Ground-Satellite QKD Through Free Space. Steven Taylor

Transcription

1 Ground-Satellite QKD Through Free Space Steven Taylor Quantum Computation and Quantum Information, Spring 2014

2 Introduction: In this paper I will provide a brief introduction on what Quantum Key Distribution (QKD) is and how it works, then talk about experiments that are currently being performed to try and make the process of QKD and quantum information transfer a more viable real world idea. I'll start with explaining the basics of QKD followed by some of the problems with it. Afterworlds, I'll explain one of the possible solution of using Ground-Satellite connections over free space. To add breadth to this I'll summarize a few experiments on the subject of QKD over free space Ground-Satellite connections with some of their experimental results. What is Quantum Key Distribution and Cryptography? Quantum key distribution is the quantum computing form of classical cryptography. The basic idea of cryptography is sending sensitive information across open public channels. This is done by encrypting the information on the senders end and decrypting the same information on the receivers end. The sender, usually denoted as Alice, uses a key to encrypt her data, then the receiver, usually denoted as Bob, uses the same key to decrypt the information sent by Alice. This encryption key also needs to be sent to Bob in some way. Should the data be intercepted on the way from Alice to Bob by an eavesdropper, usually denoted as Eve, the information should be readable only as a bunch of binary digits with no meaning. [2] Cryptography works in two general ways. The first deemed Computational Security relies on Eve having limited computational power. This makes it so a certain mathematical problem takes a very long time to solve. One specific example of this is RSA security, which uses the difficulty to factorize a very large number into it's prime number counterparts. [2] This is the most popular current approach to cryptography, but is now in jeopardy due to strong research in quantum computers as well as more powerful computers being more readily available. Instead of where classical computers taking

3 exponentially longer to factorize larger and larger bit numbers, quantum computers scale as a polynomial with increasing bit numbers, thus new ideas will need to be implemented in the future. [2] The second general cryptographic method is called Information-Theoretic Security. This method doesn't care about how much computing power Eve has. Instead it uses a One-Time Pad, which is combined bit by bit with a random binary key, where the key is only used once. If used more than once, intercepting the two different cryptic messages and performing an XOR operation between the two can yield the unencrypted versions of both. This key must be the same size as the data being sent and both Alice and Bob need to know it. Without the key, Eve will never be able to decrypt the information. An XOR operation between the information and the key is performed to encrypt the information, and then an XOR operation using the same key will decrypt the same information. [2] Fig 1: Example of One-Time Pad Usage. [2] One problem with this method however is getting the key from Alice to Bob. Classically a trusted delivery person was one possible way to achieve this, but its slow and still leaves an opening for an eavesdropper to obtain the key, with no way for Bob to tell if the key was intercepted or not. Here's where QKD can solve both problems. It allows for faster distribution of the key as well as interception checking. QKD uses properties of individual photons to give Alice and Bob long secret keys, as long as each has a short authentication key available to sent up and authenticated channel. Information is encoded in the polarization state of the photons, while other degrees of freedom, such as phase and

4 wavelength, can not contain any information. [2] These photons are now qubits, which are now impossible for Eve to extract information from without altering them, in which the altered qubits would let Alice and Bob know that an eavesdropper was watching. Using QKD with the one-time pad approach gives us information-theoretic secure communication. This withstands eavesdropper attacks even with any technological advances, including quantum computers. [2] This idea is named BB84 protocol, after Charles Bennett and Gilles Brassard proposed it in BB84 uses 4 states that form two pairs, such as horizontal( H>) and vertical( V>), as well as +45 degrees ( +>) and -45 degrees ( - >) where horizontal and -45 correspond to bit 0, and vertical and +45 correspond to bit 1. [2] Alice randomly selects one of the four possibilities for each qubit that she sends to Bob, who randomly selects a pair to attempt to measure. As an example, Let us use the example of Alice sending state H) to make this concept more concrete: If Bob makes the correct measurement (i.e. the measurement that distinguishes between H) and V ), he will find the result H ). Hence, Alice and Bob have sent and received the same bit value: 0. However, if Bob choses the measurement that distinguishes between +) and ), he will randomly obtain one of these two possible outcomes, and hence randomly obtain the bit value 0 or 1. -[2] Fig 2: Cartoon of QKD Example. [2] After this has been done, everything else is performed under Classical Post-Processing. But what if Eve decided to intercept the photons from Alice before they reach Bob, and then tries to duplicate them to send to Bob without him knowing? The no-cloning theorem denies her from

