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{{Short description|Physical phenomenon}}{{More footnotes|date=June 2012}}
'''Quantum teleportation''' is a process in which [[quantum information]] (e.g. the exact state of an atom or photon) can be transmitted (exactly, in principle)  from one location to another, with the help of [[Classical information#Classical versus quantum information|classical communication]] and previously shared [[quantum entanglement]] between the sending and receiving location. Because it depends on classical communication, which can proceed no faster than the speed of light, it cannot be used for [[faster-than-light]] transport or communication of classical bits. While it has proven possible to teleport one or more [[qubit]]s of information between two (entangled) quanta,<ref name="nyt"/><ref name="riebe"/><ref name="barrett"/> this has not yet been achieved between anything larger than [[molecules]].<ref>{{Cite journal | url=https://www.popularmechanics.com/science/a25699/how-quantum-teleportation-works/ | title=How Quantum Teleportation Actually Works| journal=Proceedings of the Royal Society of London, Series A| volume=456| issue=1999| pages=1759| date=2017-03-16| last1=Deutsch| first1=David| last2=Hayden| first2=Patrick| doi=10.1098/rspa.2000.0585| arxiv=quant-ph/9906007}}</ref>

Although the name is inspired by the [[teleportation]] commonly used in [[fiction]], quantum teleportation is limited to the transfer of information rather than matter itself. Quantum teleportation is not a form of transportation, but of communication: it provides a way of transporting a qubit from one location to another without having to move a physical particle along with it.

The term was coined by physicist [[Charles H. Bennett (computer scientist)|Charles Bennett]]. The seminal paper<ref name="BBCJPW93">{{cite journal |authors=[[Charles H. Bennett (computer scientist)|C. H. Bennett]], [[Gilles Brassard|G. Brassard]], [[Claude Crépeau|C. Crépeau]], [[Richard Jozsa|R. Jozsa]], [[Asher Peres|A. Peres]], [[William Wootters|W. K. Wootters]] |title=Teleporting an Unknown Quantum State via Dual Classical and Einstein–Podolsky–Rosen Channels |journal=[[Phys. Rev. Lett.]] |volume=70 |issue=13 |pages=1895–1899 |date=1993 |doi=10.1103/PhysRevLett.70.1895 |pmid=10053414 |citeseerx=10.1.1.46.9405 |bibcode=1993PhRvL..70.1895B }}</ref> first expounding the idea of quantum teleportation was published by C. H. Bennett, [[Gilles Brassard|G. Brassard]], [[Claude Crépeau|C. Crépeau]], [[Richard Jozsa|R. Jozsa]], [[Asher Peres|A. Peres]], and [[William Wootters|W. K. Wootters]] in 1993.<ref>[[Anton Zeilinger|A. Zeilinger]], ''Dance of the Photons'', Farrar, Straus and Giroux, New York, 2010, p. 46. ("The quantum mechanical solution [to teleportation] was proposed in 1993 by an international collaboration of six theoretical physicists: Charles Bennett of IBM; Gilles Brassard, Claude Crépeau, and Richard Jozsa of the University of Montreal; Asher Peres of the Technion (the Israel Institute of Technology in Haifa), and William K. Wootters of Williams College... The Bennett-Brassard-Crépeau-Jozsa-Peres-Wootters paper has the title 'Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen channels.' To have the word 'teleporting' in the title of a physics paper was quite unusual at the time, since teleportation was considered to be part of science fiction and a somewhat shaky topic. But apparently, there was no better name for the interesting theoretical discovery these scientists  made, and it was a very fitting name indeed.")</ref> Quantum teleportation was first realized in single photons,<ref>{{cite journal |last1=Bouwmeester | first1 = D. |display-authors=etal  |year=1997 |title=Experimental quantum teleportation |journal=Nature |volume=390 |issue=6660 |pages=575–579 |doi=10.1038/37539 |bibcode=1997Natur.390..575B| arxiv = 1901.11004 }}</ref> later being demonstrated in various material systems such as atoms, ions, electrons and superconducting circuits. The latest reported record distance for quantum teleportation is {{convert|1400|km|mi|abbr=on}} by the group of [[Jian-Wei Pan]] using the [[Quantum Experiments at Space Scale|Micius satellite]] for space-based quantum teleportation.<ref>{{cite journal |last=Ren|first=Ji-Gang|last2=Xu|first2=Ping|last3=Yong|first3=Hai-Lin|last4=Zhang|first4=Liang|last5=Liao|first5=Sheng-Kai|last6=Yin|first6=Juan|last7=Liu|first7=Wei-Yue|last8=Cai|first8=Wen-Qi|last9=Yang|first9=Meng |year=2017 |title=Ground-to-satellite quantum teleportation |journal=Nature |volume=549 |issue=7670|pages=70–73|doi=10.1038/nature23675|pmid=28825708|arxiv=1707.00934|bibcode=2017Natur.549...70R}}</ref><ref>{{Cite web|url=http://time.com/4856222/a-teleportation-to-outer-space/|title=A 'Teleportation' to Outer Space|last=Kluger|first=Jeffrey|website=Time|access-date=2017-07-16}}</ref><ref>{{Cite news|url=http://www.huffingtonpost.co.uk/entry/scientists-teleport-a-photon-from-earth-to-orbit-for-the-first-time_uk_5965ea7de4b09b587d636526|title=Scientists Teleport A Photon From Earth To Orbit For The First Time|date=2017-07-12|work=Huffington Post|access-date=2017-07-16|language=en-AU}}</ref>

