17.1 Aunt Martha

After learning about the first quantum communication protocol, the BB84 protocol enabling secure key exchange, one might think that it is straightforward to set up the experiment. Yet, it took quite a few years, and in particular also the initiative of the inventers Bennett and Brassard, to start, together with Besette, Savail, and Smolin, the first experiment on Quantum Key Distribution (QKD). The first secure quantum key between Alice and Bob was established back in 1991 in laboratories of IBM Research Center at Yorktown Heights (Figure 17.1) (1). In this setup, called “Aunt Martha,” attenuated light pulses have been transmitted over 32 cm between the sender and the receiver unit. Based on the BB84 protocol, the authors demonstrated how Alice and Bob, indeed, can verify whether an eavesdropper disturbs the transmission or whether they can extract a secure key. The first experiment used a light‐emitting diode as the light source and fast Pockels cells to choose the polarization direction. In this first experiment, a key rate of a few hundred bits per second was achieved and a number of eavesdropping attacks simulated. Already there it was demonstrated how to correct residual bit errors and how to guarantee full security even in the presence of (experimental) noise.

This shining example became the model for numerous quantum cryptography systems developed world wide. This chapter gives an overview of developments, which lead to the first commercial systems, to secure communication in networks and first steps toward global key‐exchange via satellites (for a detailed review of QKD see also (2,3)). In Addition, it gives a brief introduction to experiments on other quantum communication protocols such as quantum dense coding and first demonstrations of quantum error correction.

17.2 Quantum Cryptography

The most important criteria for quantum cryptography are high key rates and long distances. Usually, one cannot optimize both simultaneously, and some compromises have to be made. No compromise, however, is acceptable on reliability and user friendliness. To make QKD a real application, it is thus necessary to develop new optics, quite different from the standard quantum optics setups. It also remains a challenge not to compromise the security of the systems when using practical devices in real‐world scenarios (4).

The distance between Alice and Bob is limited mainly by losses in the quantum channel and by the efficiency and noise of single‐ photon detectors. Loss or low efficiency reduces the number of detected photons and thus the number of bits in the raw key. Noise (dark counts and stray light) in Bob's detectors results in a noise floor from bit errors, which are indistinguishable from those caused by eavesdropping attacks. It can be corrected for, but only at the cost of raw key material. For low efficiency or high loss, this noise floor can easily reach the 11% level, where no secure key can be distilled anymore. Any attempts to amplify the single‐ photon signal have to fail as well, since, according to the no‐cloning theorem, any amplifier introduces the same noise as an eavesdropper would do. This would therefore ruin the remarkable advantages of quantum key distribution. Only the quantum repeater, intermediate quantum error correction and memory stages along the quantum channel, could enable truly long‐distance communication. Its basic components are being developed now. As it will take some time until we will use it, we have to rely on conventional means to transmit the quantum signals.

Two options for quantum channels are available, which determine the wavelength and consequently distinguish the complete systems. Photons can be distributed either using glass fiber connecting Alice and Bob, or with telescopes aligned mutually for optimal coupling. In the following, the two systems are compared as they are implemented for prototypes or already in commercial systems. Most systems under development rely on attenuated light pulses, as this is less expensive and enables high rate systems. Single‐ photon options and entanglement‐based systems are described thereafter.

Single photons can be generated by the emission of single quantum systems. Unfortunately, it is not always straightforward to select a single quantum system. Possible candidates are single atoms or ions trapped by electromagnetic fields. Such experiments required vacuum vessels, narrowband lasers and are thus not well suited for QKD. However, they are excellent for more demanding applications, such as linear optics quantum computation. Other possibilities are quantum dots or single, fluorescing defects in diamond (5). First demonstrations show the feasibility of such systems as well as their drawbacks. Quantum dots achieve high rates but need cryogenic cooling below 4 K, NV‐defects in diamond are simple and reliably used at room temperature but still lack high rate and have too wide emission spectrum. The future will bring new and better systems, but they will have to compete with attenuated pulse QKD based on improved protocols not requiring the strong attenuation and using significantly simpler and more economic systems.

17.2.1 Faint Pulse QKD

17.2.1.1 Fiber‐Based QKD

Glass fiber systems best use the standard telecom fibers. They are already available between the main communication centers or could be installed with reasonable effort. Standard telecom wavelengths are 1300 or 1550 nm, respectively, where dispersion or loss, respectively, reach a minimum. State preparation, manipulation, and analysis can be achieved with standard telecom components. The high standard of such components allows a relatively fast development time of the basic setup of such QKD systems.

