Quantum entanglement swapping

Quantum entanglement swapping is an essential idea in quantum networking. It involves using aspects of quantum mechanics to extend entanglement from one pair of particles to another, even if those new particles have never interacted before. This process is very important for building quantum communication networks, enabling quantum teleportation and advancing quantum computing.

History

Anton Zeilinger, key contributor to the concept and realization of entanglement swapping

Artur K. Ekert, key concept of entanglement swapping in 1993, contributing significantly to quantum cryptography and quantum communication

• 1993: The idea of quantum entanglement swapping came from physicists Marek Żukowski, Anton Zeilinger, Michael A. Horne, and Artur K. Ekert in 1993. Their paper in Physical Review Letters introduced that one can extend entanglement from one particle pair to another using a method called Bell state measurement.
• 1998: Jian-Wei Pan working in Anton Zeilinger's group conducted the first experiment on entanglement swapping. They used entangled photons to show successful transfer of entanglement between pairs that never interacted.
• 2000s: Later experiments took this further, making it work over longer distances and with more complex quantum states.
• 2017: Demonstrated in satellite-based experiments, allowing entanglement distribution over 1200 kilometers.

Concept

Basic principles

Quantum entanglement swapping has three pairs of entangled particles: (A, B), (C, D), & (E, F). Particles A & B are initially entangled, just like C & D. By applying a process called Bell state measurement to one particle from each pair (like B and C), the unmeasured particles (A and D) can become entangled. This happens without any direct interaction between them.

The measurement collapses the states of B and C into one of four Bell states. Due to the laws of quantum mechanics, this instantly determines the state of A and D.

Mathematical representation

In quantum mechanics, a Bell state can be used to represent two particles in an entangled system. The mathematical expression for the swapping process is:

$$\left|\psi \right\rangle _{AB}\otimes \left|\psi \right\rangle _{CD}\xrightarrow {{\text{BSM}}_{BC}} \left|\psi \right\rangle _{AD}$$

In this expression, $\left|\psi \right\rangle _{XY}$ refers to the state of X & Y particles while BSM indicates Bell state measurement.

Development and expansions

Quantum repeaters and long-distance communication

One main use of quantum entanglement swapping is for creating quantum repeaters. These devices help stretch out quantum communication networks by allowing entanglement to be shared over long regions. Performing entanglement swapping at certain points acts like relaying information without loss.

Multi-particle entanglement

The idea of quantum entanglement swapping can be developed further into multi-particle setups. They can lead to discovering ways to create complex entangled states known as GHZ states (Greenberger–Horne–Zeilinger states). These states are crucial for quantum error correction and making fault-tolerant quantum computers.

Satellite-based quantum communication

Experiments on satellite-based quantum communication showed how entanglement can link ground stations via satellites while using entanglement swapping to increase range.

Applications

Quantum teleportation

Entanglement swapping plays an essential role in quantum teleportation, where the state of a particle can be sent from one spot to another without moving the particle itself. This relies on using entangled pairs through the swapping process.

Quantum cryptography

In the field of quantum cryptography, it helps secure communication channels better. By utilizing swapped entanglements between particles' pairs, it is possible to generate secure encryption keys that should be protected against eavesdropping.

Quantum networks

Quantum entanglement swapping also serves as a core technology for designing quantum networks, where many nodes-like quantum computers or communication points-link through these special connections made by entangled links. These networks support safely transferring quantum information over long routes and contribute significantly to building the emerging quantum internet.

Further reading

• Nielsen, M.A.; Chuang, I L. (2000). Quantum Computation and Quantum Information. Cambridge University Press. ISBN 978-1-107-00217-3. OCLC 844974180.
• Bouwmeester, D.; Ekert, A.; Zeilinger, A. (2000). The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation. Springer. doi:10.1007/978-3-662-04209-0. ISBN 978-3-540-66778-0.

External links

• "Quantum Entanglement". Stanford Encyclopedia of Philosophy.
• "Quantum Communication and Entanglement Swapping". Physics World.
• "Research on Quantum Entanglement Swapping". arXiv.org.