of stress tests; we anticipate that the field test data will prove that our QKD system is built to commercial grade. We are also working to manufacture a small and affordable QRNG chip by next year so that it can be easily integrated into most computing and communication devices in the future. We are making progress in various areas of the development of a quantum repeater, especially with ion trap technologies. We are expecting to implement entanglement generation and two-qubit gates by next year, and in addition to quantum teleportation, most of the techniques developed along this path will also allow us to develop a small-scale quantum computer based on ion trap technologies in the near future.
Finally, we welcome new ideas and suggestions for the commercialization of quantum information applications.
Acknowledgements: This work was partly supported by the ICT R&D program of MSIP/IITP R0101-16-0060 (Development of key technologies for quantum cryptography network), R0190-16-2030 (Reliable crypto-system standards and core technology development for secure quantum key distribution network), and R0101-16-0068 (Development of quantum repeater technology for the application to communication systems).
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Taehyun Kim is a project leader at the Quantum Tech. Lab at SK Telecom. He holds both a BS degree in computer engineering and an MS degree in micro-electro-mechanical systems (MEMS) from Seoul National University. He was a full-time instructor at the Korea Air Force Academy for three years. After receiving his PhD in physics from the Massachusetts Institute of Technology in 2008, where he studied quantum information processing with entangled photons, he worked at Duke University as a postdoctoral associate to develop quantum technology based on trapped ions. He joined SK Telecom in 2011, where he continued the development of a quantum repeater. His research interests lie in the development of quantum repeaters and quantum computers based on an ion trap system and quantum information processing with an individual photon system.
Sean Kwak leads the entire Quantum Tech. Lab at SK Telecom (SKT), the largest South Korean telecom operator. He is also a member of the Korean government's Quantum Information and Communication Technology (QICT) Task Force. Since joining SKT in 1997, he has also managed the commercialization of SMS, PDSN (Packet Data Serving Node), and IMS (IP Multimedia Subsystem) at SK Telecom. He was responsible for CDMA core network development and represented SKT in 3GPP2 developing CDMA global standards. While working on solutions for packet core security, he became acquainted with quantum cryptography and led the founding of Quantum Tech. Lab in 2011. The lab has been developing QKD systems, quantum true random number generators as chips, and quantum repeaters and computers based on trapped ions. Sean holds a master's degree in electronics engineering from Sejong University.