entanglement swapping

File:Entanglement swapping.svg

Entanglement swapping has two pairs of entangled particles: (A, B) and (C, D). Pair of particles (A, B) is initially entangled, as is the pair (C, D). The pair (B, C) taken from the original pairs, is projected onto one of the four possible Bell states, a process called a Bell state measurement. The unmeasured pair of particles (A, D) can become entangled. This effect happens without any previous direct interaction between particles A and D.{{Cite journal

|first1=Zhaoxu |last1=Ji

|first2=Peiru |last2=Fan

|first3=Huanguo |last3=Zhang

|year=2022

|title=Entanglement swapping for Bell states and Greenberger–Horne–Zeilinger states in qubit systems.

|journal=Physica A: Statistical Mechanics and Its Applications

|volume=585

|issue=585

|page=126400

|doi=10.1016/j.physa.2021.126400

|url=https://www.sciencedirect.com/science/article/abs/pii/S0378437121006737

|arxiv=1911.09875

|bibcode=2022PhyA..58526400J

}}

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.{{Cite journal

|title=Progress in quantum teleportation

|last1=Hu |first1=Xiao-Min

|last2=Guo |first2=Yu

|last3=Liu |first3=Bi-Heng

|last4=Li |first4=Chuan-Feng

|last5=Guo |first5=Guang-Can

|journal=Nat. Rev. Phys.

|volume=5

|pages=339–353

|year=2023

|issue=6 |doi=10.1038/s42254-023-00588-x

|bibcode=2023NatRP...5..339H |url=https://www.nature.com/articles/s42254-023-00588-x

|access-date=1 September 2024

}} 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.{{rp|876}}

The mathematical expression for the swapping process is:{{cite journal

|last1 = Horodecki

|first1 = Ryszard

|last2 = Horodecki

|first2 = Pawel

|last3 = Horodecki

|first3 = Michal

|last4 = Horodecki

|first4 = Karol

|title = Quantum entanglement

|journal = Reviews of Modern Physics

|arxiv=quant-ph/0702225

|doi =10.1103/RevModPhys.81.865

|year=2009

|pages=865–942

|bibcode=2009RvMP...81..865H

|volume=81

|issue=2

|s2cid=59577352 }}{{rp|876}}

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

In this expression, $\backslash left|\; \backslash psi\; \backslash right\backslash rangle\_\{XY\}$ refers to an entangled state of pair of particles (X,Y) 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.{{rp|813}}

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.{{Cite journal

|last1=Gisin |first1=N.

|last2=Ribordy |first2=G.

|last3=Tittel |first3=W.

|last4=Zbinden |first4=H.

|year=2002

|title=Quantum cryptography

|journal=Rev. Mod. Phys.

|volume=74 |issue=1

|pages=145–195

|doi=10.1103/RevModPhys.74.145

|arxiv=quant-ph/0101098

|bibcode=2002RvMP...74..145G

|url=https://cdn.journals.aps.org/files/RevModPhys.74.145.pdf

}}

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.{{Cite journal

|title=Experimental Multiparticle Entanglement Swapping for Quantum Networking

|journal=Phys. Rev. Lett.

|first1=Chao-Yang |last1=Lu

|first2=Tao |last2=Yang

|first3=Jian-Wei |last3=Pan

|volume=103 |issue=20501 |date=10 July 2009

|page=020501

|doi=10.1103/PhysRevLett.103.020501

|pmid=19659188

|bibcode=2009PhRvL.103b0501L

|url=https://harvest.aps.org/v2/journals/articles/10.1103/PhysRevLett.103.020501/fulltext

|access-date=1 September 2024

}}

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.{{Cite journal

|title=Optimal Entanglement Swapping in Quantum Repeaters

|journal=Phys. Rev. Lett.

|first1=Evgeny |last1=Shchukin

|first2=Peter |last2=van Loock

|volume=128 |page=150502

|date=13 April 2022

|issue=15

|doi=10.1103/PhysRevLett.128.150502 |pmid=35499889

|url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.150502

|access-date=1 September 2024

|arxiv=2109.00793

|bibcode=2022PhRvL.128o0502S

}}{{Cite journal

|first1=H.-J. |last1=Briegel

|first2=W. |last2=Dür

|first3=J. I. |last3=Cirac

|first4=P. |last4=Zoller

|year=1998

|title=Quantum repeaters:The role of imperfect local operations in quantum messages

|journal=Phys. Rev. Lett.

