Quantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information in the form of quantum bits, also called qubits, between physically separated quantum processors. A quantum processor is a small quantum computer being able to perform quantum logic gates on a certain number of qubits. Quantum networks work in a similar way to classical networks. The main difference, as will be detailed more in later paragraphs, is that quantum networking like quantum computing is better at solving certain problems, such as modeling quantum systems.
- 1 Basics
- 2 Elements of a quantum network
- 3 Applications
- 4 Current status
- 5 See also
- 6 References
- 7 External links
Quantum networks for computation
Networked quantum computing or distributed quantum computing works by linking multiple quantum processors through a quantum network by sending qubits in-between them. Doing this creates a quantum computing cluster and therefore creates more computing potential. Less powerful computers can be linked in this way to create one more powerful processor. This is analogous to connecting several classical computers to form a computer cluster in classical computing. Like classical computing this system is scale-able by adding more and more quantum computers to the network. Currently quantum processors are only separated by short distances.
Quantum networks for communication
In the realm of quantum communication, one wants to send qubits from one quantum processor to another over long distances. This way local quantum networks can be intra connected into a quantum internet. A quantum internet supports many applications, which derive their power from the fact that by creating quantum entangled qubits, information can be transmitted between the remote quantum processors. Most applications of a quantum internet require only very modest quantum processors. For most quantum internet protocols, such as quantum key distribution in quantum cryptography, it is sufficient if these processors are capable of preparing and measuring only a single qubit at a time. This is in contrast to quantum computing where interesting applications can only be realized if the (combined) quantum processors can easily simulate more qubits than a classical computer (around 60). Quantum internet applications require only small quantum processors, often just a single qubit, because quantum entanglement can already be realized between just two qubits. A simulation of an entangled quantum system on a classical computer can not simultaneously provide the same security and speed.
Overview of the elements of a quantum network
The basic structure of a quantum network and more generally a quantum internet is analogous to a classical network. First, we have end nodes on which applications are ultimately run. These end nodes are quantum processors of at least one qubit. Some applications of a quantum internet require quantum processors of several qubits as well as a quantum memory at the end nodes.
Second, to transport qubits from one node to another, we need communication lines. For the purpose of quantum communication, standard telecom fibers can be used. For networked quantum computing, in which quantum processors are linked at short distances, different wavelengths are chosen depending on the exact hardware platform of the quantum processor.
Third, to make maximum use of communication infrastructure, one requires optical switches capable of delivering qubits to the intended quantum processor. These switches need to preserve quantum coherence, which makes them more challenging to realize than standard optical switches.
Finally, one requires a quantum repeater to transport qubits over long distances. Repeaters appear in-between end nodes. Since qubits cannot be copied, classical signal amplification is not possible. By necessity, a quantum repeater works in a fundamentally different way than a classical repeater.
Elements of a quantum network
End nodes: quantum processors
End nodes can both receive and emit information. Telecommunication lasers and parametric down-conversion combined with photodetectors can be used for quantum key distribution. In this case, the end nodes can in many cases be very simple devices consisting only of beamsplitters and photodetectors.
However, for many protocols more sophisticated end nodes are desirable. These systems provide advanced processing capabilities and can also be used as quantum repeaters. Their chief advantage is that they can store and retransmit quantum information without disrupting the underlying quantum state. The quantum state being stored can either be the relative spin of an electron in a magnetic field or the energy state of an electron. They can also perform quantum logic gates.
One way of realizing such end nodes is by using color centers in diamond, such as the nitrogen-vacancy center. This system forms a small quantum processor featuring several qubits. NV centers can be utilized at room temperatures. Small scale quantum algorithms and quantum error correction has already been demonstrated in this system, as well as the ability to entangle two remote quantum processors, and perform deterministic quantum teleportation.
Another possible platform are quantum processors based on Ion traps, which utilize radio-frequency magnetic fields and lasers. In a multispecies trapped-ion node network, photons entangled with a parent atom are used to entangle different nodes. Also, cavity quantum electrodynamics (Cavity QED) is one possible method of doing this. In Cavity QED, photonic quantum states can be transferred to and from atomic quantum states stored in single atoms contained in optical cavities. This allows for the transfer of quantum states between single atoms using optical fiber in addition to the creation of remote entanglement between distant atoms.