==Non-technical summary==
In matters relating to quantum or classical [[information theory]], it is convenient to work with the simplest possible unit of information, the two-state system. In classical information, this is a [[bit]], commonly represented using one or zero (or true or false). The quantum analog of a bit is a quantum bit, or qubit. Qubits encode a type of information, called [[quantum information]], which differs sharply from "classical" information. For example, quantum information can be neither copied (the [[no-cloning theorem]]) nor destroyed (the [[no-deleting theorem]]).

Quantum teleportation provides a mechanism of moving a qubit from one location to another, without having to physically transport the underlying particle to which that qubit is normally attached. Much like the invention of the [[telegraph]] allowed classical bits to be transported at high speed across continents, quantum teleportation holds the promise that one day, qubits could be moved likewise.<ref>{{cite journal |title=The quantum internet |first1=H. J. |last1=Kimble |journal=Nature |volume=453 |issue=7198 |pages=1023–1030 |date=2008 |doi=10.1038/nature07127|pmid=18563153 |bibcode=2008Natur.453.1023K |arxiv=0806.4195 }}</ref><ref>{{cite journal |title=The quantum internet is already being built |author=Michael Lucy |date=2018-04-13 |journal=Cosmos |issue=78 |url=https://cosmosmagazine.com/technology/the-quantum-internet-is-already-being-built |accessdate=2018-10-08}}</ref> {{As of|2015|post=,}} the quantum states of single photons, photon modes, single atoms, atomic ensembles, defect centers in solids, single electrons, and superconducting circuits have been employed as information bearers.<ref>{{cite journal |title=Advances in quantum teleportation |authors=S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa, and S. L. Braunstein |journal=Nature Photonics |volume=9 |issue=10 |pages=641–652 |year=2015 |doi=10.1038/nphoton.2015.154 |arxiv=1505.07831|bibcode=2015NaPho...9..641P }}</ref>

The movement of qubits does not require the movement of "things" any more than communication over the internet does: no quantum object needs to be transported, but it is necessary to communicate two classical bits per teleported qubit from the sender to the receiver. The actual teleportation protocol requires that an [[entangled state|entangled quantum state]] or [[Bell state]] be created, and its two parts shared between two locations (the source and destination, or [[Alice and Bob]]). In essence, a certain kind of [[quantum channel]] between two sites must be established first, before a qubit can be moved. Teleportation also requires a [[communication channel|classical information channel]] to be established, as two classical bits must be transmitted to accompany each qubit. The reason for this is that the results of the measurements must be communicated, and this must be done over ordinary classical communication channels. The need for such classical channels may, at first, seem disappointing; however, this is not unlike ordinary communications, which requires wires, radios or lasers.{{explain|date=April 2018}}{{citation needed|date=April 2018}} What's more, Bell states are most easily shared using [[photon]]s from [[laser]]s,{{citation needed|date=April 2018}} and so teleportation could be done, in principle, through open space, i.e., without the need to send the light through cables or optical fibers.

