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Quantum Entanglement
Published in Yanhua Shih, An Introduction to Quantum Optics, 2020
The most widely used entangled two-particle states might have been the “Bell states” (or EPR-Bohm-Bell states). Bell states are a set of polarization states for a pair of entangled photons. The four Bell states which form a complete orthonormal basis of two-photon state are usually represented as () |Φ12(±)〉=12[01,02〉±|1112〉],|Ψ12(±)〉=12[01,12〉±|1102〉]
Lasers in Quantum Information Science
Published in Pradip Narayan Ghosh, Laser Physics and Spectroscopy, 2018
We define Bell States as maximally entangled two-qubit states. () |Φ1〉=12[|00〉+|11〉], () |Φ2〉=12[|00〉−|11〉], () |ψ1〉=12[|01〉+|10〉], () |ψ2〉=12[|01〉−|10〉].
It Takes Two to Tangle
Published in Jonathan P. Dowling, Schrödinger’s Web, 2020
There are four two-photon entangled states, called the Bell states, and they are |Φ±⟩AB=H⟩AH⟩B±V⟩AV⟩B and |Ψ±⟩AB=H⟩AV⟩B±V⟩AH⟩B. Given any one of them, we can manipulate it into any other using polarization rotators. In this way, the Bell states are all just one kind of state. We now have very bright sources that can produce any one of these at the rate of about a million pairs per second, compared to Clauser’s rate of about 100 pairs per second. This bright source is mounted on the Chinese satellite. As we shall show, the quantum internet will be composed of nodes that do nothing but spew out these Bell states to other members on the network. Once Alice and Bob share a large number of Bell states, they can use them to do quantum teleportation, distributed quantum computing, build a quantum repeater, and carry out quantum cryptographic key distribution. All of these protocols allow us to move quantum information around on the network securely. One protocol we’ll discuss is the entanglement-based cryptography protocol developed in 1991 by Polish physicist Artur Ekert. His scheme uses the Bell test and entangled photon pairs to establish an unbreakable cryptographic key. When Ekert showed this idea to Bell, Bell exclaimed, “Are you telling me that this could be of practical use!?”
A perfect multi-hop teleportation scheme for transfer of five-qubit entangled states using intermediate nodes
Published in Journal of Modern Optics, 2018
Binayak S. Choudhury, Soumen Samanta
Two-qubit entangled states are teleported by following a number of protocols which appear in works like [6,18–23]. In 2005, Gustavo Rigolin [18] presented a teleportation scheme in which an arbitrary two-qubit state is deterministically teleported from Alice to Bob using Bell states. In the same year, Cola et al. [19] a teleportation protocol was described for bipartite states with the help of an entangled pair and an additional qubit. After that, Tsai et al. [20] presented a teleportation scheme in which a pure EPR state could be perfectly teleported using GHZ-like states. In 2014, Zhu [21] described a perfect teleportation protocol of an arbitrary two-qubit state via GHZ-like states.
Effect of Fourier transform on the streaming in quantum lattice gas algorithms
Published in Radiation Effects and Defects in Solids, 2018
Armen Oganesov, George Vahala, Linda Vahala, Min Soe
But now consider the so-called Bell state (1): This cannot be represented by the classical tensor product space spanned by Equation (2): e.g. to omit the -term from the Bell state, we must have either or . However, would drop the -state from the Bell state, while if then the ket would be missing from the Bell state. Classically, one is treating the two qubits as independent of each other – but the Bell state requires correlations between the two qubits, i.e. the qubits are ‘entangled’. It is the exploitation of this quantum entanglement that can lead to quantum algorithms that are faster than any classical counterpart.