Quantum complex networks are complex networks whose nodes are quantum computing devices. Quantum mechanics has been used to create secure quantum communications channels that are protected from hacking. Quantum communications offer the potential for secure enterprise-scale solutions.
Motivation In theory, it is possible to take advantage of quantum mechanics to create secure communications using features such as quantum key distribution is an application of quantum cryptography that enables secure communications Quantum teleportation can transfer data at a higher rate than classical channels.
History Successful quantum teleportation experiments in 1998. Prototypical quantum communication networks arrived in 2004. Large scale communication networks tend to have non-trivial topologies and characteristics, such as small world effect, community structure, or scale-free.
Concepts
Qubits In quantum information theory, qubits are analogous to bits in classical systems. A qubit is a quantum object that, when measured, can be found to be in one of only two states, and that is used to transmit information. Photon polarization or nuclear spin are examples of binary phenomena that can be used as qubits.
Entanglement Quantum entanglement is a physical phenomenon characterized by correlation between the quantum states of two or more physically separate qubits. Maximally entangled states are those that maximize the entropy of entanglement. In the context of quantum communication, entangled qubits are used as a quantum channel.
Bell measurement Bell measurement is a kind of joint quantum-mechanical measurement of two qubits such that, after the measurement, the two qubits are maximally entangled.
Entanglement swapping Entanglement swapping is a strategy used in the study of quantum networks that allows connections in the network to change. For example, given 4 qubits, A, B, C and D, such that qubits C and D belong to the same station, while A and C belong to two different stations, and where qubit A is entangled with qubit C and qubit B is entangled with qubit D. Performing a Bell measurement for qubits A and B, entangles qubits A and B. It is also possible to entangle qubits C and D, despite the fact that these two qubits never interact directly with each other. Following this process, the entanglement between qubits A and C, and qubits B and D are lost. This strategy can be used to define network topology.
Network structure While models for quantum complex networks are not of identical structure, usually a node represents a set of qubits in the same station (where operations like Bell measurements and entanglement swapping can be applied) and an edge between node i {\displaystyle i} and j {\displaystyle j} means that a qubit in node i {\displaystyle i} is entangled to a qubit in node j {\displaystyle j} , although those two qubits are in different places and so cannot physically interact. Quantum networks where the links are interaction terms instead of entanglement are also of interest.
Notation Each node in the network contains a set of qubits in different states. To represent the quantum state of these qubits, it is convenient to use Dirac notation and represent the two possible states of each qubit as | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } . In this notation, two particles are entangled if the joint wave function, | ψ i j ⟩ {\displaystyle |\psi _{ij}\rangle } , cannot be decomposed as
| ψ i j ⟩ = | ϕ ⟩ i ⊗ | ϕ ⟩ j , {\displaystyle |\psi _{ij}\rangle =|\phi \rangle _{i}\otimes |\phi \rangle _{j},}
where | ϕ ⟩ i {\displaystyle |\phi \rangle _{i}} represents the quantum state of the qubit at node i and | ϕ ⟩ j {\displaystyle |\phi \rangle _{j}} represents the quantum state of the qubit at node j. Another important concept is maximally entangled states. The four states (the Bell states) that maximize the entropy of entanglement between two qubits can be written as follows:
| Φ i j + ⟩ = 1 2 ( | 0 ⟩ i ⊗ | 0 ⟩ j + | 1 ⟩ i ⊗ | 1 ⟩ j ) , {\displaystyle |\Phi _{ij}^{+}\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle _{i}\otimes |0\rangle _{j}+|1\rangle _{i}\otimes |1\rangle _{j}),}
… excerpt ends here. Continue reading the full article.