The quantum states of single atoms have been teleported.<ref name="nyt">New York Times, [https://www.nytimes.com/2004/06/17/us/scientists-teleport-not-kirk-but-an-atom.html Scientists Teleport Not Kirk, but an Atom] (2004)</ref><ref name="barrett">{{cite journal | last1 = Barrett | first1 = M. D. | last2 = Chiaverini | first2 = J. | last3 = Schaetz | first3 = T. | last4 = Britton | first4 = J. | last5 = Itano | first5 = W. M. | last6 = Jost | first6 = J. D. | last7 = Knill | first7 = E. | last8 = Langer | first8 = C. | last9 = Leibfried | first9 = D. | last10 = Ozeri | first10 = R. | last11 = Wineland | first11 = D. J. | date = 2004 | title = Deterministic quantum teleportation of atomic qubits | journal = Nature | volume = 429 | issue = 6993| pages = 737–739 | doi = 10.1038/nature02608 | pmid = 15201904 |bibcode = 2004Natur.429..737B }}</ref><ref name="riebe">{{cite journal | last1 = Riebe | first1 = M. | last2 = Häffner | first2 = H. | last3 = Roos | first3 = C. F. | last4 = Hänsel | first4 = W. | last5 = Benhelm | first5 = J. | last6 = Lancaster | first6 = G. P. T. | last7 = Körber | first7 = T. W. | last8 = Becher | first8 = C. | last9 = Schmidt-Kaler | first9 = F. | last10 = James | first10 = D. F. V. | last11 = Blatt | first11 = R. | date = 2004 | title = Deterministic quantum teleportation with atoms | journal = Nature | volume = 429 | issue = 6993| pages = 734–737 | doi = 10.1038/nature02570 | pmid = 15201903 |bibcode = 2004Natur.429..734R }}</ref> Quantum states can be encoded in various degrees of freedom of atoms. For example, qubits can be encoded in the degrees of freedom of electrons surrounding the [[atomic nucleus]] or in the degrees of freedom of the nucleus itself. It is inaccurate to say "an atom has been teleported". It is the quantum state of an atom that is teleported. Thus, performing this kind of teleportation requires a stock of atoms at the receiving site, available for having qubits imprinted on them.<ref name="barrett">{{cite journal | last1 = Barrett | first1 = M. D. | last2 = Chiaverini | first2 = J. | last3 = Schaetz | first3 = T. | last4 = Britton | first4 = J. | last5 = Itano | first5 = W. M. | last6 = Jost | first6 = J. D. | last7 = Knill | first7 = E. | last8 = Langer | first8 = C. | last9 = Leibfried | first9 = D. | last10 = Ozeri | first10 = R. | last11 = Wineland | first11 = D. J. | date = 2004 | title = Deterministic quantum teleportation of atomic qubits | journal = Nature | volume = 429 | issue = 6993| pages = 737–739 | doi = 10.1038/nature02608 | pmid = 15201904 |bibcode = 2004Natur.429..737B }}</ref> The importance of teleporting the nuclear state is unclear:{{citation needed|date=April 2018}} the nuclear state does affect{{how|date=April 2018}} the atom, e.g. in [[hyperfine splitting]], but whether such state would need to be teleported in some futuristic "practical" application is debatable.{{according to whom|date=April 2018}}

An important aspect of quantum information theory is entanglement, which imposes statistical correlations between otherwise distinct physical systems. These correlations hold even when measurements are chosen and performed independently, out of causal contact from one another, as verified in [[Bell test experiments]]. Thus, an observation resulting from a measurement choice made at one point in spacetime seems to instantaneously affect outcomes in another region, even though light hasn't yet had time to travel the distance; a conclusion seemingly at odds with [[special relativity]] ([[EPR paradox]]). However such correlations can never be used to transmit any information faster than the speed of light, a statement encapsulated in the [[no-communication theorem]]. Thus, teleportation, as a whole, can never be [[superluminal]], as a qubit cannot be reconstructed until the accompanying classical information arrives.

Understanding quantum teleportation requires a good grounding in finite-dimensional [[linear algebra]], [[Hilbert space]]s and [[projection matrix]]es. A qubit is described using a two-dimensional [[complex number]]-valued [[vector space]] (a Hilbert space), which are the primary basis for the formal manipulations given below. A working knowledge of quantum mechanics is not absolutely required to understand the mathematics of quantum teleportation, although without such acquaintance, the deeper meaning of the equations may remain quite mysterious.