Communication lines: physical layer
Over long distances, the primary method of operating quantum networks is to use optical networks and photon-based qubits. This is due to optical networks having a reduced chance of decoherence. Optical networks have the advantage of being able to re-use existing optical fiber. Alternately, free space networks can be implemented that transmit quantum information through the atmosphere or through a vacuum.
Fiber optic networks
Optical networks using existing telecommunication fiber can be implemented using hardware similar to existing telecommunication equipment. This fiber can be either single-mode or multi-mode, with multi-mode allowing for more precise communication. At the sender, a single photon source can be created by heavily attenuating a standard telecommunication laser such that the mean number of photons per pulse is less than 1. For receiving, an avalanche photodetector can be used. Various methods of phase or polarization control can be used such as interferometers and beam splitters. In the case of entanglement based protocols, entangled photons can be generated through spontaneous parametric down-conversion. In both cases, the telecom fiber can be multiplexed to send non-quantum timing and control signals.
Free space networks
Free space quantum networks operate similar to fiber optic networks but rely on line of sight between the communicating parties instead of using a fiber optic connection. Free space networks can typically support higher transmission rates than fiber optic networks and do not have to account for polarization scrambling caused by optical fiber. However, over long distances, free space communication is subject to an increased chance of environmental disturbance on the photons.
Importantly, free space communication is also possible from a satellite to the ground. A quantum satellite capable of entanglement distribution over a distance of 1,203 km has been demonstrated. The experimental exchange of single photons from a global navigation satellite system at a slant distance of 20,000 km has also been reported . These satellites can play an important role in linking smaller ground-based networks over larger distances.
Long distance communication is hindered by the effects of signal loss and decoherence inherent to most transport mediums such as optical fiber. In classical communication, amplifiers can be used to boost the signal during transmission, but in a quantum network amplifiers cannot be used since qubits cannot be copied – known as the no-cloning theorem. That is, to implement an amplifier, the complete state of the flying qubit would need to be determined, something which is both unwanted and impossible.
An intermediary step which allows the testing of communication infrastructure are trusted repeaters. Importantly, a trusted repeater cannot be used to transmit qubits over long distances. Instead, a trusted repeater can only be used to perform quantum key distribution with the additional assumption that the repeater is trusted. Consider two end nodes A and B, and a trusted repeater R in the middle. A and R now perform quantum key distribution to generate a key . Similarly, R and B run quantum key distribution to generate a key . A and B can now obtain a key between themselves as follows: A sends to R encrypted with the key . R decrypts to obtain . R then re-encrypts using the key and sends it to B. B decrypts to obtain . A and B now share the key . The key is secure from an outside eavesdropper, but clearly the repeater R also knows . This means that any subsequent communication between A and B does not provide end to end security, but is only secure as long as A and B trust the repeater R.
A true quantum repeater allows the end to end generation of quantum entanglement, and thus - by using quantum teleportation - the end to end transmission of qubits. In quantum key distribution protocols one can test for such entanglement. This means that when making encryption keys, the sender and receiver are secure even if they do not trust the quantum repeater. Any other application of a quantum internet also requires the end to end transmission of qubits, and thus a quantum repeater.
In this case, the quantum network consists of many short distance links of perhaps tens or hundreds of kilometers. In the simplest case of a single repeater, two pairs of entangled qubits are established: and located at the sender and the repeater, and a second pair and located at the repeater and the receiver. These initial entangled qubits can be easily created, for example through parametric down conversion, with one qubit physically transmitted to an adjacent node. At this point, the repeater can perform a bell measurement on the qubits and thus teleporting the quantum state of onto . This has the effect of "swapping" the entanglement such that and are now entangled at a distance twice that of the initial entangled pairs. It can be seen that a network of such repeaters can be used linearly or in a hierarchical fashion to establish entanglement over great distances.
Hardware platforms suitable as end nodes above can also function as quantum repeaters. However, there are also hardware platforms specific only to the task of acting as a repeater, without the capabilities of performing quantum gates.