Glass fiber is slightly birefringent. Over the long distances, this effect sums up. Care has to be taken, as this birefringence might vary, depending on the stress or temperature of the fiber. As a result, a well‐defined initial polarization fluctuates strongly at the receiver. In principle, one can try to compensate birefringence, but it is more advisable to define a new encoding for the qubit. The two‐state system in this case is defined by two possible times, where the photon can be detected (“time‐bin coding”). A (variable) beam splitter (Figure 17.2a) determines the relative size between the amplitudes, and a phase shifter in one of the arms behind the beam splitter enables to set any desired state. The two arms are recombined at a second beam splitter, and one of the outputs is coupled to the quantum channel. If the length of the two arms between the beam splitters differs by more than the coherence time of the light, no interference occurs at the second beam splitter, and the light exits at two time slots this unbalanced interferometer. Thanks to the short time difference, any external influences will affect both amplitudes equally, and fluctuations along the quantum channel thus do not degrade the quality of the quantum state. At Bob, an equivalent, unbalanced interferometer is used to split the incoming amplitudes again, and, after application of Bob's phase, allows to observe the interference depending on Alice's and Bob's phase with 50% efficiency. Accepting this reduction, one is thus able to observe interference over very large distances independent of possible phase fluctuations along the quantum channel.

Disadvantage of this wavelength regime is high noise and the relatively low efficiency of the single‐photon detectors available (germanium‐ or InGaAs‐avalanche diodes). Optimization of these detectors enabled to steadily increase the distance to more than 100 km over the last years (7). New superconducting single‐photon detectors provide high detection efficiency and very low noise, such that now the distance record could be extended to amazing 307 km (8). Secure communication over longer distances will require trusted nodes, relays, or the quantum repeater (9).

A very reliable and stable system was developed at the University of Geneva. The group of Nicolas Gisin and Hugo Zbinden found a clever extension of the basic principle, which significantly increased the stability and quality of the system (2). In addition to using time‐bin coding to reduce the influence of the fiber, they made Bob's receiver the source of the light pulses (Figure 17.2b). He first generates bright coherent pulses at two different times with a polarizing, unbalanced interferometer and sends them to Alice. She now can use the bright pulses to easily synchronize her actions consisting of the application of one out of four possible phase shifts, backreflection at a Faraday mirror, and attenuation to the single‐photon level. On the way back to Bob, the light undoes all rotations and, only then, Bob applies his phase shift. Under the assumption that all fluctuations occur on a much slower timescale as it takes the light to travel from Bob to Alice and back again, all disturbances cancel. Only the phase difference between Alice's and Bob's modulations stays and determines the result of the measurement. By using the polarizing interferometer together with Faraday mirror (rotates the polarization of the reflected light by ), this system does not suffer from the usual 50% reduction of time‐bin coding systems. From the measurement results, Alice and Bob can infer the mutual phase settings and obtain the key bits, which are now more or less immune to any disturbance.

With such a so‐called “plug & play”‐system, QKD was demonstrated between Geneva and Lausanne over a distance of 67 km at a rate of about 150 bit already in 1998. Even more remarkable, the glass fiber connecting Alice and Bob was a standard fiber of Swisscom. Sender and receiver modules were integrated in 19″‐racks and placed in buildings of Swisscom, which are by far not the air‐conditioned laboratories of standard quantum optics experiments. This very reliable system was the basis for the development of the first commercial QKD ‐system by the spin‐off company ID Quantique. Now, companies from different countries offer secure point‐to‐point connection integrable into standard communication networks.

The achievable key generation rate is proportional to the rate of signals sent by Alice. This rate, in turn, is limited by the rate the detectors can accept signals, typically depending on the dead time of the detectors. Novel modulation techniques (10) enabled detection rates up to GHz and made a new type of protocols possible. In these so‐called distributed‐phase‐reference QKD protocols either phase (11) or amplitude ( 8,12) relation between neighboring pulses sent at very high rates are used to secure the key exchange. The principle scheme of the latter method is shown in Figure 17.2c, where the logical encoding is done whether light is sent in the first or the second of two consecutive time slots and where an eavesdropper analyzing such signals is monitored using the decoy signals. Any attack would destroy the phase coherence of the decoy pulses, which is seen when their light is detected behind the unbalanced interferometer.

