Quantum entanglement swapping explained

Quantum entanglement swapping is a quantum mechanical concept to extend entanglement from one pair of particles to another, even if those new particles have never interacted before. This process may have application in quantum communication networks and quantum computing.

Concept

Basic principles

Quantum entanglement swapping has three pairs of entangled particles: (A, B), (C, D), & (A, D). Particles A & B are initially entangled, as are particles C & D. One particle from each pair is projected (call them B and C) onto one of the four possible Bell states, a process called a Bell state measurement. The unmeasured particles (A and D) can become entangled. This happens without any direct interaction between them.^[1]

Entanglement swapping is a form of the three component Greenberger–Horne–Zeilinger state; experimental apparatus to demonstrate entanglement swapping are equivalent to the three-particle form of Mermin's device, a thought experiment model designed to explain entanglement.

Entanglement swapping is a form of quantum teleportation.In quantum teleportation, the unknown state of a particle can be sent from one location to another using the combination of a quantum and classical channel. The unknown state is projected by Alice onto a Bell state and the result is communicated to Bob through the classical channel.^[2] In entanglement swapping, the state from one of the two sources is the quantum channel of teleportation and the state from the other source is the unknown being sent to Bob.

Mathematical representation

The mathematical expression for the swapping process is:^[3]

$$\backslash left|\; \backslash psi\; \backslash right\backslash rangle\_\; \backslash otimes\; \backslash left|\; \backslash psi\; \backslash right\backslash rangle\_\; \backslash xrightarrow\; \backslash left|\; \backslash psi\; \backslash right\backslash rangle\_$$

In this expression,

\left| \psi \right\rangle _{XY} refers to an entangled state of X & Y particles while BSM indicates Bell state measurement. A Bell state is one of four specific states of representing two particles with maximal entanglement; a Bell state measurement projects a quantum state onto this basis set.

Potential applications

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.^[4]

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 may support safely transferring quantum information over long routes.^[5]

Quantum repeaters and long-distance communication

Quantum entanglement swapping may allow the construction of quantum repeaters to stretch out quantum communication networks by allowing entanglement to be shared over long distances. Performing entanglement swapping at certain points acts like relaying information without loss.^{[6] [7]}

History

• 1992: Yurke and Stoler show theoretically that entanglement does not require interaction of the final measured particles.^{[8] [3] [9]}
• 1993: The term "entanglement swapping" came from physicists Marek Żukowski, Anton Zeilinger, Michael A. Horne, and Artur K. Ekert in their 1993 paper. They refined the concept to show one can extend entanglement from one particle pair to another using a method called Bell state measurement.^[10]
• 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.^[11]
• 2000s: Later experiments took this further, making it work over longer distances and with more complex quantum states.

Further reading

• Book: Nielsen . M.A. . Chuang . I L. . 2000 . . . 978-1-107-00217-3 . 844974180.
• Book: Bouwmeester . D. . Ekert . A. . Zeilinger . A. . 2000 . The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation . 10.1007/978-3-662-04209-0 . Springer . 978-3-540-66778-0.

External links

• Encyclopedia: Quantum Entanglement . Quantum Entanglement and Information . Stanford Encyclopedia of Philosophy . 2023 . Metaphysics Research Lab, Stanford University . https://plato.stanford.edu/entries/qt-entangle/.
• Web site: Quantum Communication and Entanglement Swapping . Physics World .

Notes and References

1. Zhaoxu . Ji . Peiru . Fan . Huanguo . Zhang . 2022 . Entanglement swapping for Bell states and Greenberger–Horne–Zeilinger states in qubit systems. . Physica A: Statistical Mechanics and Its Applications . 585 . 585 . 126400 . 10.1016/j.physa.2021.126400 . 1911.09875. 2022PhyA..58526400J .
2. Progress in quantum teleportation . Hu . Xiao-Min . Guo . Yu . Liu . Bi-Heng . Li . Chuan-Feng . Guo . Guang-Can . . 5 . 339–353 . 2023 . 6 . 10.1038/s42254-023-00588-x . 2023NatRP...5..339H . 1 September 2024.
3. Horodecki . Ryszard . Horodecki . Pawel . Horodecki . Michal . Horodecki . Karol . Quantum entanglement . Reviews of Modern Physics . quant-ph/0702225 . 10.1103/RevModPhys.81.865 . 2009 . 865–942 . 2009RvMP...81..865H . 81 . 2 . 59577352 .
4. Gisin . N. . Ribordy . G. . Tittel . W. . Zbinden . H. . 2002 . Quantum cryptography . . 74 . 1 . 145–195 . 10.1103/RevModPhys.74.145 . quant-ph/0101098 . 2002RvMP...74..145G .
5. Experimental Multiparticle Entanglement Swapping for Quantum Networking . . Chao-Yang . Lu . Tao . Yang . Jian-Wei . Pan . 103 . 20501 . 10 July 2009 . 020501 . 10.1103/PhysRevLett.103.020501 . 19659188 . 2009PhRvL.103b0501L . 1 September 2024.
6. Optimal Entanglement Swapping in Quantum Repeaters . . Evgeny . Shchukin . Peter . van Loock . 128 . 150502 . 13 April 2022 . 15 . 10.1103/PhysRevLett.128.150502 . 35499889 . 1 September 2024 . 2109.00793. 2022PhRvL.128o0502S .
7. H.-J. . Briegel . W. . Dür . J. I. . Cirac . P. . Zoller . 1998 . Quantum repeaters:The role of imperfect local operations in quantum messages . . 81 . 26 . 5932. 10.1103/PhysRevLett.81.5932 .
8. Yurke . Bernard . Stoler . David . 1992-03-02 . Einstein-Podolsky-Rosen effects from independent particle sources . Physical Review Letters . en . 68 . 9 . 1251–1254 . 10.1103/PhysRevLett.68.1251 . 1992PhRvL..68.1251Y . 0031-9007.
9. Pan . Jian-Wei . Chen . Zeng-Bing . Lu . Chao-Yang . Weinfurter . Harald . Zeilinger . Anton . Żukowski . Marek . 2012-05-11 . Multiphoton entanglement and interferometry . Reviews of Modern Physics . en . 84 . 2 . 777–838 . 10.1103/RevModPhys.84.777 . 0805.2853 . 2012RvMP...84..777P . 0034-6861.
10. . "Event-ready-detectors" Bell experiment via entanglement swapping . M. . Żukowski . Marek Żukowski . A. . Zeilinger . Anton Zeilinger . M. A. . Horne . Michael Horne (physicist) . A. K. . Ekert . Artur Ekert . 71 . 4287 . 27 December 1993 . 26 . 10.1103/PhysRevLett.71.4287 . 1993PhRvL..71.4287Z . 1 September 2024.
11. Pan . J.-W. . Bouwmeester . D. . Weinfurter . H. . Zeilinger . A. . 1998 . Experimental entanglement swapping: Entangling photons that never interacted . . 80 . 18 . 3891–3894 . 10.1103/PhysRevLett.80.3891. 1998PhRvL..80.3891P .