Error correction can be used in quantum repeaters. Due to technological limitations, however, the applicability is limited to very short distances as quantum error correction schemes capable of protecting qubits over long distances would require an extremely large amount of qubits and hence extremely large quantum computers.
Errors in communication can be broadly classified into two types: Loss errors (due to optical fiber/environment) and operation errors (such as depolarization, dephasing etc.). While redundancy can be used to detect and correct classical errors, redundant qubits cannot be created due to the no-cloning theorem. As a result, other types of error correction must be introduced such as the Shor code or one of a number of more general and efficient codes. All of these codes work by distributing the quantum information across multiple entangled qubits so that operation errors as well as loss errors can be corrected.
In addition to quantum error correction, classical error correction can be employed by quantum networks in special cases such as quantum key distribution. In these cases, the goal of the quantum communication is to securely transmit a string of classical bits. Traditional error correction codes such as Hamming codes can be applied to the bit string before encoding and transmission on the quantum network.
Quantum decoherence can occur when one qubit from a maximally entangled bell state is transmitted across a quantum network. Entanglement purification allows for the creation of nearly maximally entangled qubits from a large number of arbitrary weakly entangled qubits, and thus provides additional protection against errors. Entanglement purification (also known as Entanglement distillation) has already been demonstrated in Nitrogen-vacancy centers in diamond.
A quantum internet supports numerous applications, enabled by quantum entanglement. In general, quantum entanglement is well suited for tasks that require coordination, synchronization or privacy.
Examples of such applications include quantum key distribution, clock synchronization, protocols for distributed system problems such as leader election or byzantine agreement, extending the baseline of telescopes, as well as position verification, secure identification and two-party cryptography in the noisy-storage model. A quantum internet also enables secure access to a quantum computer in the cloud. Specifically, a quantum internet enables very simple quantum devices to connect to a remote quantum computer in such a way that computations can be performed there without the quantum computer finding out what this computation actually is.
When it comes to communicating in any form the largest issue has always been keeping your communications private. From when couriers were used to send letters between ancient battle commanders to secure radio communications that exist today the main purpose is to ensure that what a sender sends out to the receiver reaches the receiver unmolested. This is an area in which Quantum Networks particularly excel. By applying a quantum operator that the user selects to a system of information the information can then be sent to the receiver without a chance of an eavesdropper being able to accurately be able to record the sent information without either the sender or receiver knowing. This works because if a listener tries to listen in then they will change the information in an unintended way by listening thereby tipping their hand to the people on whom they are attacking. Secondly, without the proper quantum operator to decode the information they will corrupt the sent information without being able to use it themselves.
Quantum networks can also be used to protect against jamming. A user can use a quantum network by using frequency-hopping spread spectrum. This method is currently used by the United States Army. In this method the user hops from frequency to frequency many times a second so that it is hard for an attacker to keep up and successfully attack the user. Direct-sequence spread spectrum can be used by applying a quantum operator to the system and then freely transmitting the information over the frequencies because an attacker cannot read the information without knowing the key (a quantum operator). These two techniques can be used together to produce a more secure communications system.
Frequency-hopping spread spectrum
Frequency-hopping spread spectrum (FHSS) is a method of protecting information transfer that involves the user switching from one frequency to another frequency hundreds of times a second. For this method to work one computer is set as the main computer and will regulate when the other computers will switch frequencies and how often. By switching frequencies hundreds of times a second a user can be assured that any would be attacker will have an extremely hard time both trying to read the data and trying to jam the frequency.
Direct-sequence spread spectrum
Direct-sequence spread spectrum (DSSS) is a method of protecting information transfer that involves the user applying a predetermined quantum operator to the information that is being sent so that only the receiver and the sender can decipher the information using the operator. This method makes it difficult for a potential listener to eavesdrop because without the operator they will not be able to determine the information. At the same time if a listener does try to decode the sent information by doing so they will change the information which will immediately tell the receiver that someone is listening to them.
When using any computer to communicate with another computer the name of the game is security. "Attackers", people who want to receive information that was not intended for them or people who want to stop the proper receiver of the transmission from receiving their information. Quantum networks are particularly useful in this area as there are many different types of jamming techniques that are found in both classical and quantum systems.
