# Quantum entanglement

Spontaneous parametric down-conversion process can split photons into type II photon pairs with mutually perpendicular polarization.

Quantum entanglement is the physical phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics lacking in classical mechanics.

Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior gives rise to seemingly paradoxical effects: any measurement of a particle's properties results in an irreversible wave function collapse of that particle and changes the original quantum state. With entangled particles, such measurements affect the entangled system as a whole.

Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen,[1] and several papers by Erwin Schrödinger shortly thereafter,[2][3] describing what came to be known as the EPR paradox. Einstein and others considered such behavior impossible, as it violated the local realism view of causality (Einstein referring to it as "spooky action at a distance")[4] and argued that the accepted formulation of quantum mechanics must therefore be incomplete.

Later, however, the counterintuitive predictions of quantum mechanics were verified[5][6][7] in tests where polarization or spin of entangled particles was measured at separate locations, statistically violating Bell's inequality. In earlier tests, it couldn't be ruled out that the result at one point could have been subtly transmitted to the remote point, affecting the outcome at the second location.[7] However, so-called "loophole-free" Bell tests have been performed where the locations were sufficiently separated that communications at the speed of light would have taken longer—in one case, 10,000 times longer—than the interval between the measurements.[6][5]

According to some interpretations of quantum mechanics, the effect of one measurement occurs instantly. Other interpretations which don't recognize wavefunction collapse dispute that there is any "effect" at all. However, all interpretations agree that entanglement produces correlation between the measurements and that the mutual information between the entangled particles can be exploited, but that any transmission of information at faster-than-light speeds is impossible.[8][9]

Quantum entanglement has been demonstrated experimentally with photons,[10][11] neutrinos,[12] electrons,[13][14] molecules as large as buckyballs,[15][16] and even small diamonds.[17][18] The utilization of entanglement in communication, computation and quantum radar is a very active area of research and development.

1. ^ Einstein A, Podolsky B, Rosen N; Podolsky; Rosen (1935). "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?". Phys. Rev. 47 (10): 777–780. Bibcode:1935PhRv...47..777E. doi:10.1103/PhysRev.47.777.{{cite journal}}: CS1 maint: multiple names: authors list (link)
2. ^ Schrödinger E (1935). "Discussion of probability relations between separated systems". Mathematical Proceedings of the Cambridge Philosophical Society. 31 (4): 555–563. Bibcode:1935PCPS...31..555S. doi:10.1017/S0305004100013554.
3. ^ Schrödinger E (1936). "Probability relations between separated systems". Mathematical Proceedings of the Cambridge Philosophical Society. 32 (3): 446–452. Bibcode:1936PCPS...32..446S. doi:10.1017/S0305004100019137.
4. ^ Physicist John Bell depicts the Einstein camp in this debate in his article entitled "Bertlmann's socks and the nature of reality", p. 143 of Speakable and unspeakable in quantum mechanics: "For EPR that would be an unthinkable 'spooky action at a distance'. To avoid such action at a distance they have to attribute, to the space-time regions in question, real properties in advance of observation, correlated properties, which predetermine the outcomes of these particular observations. Since these real properties, fixed in advance of observation, are not contained in quantum formalism, that formalism for EPR is incomplete. It may be correct, as far as it goes, but the usual quantum formalism cannot be the whole story." And again on p. 144 Bell says: "Einstein had no difficulty accepting that affairs in different places could be correlated. What he could not accept was that an intervention at one place could influence, immediately, affairs at the other." Downloaded 5 July 2011 from Bell, J. S. (1987). Speakable and Unspeakable in Quantum Mechanics (PDF). CERN. ISBN 0521334950. Archived from the original (PDF) on 12 April 2015. Retrieved 14 June 2014.
5. ^ a b Yin, Juan; Cao, Yuan; Yong, Hai-Lin; Ren, Ji-Gang; Liang, Hao; Liao, Sheng-Kai; Zhou, Fei; Liu, Chang; Wu, Yu-Ping; Pan, Ge-Sheng; Li, Li; Liu, Nai-Le; Zhang, Qiang; Peng, Cheng-Zhi; Pan, Jian-Wei (2013). "Bounding the speed of 'spooky action at a distance". Physical Review Letters. 110 (26): 260407. arXiv:1303.0614. Bibcode:2013PhRvL.110z0407Y. doi:10.1103/PhysRevLett.110.260407. PMID 23848853. S2CID 119293698.
6. ^ a b Matson, John (13 August 2012). "Quantum teleportation achieved over record distances". Nature News. doi:10.1038/nature.2012.11163. S2CID 124852641.
7. ^ a b Francis, Matthew. Quantum entanglement shows that reality can't be local, Ars Technica, 30 October 2012
8. ^ Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, London, 2004, p. 603.
9. ^ Griffiths, David J. (2004), Introduction to Quantum Mechanics (2nd ed.), Prentice Hall, ISBN 978-0-13-111892-8
10. ^ Kocher, CA; Commins, ED (1967). "Polarization Correlation of Photons Emitted in an Atomic Cascade". Physical Review Letters. 18 (15): 575–577. Bibcode:1967PhRvL..18..575K. doi:10.1103/PhysRevLett.18.575.
11. ^ Carl A. Kocher, Ph.D. Thesis (University of California at Berkeley, 1967). Polarization Correlation of Photons Emitted in an Atomic Cascade
12. ^ J. A. Formaggio, D. I. Kaiser, M. M. Murskyj, and T. E. Weiss (2016), "Violation of the Leggett-Garg inequality in neutrino oscillations". Phys. Rev. Lett. Accepted 23 June 2016.
13. ^ Hensen, B.; et al. (21 October 2015). "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres". Nature. 526 (7575): 682–686. arXiv:1508.05949. Bibcode:2015Natur.526..682H. doi:10.1038/nature15759. hdl:2117/79298. PMID 26503041. S2CID 205246446. See also free online access version.
14. ^ Markoff, Jack (21 October 2015). "Sorry, Einstein. Quantum Study Suggests 'Spooky Action' Is Real". The New York Times. Retrieved 21 October 2015.
15. ^ Arndt, M; Nairz, O; Vos-Andreae, J; Keller, C; van der Zouw, G; Zeilinger, A (14 October 1999). "Wave–particle duality of C60 molecules". Nature. 401 (6754): 680–682. Bibcode:1999Natur.401..680A. doi:10.1038/44348. PMID 18494170. S2CID 4424892. (subscription required)
16. ^ Olaf Nairz, Markus Arndt, and Anton Zeilinger, "Quantum interference experiments with large molecules", American Journal of Physics, 71 (April 2003) 319–325.
17. ^ Lee, K. C.; Sprague, M. R.; Sussman, B. J.; Nunn, J.; Langford, N. K.; Jin, X.- M.; Champion, T.; Michelberger, P.; Reim, K. F.; England, D.; Jaksch, D.; Walmsley, I. A. (2 December 2011). "Entangling macroscopic diamonds at room temperature". Science. 334 (6060): 1253–1256. Bibcode:2011Sci...334.1253L. doi:10.1126/science.1211914. PMID 22144620. S2CID 206536690.
18. ^ sciencemag.org, supplementary materials