17.2.1.2 Free‐Space QKD

If direct line of sight is available, coupling sender and receiver with telescopes becomes possible. High transmission through air is achieved for wavelengths in the range from 780 to 850 nm. For this range, highly efficient, low‐noise, silicon‐avalanche photodiodes are available. All components, particularly the laser diodes, are low‐cost, standard products. Compared to costly polarization modulators, using four differently oriented laser diodes is more economical. By activating only one of the four laser diodes at a time, the required polarized, attenuated light pulses are generated. Similarly, in the receiver, the light is divided by a beam splitter and analyzed in either horizontal/vertical linear polarization in one output or +45°/−45° in the other output. The randomness of detection behind a beam splitter here in addition saves the random number generator. Free‐space links mainly suffer from air turbulences, which reduce the effective aperture of the telescopes significantly. Thus, for collecting a maximum number of attenuated pulses, large receiver telescopes are required.

Figure 17.3 shows the principle scheme of free‐space QKD, on the example of the first link of more than 20 km. Compact and robust design warranted high stability under harsh conditions, demonstrated in a collaboration between the Munich University, Germany, and QinetiQ, UK, led by Kurtsiefer (13). To work in calm and clean air, the test range was set up in the Alps between Zugspitze and Westliche Karwendelspitze. In spite of the quite tough atmospheric conditions, such as temperatures down to and strong winds, shifted key could be generated with a rate of about 1000 bit/s.

Such free‐space links offer a range of possible applications. Over a short range, a mobile system could be used for authentication or secure upload of keys and PIN to the mobile system. Highly integrated modules have been developed together with tracking of the mobile, handheld system in first proof‐of‐principle demonstrations (14). Secure links can be also established between buildings of a city (distance up to 4 km). For example, between the buildings of a bank or a company, or the last mile from the network provider to the user, quantum cryptography can then enable secure communication for low price.

In the future, the direct coupling via telescopes could also enable QKD to low‐earth‐orbit satellites. From a height of about 500 to 1000 km, the sender tracks the ground station and sends light pulses, which, in turn, should be collected by a big telescope on the earth to exchange a first secret key. If the satellite flies over another ground station, the second secret key can be exchanged. Combining the two keys at the satellite gives a secure key between the ground stations and enables worldwide communication.

Besides the aforementioned experiment, which due to the snow around Alice's sender telescope could operate only during night, the group of Richard Hughes, Los Alamos, demonstrated also the feasibility of daylight key exchange over a distance of 10 km (15). Necessary for this are fine filtering in the frequency domain and the spatial domain as well as fine selection of the detection time. Further tests showed the feasibility to link over significantly longer distances of 144 km between the Canary Islands of Tenerife and LaPalma (16), to moving platforms (17). Care has to be taken for beam distortion due to turbulence by using adaptive optics (18). This development finally led to the first satellite built by a Chinese research group led by J.W. Pan and launched in 2016 (19), which will surely enable secure communication on a global scale in the near future.

17.3 Entanglement‐Based Quantum Communication

Quantum teleportation is, of course, the best‐known representative of the new protocols showing improvements of classical communication by quantum means. But there are also other methods for quite diverse purposes (for an extensive review see (24)).

17.3.1 Quantum Dense Coding

The closest protocol to teleportation is quantum dense coding. It enables the transmission of two bits of classical information by sending only a single qubit. Assume Alice and Bob want to communicate classical information. Alice might use quantum particles, all prepared in the same state by some source. She translates the bit values of the message to either leaving the state of the qubit unchanged or to flip it to the other orthogonal state, and Bob consequently will observe the particle in one or the other state. It means that Alice can encode one bit of information in a single qubit. Obviously, she cannot do better, since in order to avoid errors, the states arriving at Bob have to be distinguishable, which is only guaranteed when using orthogonal states. In this respect, they do not gain anything by using qubits compared to classical bits. Also, if she wants to communicate two bits of information, Alice has to send two qubits.

C.H. Bennett and S. Wiesner found a clever way to circumvent the classical limit and demonstrated to increase the channel capacity by using entangled particles (25). Suppose the particle which Alice obtained from the source is entangled with another particle, which was directly sent to Bob (Figure 17.4). The two particles are in one of the four Bell‐states, say . Alice now can use the particular feature of the Bell‐basis, that is, manipulation of only one of the two entangled particles suffices to transform to any other of the four Bell‐states. Thus, she can perform one out of four possible transformations – that is, doing nothing, shift the phase by , flip the state, or flip and phase shift the state – to transform the two‐particle state of their common pair to another one. After Alice has sent the transformed two‐state particle to Bob, he can read the information by performing a combined measurement on both particles. He will make a measurement in the Bell‐state basis and can identify which of the four possible messages was sent by Alice. Thus, it is possible to encode two bits of classical information by manipulating and by transmitting a single two‐state system. Entanglement enables one to communicate information more efficiently than any classical system could do.