Spot jamming is a process wherein an attacker fully attacks one frequency at a time. For this method to be successful the attacker must send their transmission with more power than the original sender. By doing this the attacker will essentially overpower the original sender's message. The problem with this method is that it takes a tremendous amount of power to overpower a transmission as stated. Another issue with this method is that the original sender can easily switch to another frequency and if the original sender is using frequency-hopping spread spectrum the user will switch frequencies automatically with little hindrance to the original sender.
Sweep jamming is similar to spot jamming except it switches rapidly from one frequency to another in rapid succession. In this method the attacker is still attacking by sending a much more powerful message at the same time as the original sender. The advantage of this method over spot jamming is that sweep jamming has a much larger chance of disrupting the sender's frequency and costs the same amount of energy as spot.
Barrage jamming is when an attacker attacks many frequencies at one time, but as the range grows the ability to jam decreases. By attacking a few frequencies at a time the attacker increases the change that they might hit one of the sender's frequencies. The main problem with this method is that the attacker's power is greatly lessened because they are attacking many frequencies at once and therefore they decrease their power overall so it is possible that the attacker could hit the sender's frequency and not affect it due to the low power of their jamming frequency.
At present, there is no network connecting quantum processors, or quantum repeaters deployed outside a lab.
Quantum key distribution networks
Several test networks have been deployed that are tailored to the task of quantum key distribution either at short distances (but connecting many users), or over larger distances by relying on trusted repeaters. These networks do not yet allow for the end to end transmission of qubits or the end to end creation of entanglement between far away nodes.
|DARPA Quantum Network||2001||Yes||No||No||No||No|
|SECOCQ QKD network in Vienna||2003||Yes||Yes||No||No||Yes|
|Tokyo QKD network||2009||Yes||Yes||No||Yes||No|
|Hierarchical network in Wuhu, China||2009||Yes||No||No||No||No|
|Geneva area network (SwissQuantum)||2010||Yes||No||No||No||Yes|
- DARPA Quantum Network
- Starting in the early 2000s, DARPA began sponsorship of a quantum network development project with the aim of implementing secure communication. The DARPA Quantum Network became operational within the BBN Technologies laboratory in late 2003 and was expanded further in 2004 to include nodes at Harvard and Boston Universities. The network consists of multiple physical layers including fiber optics supporting phase-modulated lasers and entangled photons as well free-space links.
- SECOQC Vienna QKD network
- From 2003 to 2008 the Secure Communication based on Quantum Cryptography (SECOQC) project developed a collaborative network between a number of European institutions. The architecture chosen for the SECOQC project is a trusted repeater architecture which consists of point-to-point quantum links between devices where long distance communication is accomplished through the use of repeaters.
- Chinese hierarchical network
- In May 2009, a hierarchical quantum network was demonstrated in Wuhu, China. The hierarchical network consists of a backbone network of four nodes connecting a number of subnets. The backbone nodes are connected through an optical switching quantum router. Nodes within each subnet are also connected through an optical switch and are connected to the backbone network through a trusted relay.
- Geneva area network (SwissQuantum)
- The SwissQuantum network developed and tested between 2009 and 2011 linked facilities at CERN with the University of Geneva and hepia in Geneva. The SwissQuantum program focused on transitioning the technologies developed in the SECOQC and other research quantum networks into a production environment. In particular the integration with existing telecommunication networks, and its reliability and robustness.
- Tokyo QKD network
- In 2010, a number of organizations from Japan and the European Union setup and tested the Tokyo QKD network. The Tokyo network build upon existing QKD technologies and adopted a SECOQC like network architecture. For the first time, one-time-pad encryption was implemented at high enough data rates to support popular end-user application such as secure voice and video conferencing. Previous large-scale QKD networks typically used classical encryption algorithms such as AES for high-rate data transfer and use the quantum-derived keys for low rate data or for regularly re-keying the classical encryption algorithms.
- Beijing-Shanghai Trunk Line
- In September 2017, a 2000-km quantum key distribution network between Beijing and Shanghai, China, was officially opened. This trunk line will serve as a backbone connecting quantum networks in Beijing, Shanghai, Jinan in Shandong province and Hefei in Anhui province. During the opening ceremony, two employees from the Bank of Communications completed a transaction from Shanghai to Beijing using the network. The State Grid Corporation of China is also developing a managing application for the link. The line uses 32 trusted nodes as repeaters. A quantum telecommunication network has been also put into service in Wuhan, capital of central China's Hubei Province, which will be connected to the trunk. Other similar city quantum networks along the Yangtze River are planned to follow.
