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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.
Contents
- Quantum key distribution
- Quantum state transfer
- Physical layer
- Fiber optic networks
- Free space networks
- Cavity QED networks
- Quantum repeaters
- Error correction
- Entanglement purification
- Current status
- References
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.
Quantum key distribution
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.
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 protocol proposed by Artur Ekert, and the BBM92 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:
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.
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 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.
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 is 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.
Quantum repeaters
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 and can be established at distant nodes without physically sending an entangled qubit the entire distance.
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:
Error correction
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 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.