5 accomplishing this. The no-cloning theorem basically says that it is impossible to make a perfect duplicate photon in an unknown state. Bob would see errors in bits that otherwise would be correlated, thus telling him that Eve was looking in. [2] The classical post-processing consists of 4 parts. First they perform key sifting, where Bob lets Alice know which photons he detected and which pair he type he measured, but not his result. Keeping only the bits detected, they now have a sifted key. Hopefully the quantum bit error rate (QBER), errors caused by the communication infrastructure, is small. Also, Eve would have induced errors in the sifted key. [2] Error correction is next step. Alice sends more information so he can make an error-corrected key identical to Alice's, as well as find the QBER. Thus there is some back and forth between Alice and Bob, but new emerging ideas are finding ways to improve this. They then estimate the amount of information that Eve may have obtained. They measure the error rate induced into the sifted key, and assume that any errors were due to Eve. [2] Most QKD is done with faint laser pulses which is practical but susceptible to photon number splitting (PNS) attacks, which uses the fact that the pulses sometimes contain more than one photon. To combat this decoy states are added, which are qubits in pulses with different mean photon number. This allows for determining what Eve obtained from a PNS attack. [3] Implementing the BB84 protocol with decoy states requires that the output photons have at least two levels of average photon number. In the simplest case, this entails a signal state with average photon number μ and a decoy state with average photon number ν. For both levels, the modulator should output one of four polarization states (horizontal, vertical, diagonal, or anti-diagonal), chosen randomly. -[3] They implemented this using a 532nm laser with sum-frequency generation (SFG) using 810nm pulsed light, as seen in figure 3.

6 Fig 3: SFG Example. [3] Eve will also gain additional information while the error-correction procedure is taking place, Also, some loss due to imperfections in measurement devices has to be taken into account. Combining all of these, the length of the secret key after errors is unity minus the loss due to imperfections, the loss due to extra info gained by Eve during error-correction, and the loss due to the initial information Eve gained. [2] Lastly authentication has to occur between Alice and Bob, to make sure Eve wasn't playing a middle-man role, acting as Bob with Alice, and as Alice with Bob. This authentication can be done over classical channels, where a short key initially is sent. [2] Problems With Ground Type (Fiber) QKD: QKD can and has been implemented in fiber based ground networks. Great progress has been made in making QKD a feasible way to send information securely. There are some limitations however to using fiber connections. A Trojan-Horse type attack can use the fact that optical instruments reflect some incident light. This reflected light could be detected by Eve to find information about the qubit state. [2] This attack is easier to perform on a ground based fiber network, compared to a free space type network. Counter measures such as light input monitoring done by Alice and Bob can help, but the problem still exists.

7 Another problem is the distance that we can currently send QKD encrypted information over. Currently the maximum distance is roughly 100km. [1] The reason for this is that the qubits send over a fiber network compared to free space networks have a higher chance of interacting with the medium, which would cause channel losses. Due to the high channel loss experienced, the secret key rates are typically limited to 10 bps. On the other hand, QKD systems have been demonstrated to deliver secret key rates up to 1 Mbps. Obviously, the distances are reduced compared to those mentioned previously; the current maximum is 50 km. It is likely that these two benchmarks will not be improved significantly over the next few years, the only exception possibly being QKD over a free-space link between a ground station and a (very distant) satellite. -[2] Using Ground-Satellite Free Space Connections: Ground-Satellite free space connections will have to play a role in the near future for QKD. Due to low atmospheric interference compared to fiber based networks, qubit can be sent much more reliably over the long distances needed for secure communications around the globe. Currently there have been proof of concept experiments that used stationary sites, but to achieve the global scale, moving satellites will be needed. Recently, an experiment over a distance of 144 km has been performed successfully by Zeilinger s group, demonstrating that long-distance atmospheric turbulence has little effect on quantum communication. -[1] Quantum communication using satellites must deal with a few different issues. First, the satellite may have rapid angular motion with respect to ground stations. Second, the satellite will have some unwanted random motion. Lastly, turbulence in the atmosphere will have to be overcome under a condition of a high-loss regime. [1] Satellites in orbit average around a 600 km altitude, with angular velocity of about 20 mrad/s. All of the above issues need to be tested to optimize the delivery of qubits from a ground station to the satellite.