- Kimble, H. J. (2008-06-19). "The quantum internet". Nature. 453 (7198): 1023–1030. arXiv:0806.4195. Bibcode:2008Natur.453.1023K. doi:10.1038/nature07127. ISSN 0028-0836. PMID 18563153.
- Caleffi, Marcello; Cacciapuoti, Angela Sara; Bianchi, Giuseppe (5 September 2018). Quantum internet: from communication to distributed computing!. NANOCOM '18 Proceedings of the 5th ACM International Conference on Nanoscale Computing and Communication. Reykjavik, Iceland: ACM. doi:10.1145/3233188.3233224.
- Pednault, Edwin; Gunnels, John A.; Nannicini, Giacomo; Horesh, Lior; Magerlein, Thomas; Solomonik, Edgar; Wisnieff, Robert (2017-10-16). "Breaking the 49-Qubit Barrier in the Simulation of Quantum Circuits". arXiv:1710.05867 [quant-ph].
- Van Meter, Rodney (2014). Quantum Networking. Hoboken: Wiley. pp. 127–196. ISBN 9781118648926. OCLC 879947342.
- Cramer, J.; Kalb, N.; Rol, M. A.; Hensen, B.; Blok, M. S.; Markham, M.; Twitchen, D. J.; Hanson, R.; Taminiau, T. H. (2016-05-05). "Repeated quantum error correction on a continuously encoded qubit by real-time feedback". Nature Communications. 7: ncomms11526. arXiv:1508.01388. Bibcode:2016NatCo...711526C. doi:10.1038/ncomms11526. PMC 4858808. PMID 27146630.
- Hensen, B.; Bernien, H.; Dréau, A. E.; Reiserer, A.; Kalb, N.; Blok, M. S.; Ruitenberg, J.; Vermeulen, R. F. L.; Schouten, R. N. (2015-10-29). "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres". Nature. 526 (7575): 682–686. arXiv:1508.05949. Bibcode:2015Natur.526..682H. doi:10.1038/nature15759. ISSN 0028-0836. PMID 26503041.
- Pfaff, Wolfgang; Hensen, Bas; Bernien, Hannes; van Dam, Suzanne B.; Blok, Machiel S.; Taminiau, Tim H.; Tiggelman, Marijn J.; Schouten, Raymond N.; Markham, Matthew (2014-08-01). "Unconditional quantum teleportation between distant solid-state qubits". Science. 345 (6196): 532–535. arXiv:1404.4369. Bibcode:2014Sci...345..532P. doi:10.1126/science.1253512. ISSN 0036-8075. PMID 25082696.
- Inlek, I. V.; Crocker, C.; Lichtman, M.; Sosnova, K.; Monroe, C. (2017-06-23). "Multispecies Trapped-Ion Node for Quantum Networking". Physical Review Letters. 118 (25): 250502. arXiv:1702.01062. Bibcode:2017PhRvL.118y0502I. doi:10.1103/PhysRevLett.118.250502. PMID 28696766.