For the experiment, the source of entangled photons was aligned such that the state was prepared. One photon was sent directly to Bob, the other to Alice, where half‐wave and quarter‐wave retardation plates were used to apply the desired manipulation encoding the classical information. Then, this photon is also sent to Bob, where, for correct path length adjustment, two‐photon interference can be used to distinguish at least three of the four Bell‐states (26). In principle, interferometric Bell‐state analysis can identify two of the four Bell‐states, with the other two giving the same result. If Alice thus uses only three encodings, all three types of messages can be distinguished. In principle, only the application of quantum logic gates allows the full analysis of the four Bell‐states. However, this is not possible for photons, yet. More recently, new approaches to Bell‐state analysis have been demonstrated. One uses general, so called positive-operator valued measure (POVM) measurements to identify also three states, another employs entanglement in another degree of freedom to enable the analysis of all four states (27). Recently, Knill et al. showed that efficient quantum computation is possible using only beam splitters, phase shifter, single‐photon sources and photodetectors distinguishing between one, two photons, and so on (28). The method exploits feedback from photodetectors and is robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology; however, the full implementation still needs a significant amount of photons and thus is not possible to be performed at present. Bell‐state analysis with linear optics quantum logic gates was achieved now, but without using a significant amount of ancilla photons, the gate employed has a success rate of only 1/9 (29).

17.3.2 Error Correction

For any quantum communication application, a reliable quantum channel is of tremendous importance. As any link will introduce some noise, it is necessary to either try to compensate the disturbance, or, if this is not possible, to correct for the errors occurring. This, similarly to Bell‐state analysis, requires quantum logic operations, which, however, are not available. In addition, quantum memories would be required. Fortunately, two pairs of entangled photons can be obtained from parametric downconversion, which allows to demonstrate the first step without memories, and two‐photon interference once again proves to be an excellent tool to circumvent the necessity of logic gates.

Two options are available: for global errors, that is, several qubits are influenced by the same transformation, “decoherence‐free” coding can immunize a quantum state if it is encoded in (at least) four qubits (30). The other possibility is to combine noisy realizations of a state and perform logic operations and measurements such that one can identify the error and correct it. Due to the lack of gates, again, this is not fully possible for photons yet, but quite a number of initial steps can be performed based on two‐photon interference.

To show this, we consider qubits defined by the polarization states of photons, that is, we identify and by linear horizontal polarization and vertical polarization , respectively. The entanglement purification is based on a simple optical element, the polarizing beam splitter (PBS). Initially, two photons are entering the PBS from two different inputs. The PBS has the property that horizontally polarized photons are transmitted and vertically polarized ones are reflected. If we find one photon in each of the two outputs, then either both have been transmitted, and are , or both have been reflected, and are thus . We see both have the same polarization. If the two incident photons have different polarization ( and ), then they will end up in the same output mode of the PBS and are not considered any longer. This feature of the PBS has been used in the observation of multiphoton entanglement and also plays an important role in the simulation of quantum computation by linear optics (31).

From the viewpoint of error correction or entanglement Purification, the PBS together with conditioning on the detection is equivalent to a parity check and can therefore be used for that purpose (32). For the experiment, two pairs of entangled photons are created simultaneously by one laser pump pulse and pairwise overlapped at a PBS. Given that one detects one photon in each of the outputs, and given equal results from the parity check measurement on each side, the remaining two photons exhibit higher entanglement than the initial pairs (Figure 17.5).

17.4 Conclusion

Quantum cryptography was the first quantum communication experiment, and nowadays has already become a real commercial application. Methods such as quantum teleportation and quantum dense coding were demonstrated. Due to the low rate of entangled multiphoton states, it is currently difficult to use them. However, given all the necessary infrastructure, also these methods will find their application, most prominently as part of the quantum repeater, where entanglement swapping, a variation of teleportation, is one of the most crucial ingredients. First, steps in quantum error correction and entanglement distillation have been performed, yet, one still requires, of course, quantum memories. With all this at hand, long‐distance quantum communication will be possible.

Other methods are already demonstrated or just under way. Quantum cloning enables the distribution of quantum states onto several qubits (33). Multiparty applications are coming close with quantum secret sharing (the extension of quantum cryptography to several partners) (34) or communication complexity (35).

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