|volume=81 |issue=26 |page=5932

|doi=10.1103/PhysRevLett.81.5932

}}

Bernard Yurke and David Stoler showed theoretically in 1992 that entanglement does not require interaction of the final measured particles.{{Cite journal |last1=Yurke |first1=Bernard |last2=Stoler |first2=David |date=1992-03-02 |title=Einstein-Podolsky-Rosen effects from independent particle sources |url=https://link.aps.org/doi/10.1103/PhysRevLett.68.1251 |journal=Physical Review Letters |language=en |volume=68 |issue=9 |pages=1251–1254 |doi=10.1103/PhysRevLett.68.1251 |bibcode=1992PhRvL..68.1251Y |issn=0031-9007}}{{rp|876}}{{Cite journal |last1=Pan |first1=Jian-Wei |last2=Chen |first2=Zeng-Bing |last3=Lu |first3=Chao-Yang |last4=Weinfurter |first4=Harald |last5=Zeilinger |first5=Anton |last6=Żukowski |first6=Marek |date=2012-05-11 |title=Multiphoton entanglement and interferometry |url=https://link.aps.org/doi/10.1103/RevModPhys.84.777 |journal=Reviews of Modern Physics |language=en |volume=84 |issue=2 |pages=777–838 |doi=10.1103/RevModPhys.84.777 |arxiv=0805.2853 |bibcode=2012RvMP...84..777P |issn=0034-6861}}{{rp|786|q=Yurke and Stoler

(1992a, 1992b) showed that in theory multiparticle entanglement effects should in principle be observable for particles

originating from independent sources.}}

Using a three component Greenberger–Horne–Zeilinger state, they showed that Mermin's device, a thought experiment model designed to explain entanglement, was equivalent to an EPR experiment where the correlated particles had never directly interacted.

The term entanglement swapping was coined by 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.{{Cite journal

|journal=Phys. Rev. Lett.

|title="Event-ready-detectors" Bell experiment via entanglement swapping

|first1=M. |last1=Żukowski |author-link1=Marek Żukowski

|first2=A. |last2=Zeilinger |author-link2=Anton Zeilinger

|first3=M. A. |last3=Horne |author-link3=Michael Horne (physicist)

|first4=A. K. |last4=Ekert |author-link4=Artur Ekert

|volume=71 |page=4287

|date=27 December 1993

|issue=26

|doi=10.1103/PhysRevLett.71.4287

|bibcode=1993PhRvL..71.4287Z

|url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.71.4287

|access-date=1 September 2024

}}

In 1998 Jian-Wei Pan working in 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.{{Cite journal

|last1=Pan |first1=J.-W.

|last2=Bouwmeester |first2=D.

|last3=Weinfurter |first3=H.

|last4=Zeilinger |first4=A.

|year=1998

|title=Experimental entanglement swapping: Entangling photons that never interacted

|journal=Phys. Rev. Lett.

|volume=80 |issue=18

|pages=3891–3894

|doi=10.1103/PhysRevLett.80.3891

|bibcode=1998PhRvL..80.3891P

}} Later experiments took this further, making it work over longer distances and with more complex quantum states.{{Citation needed|date=November 2024}}

{{reflist}}

• {{Cite book

|last1=Nielsen |first1=M.A.

|last2=Chuang |first2=I L.

|year=2000

|title=Quantum Computation and Quantum Information

|publisher=Cambridge University Press

|isbn= 978-1-107-00217-3

|oclc=844974180

}}

• {{Cite book

|last1=Bouwmeester |first1=D.

|last2=Ekert |first2=A.

|last3=Zeilinger |first3=A.

|year=2000

|title=The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation

|doi=10.1007/978-3-662-04209-0

|publisher=Springer

|isbn=978-3-540-66778-0

}}

• {{Cite encyclopedia

|title=Quantum Entanglement

|chapter=Quantum Entanglement and Information

|encyclopedia=Stanford Encyclopedia of Philosophy

|date=2023

|publisher=Metaphysics Research Lab, Stanford University

|chapter-url=https://plato.stanford.edu/entries/qt-entangle/

}}

• {{Cite web

|title=Quantum Communication and Entanglement Swapping

|website=Physics World

|url=https://physicsworld.com/a/quantum-communication-and-entanglement-swapping/

}}

{{Quantum information}}

Entanglement swapping