- Pellizzari, T; Gardiner, SA; Cirac, JI; Zoller, P (1995), "Decoherence, continuous observation, and quantum computing: A cavity QED model", Physical Review Letters, 75 (21): 3788–3791, Bibcode:1995PhRvL..75.3788P, doi:10.1103/physrevlett.75.3788, PMID 10059732
- Ritter, Stephan; Nölleke, Christian; Hahn, Carolin; Reiserer, Andreas; Neuzner, Andreas; Uphoff, Manuel; Müicke, Martin; Figueroa, Eden; Bochmann, Joerg; Rempe, Gerhard (2012), "An elementary quantum network of single atoms in optical cavities", Nature, 484 (7393): 195–200, arXiv:1202.5955, Bibcode:2012Natur.484..195R, doi:10.1038/nature11023, PMID 22498625
- Gisson, Nicolas; Ribordy, Grégoire; Tittel, Wolfgang; Zbinden, Hugo (2002), "Quantum cryptography", Reviews of Modern Physics, 74 (1): 145, arXiv:quant-ph/0101098, Bibcode:2002RvMP...74..145G, doi:10.1103/revmodphys.74.145
- Hughes, Richard J; Nordholt, Jane E; Derkacs, Derek; Peterson, Charles G (2002), "Practical free-space quantum key distribution over 10 km in daylight and at night", New Journal of Physics, 4 (1): 43, arXiv:quant-ph/0206092, Bibcode:2002NJPh....4...43H, doi:10.1088/1367-2630/4/1/343
- Yin, Juan; Cao, Yuan; Li, Yu-Huai; Liao, Sheng-Kai; Zhang, Liang; Ren, Ji-Gang; Cai, Wen-Qi; Liu, Wei-Yue; Li, Bo (2017-07-05). "Satellite-Based Entanglement Distribution Over 1200 kilometers". Science. 356 (2017): 1140–1144. arXiv:1707.01339. Bibcode:2017arXiv170701339Y. doi:10.1126/science.aan3211. PMID 28619937.
- Calderaro, Luca; Agnesi, Costantino; Dequal, Daniele; Vedovato, Francesco; Schiavon, Matteo; Santamato, Alberto; Luceri, Vincenza; Bianco, Giuseppe; Vallone, Giuseppe; Villoresi, Paolo (2019). "Towards quantum communication from global navigation satellite system". Quantum Science and Technology. 4 (1): 015012. arXiv:1804.05022. Bibcode:2019QS&T....4a5012C. doi:10.1088/2058-9565/aaefd4.
- Bouwmeester, Dik; Pan, Jian-Wei; Mattle, Klaus; Eibl, Manfred; Weinfurter, Harald; Zeilinger, Anton (1997), "Experimental quantum teleportation", Nature, 390 (6660): 575–579, arXiv:1901.11004, Bibcode:1997Natur.390..575B, doi:10.1038/37539
- Sangouard, Nicolas; Simon, Christoph; De Riedmatten, Hugues; Gisin, Nicolas (2011), "Quantum repeaters based on atomic ensembles and linear optics", Reviews of Modern Physics, 83 (1): 33–80, arXiv:0906.2699, Bibcode:2011RvMP...83...33S, doi:10.1103/revmodphys.83.33
- Nunn, Joshua (2017-05-24). "Viewpoint: A Solid Footing for a Quantum Repeater". Physics. 10: 55. Bibcode:2017PhyOJ..10...55N. doi:10.1103/physics.10.55.
- Muralidharan, Sreraman; Li, Linshu; Kim, Jungsang; Lutkenhaus, Norbert; Lukin, Mikhail; Jiang, Liang (2016), "Optimal architectures for long distance quantum communication", Scientific Reports, Nature, 6: 20463, Bibcode:2016NatSR...620463M, doi:10.1038/srep20463, PMC 4753438, PMID 26876670
- Kalb, Norbert; Reiserer, Andreas A.; Humphreys, Peter C.; Bakermans, Jacob J. W.; Kamerling, Sten J.; Nickerson, Naomi H.; Benjamin, Simon C.; Twitchen, Daniel J.; Markham, Matthew (2017-06-02). "Entanglement Distillation between Solid-State Quantum Network Nodes". Science. 356 (6341): 928–932. arXiv:1703.03244. Bibcode:2017Sci...356..928K. doi:10.1126/science.aan0070. ISSN 0036-8075. PMID 28572386.
- Sasaki, Masahide (2017). "Quantum networks: where should we be heading?". Quantum Science and Technology. 2 (2): 020501. Bibcode:2017QS&T....2b0501S. doi:10.1088/2058-9565/aa6994. ISSN 2058-9565.
- Tajima, A; Kondoh, T; Fujiwara, M; Yoshino, K; Iizuka, H; Sakamoto, T; Tomita, A; Shimamura, E; Asami, S; Sasaki, M (2017). "Quantum key distribution network for multiple applications". Quantum Science and Technology. 2 (3): 034003. Bibcode:2017QS&T....2c4003T. doi:10.1088/2058-9565/aa7154. ISSN 2058-9565.