8 Current Experiments and Results: A few ideas on how to simulate QKD through a satellite to verify the requirements listed above have been proposed. On example is to use a plane, but this lacks the necessary amount of angular velocity that a true satellite in orbit would have. Jian-Yu Wang's group, based in China has implemented a few unique ideas to recreate the conditions of a real satellite. Using a turntable and hot air balloon the conditions of a satellite in orbit can be met. [1] Fig 4: Schematic of Experiment. [1] Their group designed had to design their own telescope and electronics so the receiver and transmitter were lightweight and portable to affix to a hot air balloon. Using 4 laser diodes in the transmitter, emitting 1ns optical pulses at 850 nm wavelength, they impinged the light on a beam splitter. They then then used irises to further the spatial filtering and finally checked that there was no difference in the detection of the light from the different lasers by checking the output with a collimator. [1]

9 To make the 4 possible qubit states for the BB84 protocol they then had two polarizing beam splitters and a half-wave plate. They used random physical noise to control which of the four qubits is made. To attenuate the average photon number per pulse to the required experimental level an attenuator was also used. They used a small reflecting telescope of aperture 200 mm, focal length 1250 mm, and 10x magnification. [1] Because of the random motion of the air balloon, tracking implements had to also be included to keep the transmitter and receiver in connection. A complementary metal-oxide semiconductor(cmos) and fast steering mirror (FSM) were used to implement the tracking. The coarse tracking CMOS was mounted on top of the telescope tube. [1] The receiver consisted of a telescope with aperture 300 mm, focal length 1500 mm, 12x magnification, and also consists of a similar tracking system. [1] Fig 5: A) Receiver and B) Transmitter The tracking light collected by the receiver contains a 532 nm beacon light, and 850 nm signal and decoy light. The tracking system uses the 532 nm light with the course tracking CMOS system. The telescope also receives 671 nm light which then gets sent to the tracking system for the fine tracking application. The research team then started testing their measurement apparatuses first with just a moving platform, then incorporating the rotating turntable to simulate the angular velocity of low earth orbit satellites. They followed this with the final experiment with the receiver mounted in the hot air balloon to add the random motion that a true satellite has. [1]

10 The moving platform and turntable experiment took place in August The turntable applied a maximum angular velocity of 21 mrad/s with angular acceleration of 8.7 mrad/s 2, about the same that a satellite in orbit has. The background rate was about 800 hz, and the collection rate was about 5000 hz. This lead to a loss of 40 db, of which 19 db was due to attenuation due to geometry, 6 db is atmospheric loss, 13 db due to the optical systems, and 1-5 db from an efficiency decrease from the moving channel link. [1] The floating platform, the hot air balloon, incorporated the random motion, which was the first time QKD has been perform with random motion as a variable. This part of the experiment took place in September The distance between the transmitter and receiver was approximately 20 km, and the main purpose of the experiment was to test the tracking system performance. The estimated random motion of the balloon consisted of and angular velocity of 10.5 mrad/s, and angular acceleration of 1.7 mrad/s 2. The fine tracking gave and accuracy of better than 5 μrad, which exceeded the requirement for 10 μrad that a true satellite would need. They also tested how quickly reconnection could happen after dramatic motion. Even with no line of sight, the system could relink in about 5 seconds. [1] Using these experiments the research group successfully was able to extract secure keys following the BB84 protocol. Fig 6: Tracking Error of System with Turntable. [1]

11 Fig 7: Tracking Error of System with Random Movement due to Balloon Conclusion: QKD through free space Ground-Satellite connections I think will be paramount to expanding quantum key cryptography to the masses. Even though Ground-Fiber connections have some flaws, these too will play a large role in the near future. In a world with faster and more powerful computers every year, as well as sensitive data being used every day, such as credit card numbers, we have to find a new more secure way to send data, before the technology out-paces the security.

12 Works Cited [1] J.Y. Wang, et al., Direct and Full-Scale Experimental Verifications Towards Ground-Satellite Quantum Key Distribution, Nature Photonics 7, (2013) [2] P. Chan, et al., Quantum Key Distribution, Femtosecond-Scale Optics, 2011 [3] Z. Yan, et al., Novell High-Speed Polarization Source for Decoy-State BB84 Quantum Key Distribution Over Free Space and Satellite Links, Journal of Lightwave Technology, Vol. 31, Issue 9, pp (2013)