==Protocol==
[[File:Quantum teleportation diagram.PNG|300px|thumb|right| Diagram for quantum teleportation of a photon]]

The prerequisites for quantum teleportation are a qubit that is to be teleported, a conventional [[communication channel]] capable of transmitting two classical bits (i.e., one of four states), and means of generating an entangled EPR pair of qubits, transporting each of these to two different locations, A and B, performing a [[Bell measurement]] on one of the EPR pair qubits, and manipulating the quantum state of the other pair. The [[protocol (computing)|protocol]] is then as follows:

# An EPR pair is generated, one qubit sent to location A, the other to B.
# At location A, a Bell measurement of the EPR pair qubit and the qubit to be teleported (the quantum state <math>|\phi \rangle</math>) is performed, yielding one of four measurement outcomes, which can be encoded in two classical bits of information. Both qubits at location A are then discarded.
# Using the classical channel, the two bits are sent from A to B. (This is the only potentially time-consuming step after step 1, due to speed-of-light considerations.)
# As a result of the measurement performed at location A, the EPR pair qubit at location B is in one of four possible states. Of these four possible states, one is identical to the original quantum state <math>|\phi \rangle</math>, and the other three are closely related. Which of these four possibilities actually obtained, is encoded in the two classical bits. Knowing this, the EPR pair qubit at location B is modified in one of three ways, or not at all, to result in a qubit identical to <math>|\phi \rangle</math>, the qubit that was chosen for teleportation.

It is worth to notice that the above protocol assumes that the qubits are individually addressable, that means the qubits are distinguishable and physically labeled. However, there can be situations where two identical qubits are indistinguishable due to the spatial overlap of their wave functions. Under this condition, the qubits cannot be individually controlled or measured. Nevertheless, a teleportation protocol analogous to that described above can still be (conditionally) implemented by exploiting two independently-prepared qubits, with no need of an initial EPR pair. This can be made by addressing the internal degrees of freedom of the qubits (e.g., spins or polarizations) by spatially localized measurements performed in separated regions A and B shared by the wave functions of the two indistinguishable qubits.<ref>{{Cite journal | doi=10.1103/PhysRevLett.120.240403| pmid=29957003|title = Indistinguishability of Elementary Systems as a Resource for Quantum Information Processing| journal=Physical Review Letters| volume=120| issue=24| pages=240403|year = 2018|last1 = Lo Franco|first1 = Rosario| last2=Compagno| first2=Giuseppe| arxiv=1712.00706}}</ref>