- Kómár, P.; Kessler, E. M.; Bishof, M.; Jiang, L.; Sørensen, A. S.; Ye, J.; Lukin, M. D. (2014-06-15). "A quantum network of clocks". Nature Physics. 10 (8): 582–587. arXiv:1310.6045. Bibcode:2014NatPh..10..582K. doi:10.1038/nphys3000. ISSN 1745-2481.
- Gottesman, Daniel; Jennewein, Thomas; Croke, Sarah (2012-08-16). "Longer-Baseline Telescopes Using Quantum Repeaters". Physical Review Letters. 109 (7): 070503. arXiv:1107.2939. Bibcode:2012PhRvL.109g0503G. doi:10.1103/PhysRevLett.109.070503. ISSN 0031-9007. PMID 23006349.
- Quantum-Assisted Telescope Arrays
- Fitzsimons, Joseph F. (2017-06-15). "Private quantum computation: an introduction to blind quantum computing and related protocols". NPJ Quantum Information. 3 (1): 23. arXiv:1611.10107. Bibcode:2017npjQI...3...23F. doi:10.1038/s41534-017-0025-3. ISSN 2056-6387.
- Mastorakis, Nikos E. Networks and Quantum Computing. Nova Science Publishers, 2012.
- Elliot, Chip (2002), "Building the quantum network", New Journal of Physics, 4 (1): 46, Bibcode:2002NJPh....4...46E, doi:10.1088/1367-2630/4/1/346
- Elliott, Chip; Colvin, Alexander; Pearson, David; Pikalo, Oleksiy; Schlafer, John; Yeh, Henry (2005), "Current status of the DARPA Quantum Network", Defense and Security, International Society for Optics and Photonics: 138–149
- Peev, Momtchil; Pacher, Christoph; Alléaume, Romain; Barreiro, Claudio; Bouda, Jan; Boxleitner, W; Debuisschert, Thierry; Diamanti, Eleni; Dianati, M; Dynes, JF (2009), "The SECOQC quantum key distribution network in Vienna", New Journal of Physics, IOP Publishing, 11 (7): 075001, Bibcode:2009NJPh...11g5001P, doi:10.1088/1367-2630/11/7/075001
- Xu, FangXing; Chen, Wei; Wang, Shuang; Yin, ZhenQiang; Zhang, Yang; Liu, Yun; Zhou, Zheng; Zhao, YiBo; Li, HongWei; Liu, Dong (2009), "Field experiment on a robust hierarchical metropolitan quantum cryptography network", Chinese Science Bulletin, Springer, 54 (17): 2991–2997, arXiv:0906.3576, Bibcode:2009ChSBu..54.2991X, doi:10.1007/s11434-009-0526-3
- Stucki, Damien; Legre, Matthieu; Buntschu, F; Clausen, B; Felber, Nadine; Gisin, Nicolas; Henzen, L; Junod, Pascal; Litzistorf, G; Monbaron, Patrick (2011). "Long-term performance of the SwissQuantum quantum key distribution network in a field environment". New Journal of Physics. IOP Publishing. 13 (12): 123001. arXiv:1203.4940. Bibcode:2011NJPh...13l3001S. doi:10.1088/1367-2630/13/12/123001.
- Sasaki, M; Fujiwara, M; Ishizuka, H; Klaus, W; Wakui, K; Takeoka, M; Miki, S; Yamashita, T; Wang, Z; Tanaka, A (2011), "Field test of quantum key distribution in the Tokyo QKD Network", Optics Express, Optical Society of America, 19 (11): 10387–10409, arXiv:1103.3566, Bibcode:2011OExpr..1910387S, doi:10.1364/oe.19.010387, PMID 21643295
- Zhang, Zhihao (2017-09-30). "Beijing-Shanghai quantum link a "new era"". China Daily.
- Courtland, Rachel (26 Oct 2016). "China's 2,000-km Quantum Link Is Almost Complete". IEEE Spectrum: Technology, Engineering, and Science News.
- "Quantum communication networks put in service in central China". Xinhua. 2017-10-31.
- Elliott, Chip (2004). "The DARPA Quantum Network". arXiv:quant-ph/0412029.