# Quantum network

Quantum networks form an important element of quantum computing and quantum cryptography systems. Quantum networks allow for the transportation of quantum information between physically separate quantum systems. In distributed quantum computing, network nodes within the network can process information by serving as quantum logic gates. Secure communication can be implemented using quantum networks through quantum key distribution algorithms.

Optical quantum networks using fiber optic links or free-space links play an important role transmitting quantum states in the form of photons across large distances. Optical cavities can be used to trap single atoms and can serve as storage and processing nodes in these networks.

## Applications

### Quantum key distribution

BB84 protocol diagram: a polarized photon from Alice is transmitted across an insecure quantum channel and detected by Bob while Eve attempts to eavesdrop on the communication.

Many existing quantum networks are designed to support quantum key distribution (QKD) between classical computing environments. In this application, the quantum network facilitates the sharing of a secret encryption key between two parties. Unlike classical key distribution algorithms such as Diffie-Hellman key exchange, quantum key distribution provides security through physical properties rather than the difficulty of a mathematical problem.

The first quantum key distribution protocol, BB84, was proposed by Charles Bennett and Gilles Brassard in 1984 and has been implemented in a number of research quantum networks. In this protocol, qubits are sent from one party to another over an insecure quantum network. Due to the properties of quantum mechanics and the no-cloning theorem, it is impossible for an eavesdropper to determine the key without being detected by the sender and receiver.[1]

While the BB84 protocol relies on the superposition of qubit states to detect eavesdropping, other protocols use entangled qubits. Examples of these protocols include the E91[2] protocol proposed by Artur Ekert, and the BBM92[3] protocol proposed by Charles H. Bennett, Gilles Brassard, and N. David Mermin.

### Quantum state transfer

In a large quantum computing system many separate quantum computers may interact and communicate across a network. In this scenario it is beneficial for the network to support the transmissions of entangled qubits. Consider the following scenario: ${\displaystyle k}$ quantum computers each containing ${\displaystyle n}$ qubits. To transmit the complete state of one quantum computer to another would require ${\displaystyle 2^{n}}$ bits of information over a classical network. However, using a quantum network the state can be transferred using only ${\displaystyle n}$ qubits. Likewise, if entanglement can be achieved between all computers in the network, the system as a whole will have a combined state spaces of ${\displaystyle 2^{kn}}$ as opposed to ${\displaystyle k2^{n}}$ for classically connected quantum computers.[4]

## Method of operation

### Physical layer

Over long distances, the primary method of operating quantum networks is to use optical networks and photon based qubits. 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.[5]

#### Fiber optic networks

Optical networks using existing telecommunication fiber can be implemented using hardware similar to existing telecommunication equipment. 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 multiplex 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.[6]

#### Cavity-QED networks

Telecommunication lasers and parametric down-conversion combined with photodetectors can be used for quantum key distribution. However, for distributed quantum entangled systems, it important to be able to store and retransmit quantum information without disrupting the underlying states. 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.[7][8]

### Noisy channels

#### Quantum repeaters

Diagram for quantum teleportation of a photon

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 transmit, however in a quantum network amplifiers cannot be used due to 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 alternate approach is to use quantum teleportation to transmit quantum information (qubits) to the receiver. This avoids the problems associated with sending single photons across a lengthy high-loss transmission line. However, quantum teleportation requires a pair of entangled qubits with one at each end. Quantum repeaters allow entanglement can be established at distant nodes without physically sending an entangled qubit the entire distance.[9]

In this case, the quantum network consists of many short distance links of perhaps tens or hundreds of kilometres. In the simplest case of a single repeater, two pairs of entangled qubits are established: ${\displaystyle |A\rangle }$ and ${\displaystyle |R_{a}\rangle }$ located at the sender and the repeater, and a second pair ${\displaystyle |R_{b}\rangle }$ and ${\displaystyle |B\rangle }$ located at the repeater and the receiver. Theses 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 ${\displaystyle |R_{a}\rangle }$ and ${\displaystyle |R_{b}\rangle }$ thus teleporting the quantum state of ${\displaystyle |R_{a}\rangle }$ onto ${\displaystyle |B\rangle }$. This has the effect of "swapping" the entanglement such that ${\displaystyle |A\rangle }$ and ${\displaystyle |B\rangle }$ 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.[10]

#### Error correction

In both classical and quantum communication, errors can be introduced at any point during sending, transmit, or receiving. 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 arbitrary single qubit 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 correct such as Hamming codes can be applied to the bit string before encoding and transmission on the quantum network.

#### Entanglement purification

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.

## Current status

Major quantum network projects and QKD protocols implemented
Quantum Network Start BB84 BBM92 E91 DPS COW
DARPA QKD 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 Wuho, 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 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.[11][12]
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 though the use of repeaters.[13]
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 though an optical switching Quantum Router. Nodes within each subnet are also connected though a optical switch and are connected to the backbone network though a trusted relay.[14]
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 it's reliability and robustness.[15]
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.[16]

## References

1. ^ Bennett, Charles H.; Brassard, Gilles (1984), "Quantum Cryptography: Public Key Distribution and Coin Tossing", Proceedings of IEEE International Conference on Computers, Systems and Signal Processing 175 (1)
2. ^ Ekert, Artur (1991), "Quantum cryptography based on Bell's theorem", Physical Review Letters 67 (6): 661–663, doi:10.1103/physrevlett.67.661
3. ^ Bennett, Charles H; Brassard, Gilles; Merin, David N, "Quantum cryptography without Bell's theorem", Physical Review Letters 68 (5): 557–559, doi:10.1103/physrevlett.68.557
4. ^ Kimble, H J (2008), "The quantum internet", Nature 453 (7198): 1023–1030, doi:10.1038/nature07127
5. ^ Gisson, Nicolas; Ribordy, Grégoire; Tittel, Wolfgang; Zbinden, Hugo (2002), "Quantum cryptography", Reviews of modern physics 74 (1): 145
6. ^ 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, doi:10.1088/1367-2630/4/1/343
7. ^ Pellizzari, T; Gardiner, SA; Cirac, JI; Zoller, P (1995), "Decoherence, continuous observation, and quantum computing: A cavity QED model", Physical Review Letters 74 (21): 3788–3791, doi:10.1103/physrevlett.75.3788
8. ^ 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, doi:10.1038/nature11023
9. ^ Bouwmeester, Dik; Pan, Jian-Wei; Mattle, Klaus; Eibl, Manfred; Weinfurter, Harald; Zeilinger, Anton (1997), "Experimental quantum teleportation", Nature 390 (6660): 575–579, doi:10.1038/37539
10. ^ 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, doi:10.1103/revmodphys.83.33
11. ^ Elliot, Chip (2002), "Building the quantum network", New Journal of Physics 4 (1): 46, doi:10.1088/1367-2630/4/1/346
12. ^ 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
13. ^ 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, doi:10.1088/1367-2630/11/7/075001
14. ^ 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, doi:10.1007/s11434-009-0526-3
15. ^ 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. doi:10.1088/1367-2630/13/12/123001.
16. ^ 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, doi:10.1364/oe.19.010387