== Experimental results and records ==
Work in 1998 verified the initial predictions,<ref name="Rome1998">{{cite journal
|journal=[[Physical Review Letters]]
|volume=80
|issue=6
|pages=1121–1125
|doi= 10.1103/PhysRevLett.80.1121
|title=Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels
|author=D. Boschi
|author2=S. Branca |author3=F. De Martini |author4=L. Hardy |author5=S. Popescu
 |date=1998
|arxiv = quant-ph/9710013 |bibcode = 1998PhRvL..80.1121B }}</ref> and the distance of teleportation was increased in August 2004 to 600 meters, using [[optical fiber]].<ref name="Danube2004">{{cite journal
|url=http://www.nature.com/nature/journal/v430/n7002/full/430849a.html
|title=Quantum teleportation across the Danube
|author=Rupert Ursin
|date=August 2004
|journal=Nature
|accessdate=2010-05-22
|volume=430
}}</ref> Subsequently, the record distance for quantum teleportation has been gradually increased to {{convert|16|km}},<ref>{{cite journal|title=Experimental free-space quantum teleportation|first1=Xian-Min|last1=Jin|first2=Ji-Gang|last2=Ren|first3=Bin|last3=Yang|first4=Zhen-Huan|last4=Yi|first5=Fei|last5=Zhou|first6=Xiao-Fan|last6=Xu|first7=Shao-Kai|last7=Wang|first8=Dong|last8=Yang|first9=Yuan-Feng|last9=Hu|first10=Shuo|last10=Jiang|first11=Tao|last11=Yang|first12=Hao|last12=Yin|first13=Kai|last13=Chen|first14=Cheng-Zhi|last14=Peng|first15=Jian-Wei|last15=Pan|date=16 May 2010|journal=Nature Photonics|volume=4|issue=6|pages=376|doi=10.1038/nphoton.2010.87|bibcode=2010NaPho...4..376J}}</ref> then to {{cvt|97|km}},<ref>{{cite journal|title=Quantum teleportation over 143 kilometres using active feed-forward|first1=Xiao-Song|last1=Ma|first2=Thomas|last2=Herbst|first3=Thomas|last3=Scheidl|first4=Daqing|last4=Wang|first5=Sebastian|last5=Kropatschek|first6=William|last6=Naylor|first7=Bernhard|last7=Wittmann|first8=Alexandra|last8=Mech|first9=Johannes|last9=Kofler|first10=Elena|last10=Anisimova|first11=Vadim|last11=Makarov|first12=Thomas|last12=Jennewein|first13=Rupert|last13=Ursin|first14=Anton|last14=Zeilinger|date=5 September 2012|journal=Nature|volume=489|issue=7415|pages=269–73|doi=10.1038/nature11472|pmid=22951967|bibcode=2012Natur.489..269M}}</ref> and is now {{cvt|143|km}}, set in open air experiments in the [[Canary Islands]], done between the two [[Astronomical observatory|astronomical observatories]] of the [[Instituto de Astrofísica de Canarias]].<ref name="ReferenceA">{{Cite journal|last2=Herbst|first2=T.|last3=Scheidl|first3=T.|last4=Wang|first4=D.|last5=Kropatschek|first5=S.|last6=Naylor|first6=W.|last7=Wittmann|first7=B.|last8=Mech|first8=A.|last9=Kofler|first9=J.|displayauthors=8|date=2012|title=Quantum teleportation over 143 kilometres using active feed-forward|journal=Nature|volume=489|issue=7415|pages=269–273|bibcode=2012Natur.489..269M|doi=10.1038/nature11472|pmid=22951967|last1=Ma|first1=X. S.}}</ref>  There has been a recent record set ({{As of|2015|September|lc=y}}) using superconducting nanowire detectors that reached the distance of {{cvt|102|km|mi}} over optical fiber.<ref>{{cite journal|last1=Takesue|first1=Hiroki|display-authors=etal|title=Quantum teleportation over 100 km of fiber using highly efficient superconducting nanowire single-photon detectors|journal=Optica|date=2015-10-20|volume=2|issue=10|pages=832–835|doi=10.1364/OPTICA.2.000832|url=https://www.osapublishing.org/abstract.cfm?URI=optica-2-10-832|accessdate=2016-07-26|arxiv=1510.00476}}</ref>  For material systems, the record distance is {{convert|21|m}}.<ref>{{Cite journal|arxiv=1212.3127|last1=Nölleke|first1=Christian|title=Efficient Teleportation between Remote Single-Atom Quantum Memories|journal=Physical Review Letters|volume=110|issue=14|pages=140403|last2=Neuzner|first2=Andreas|last3=Reiserer|first3=Andreas|last4=Hahn|first4=Carolin|last5=Rempe|first5=Gerhard|last6=Ritter|first6=Stephan|year=2013|doi=10.1103/PhysRevLett.110.140403|pmid=25166964|bibcode=2013PhRvL.110n0403N}}</ref>

A variant of teleportation called "open-destination" teleportation, with receivers located at multiple locations, was demonstrated in 2004 using five-photon entanglement.<ref>Nature 430, 54–58 (1 July 2004) http://www.nature.com/nature/journal/v430/n6995/full/nature02643.html</ref> Teleportation of a composite state of two single photons has also been realized.<ref>Experimental quantum teleportation of a two-qubit composite system Qiang Zhang, Alexander Goebel, Claudia Wagenknecht, Yu-Ao Chen, Bo Zhao, Tao Yang, Alois Mair, Jörg Schmiedmayer & Jian-Wei Pan Nature Physics 2, 678–682</ref> In April 2011, experimenters reported that they had demonstrated teleportation of wave packets of light up to a bandwidth of 10&nbsp;MHz while preserving strongly nonclassical superposition states.<ref name="Lee2011">{{cite journal|last=Lee|first=Noriyuki|author2=Hugo Benichi|author3=Yuishi Takeno|author4=Shuntaro Takeda|author5=James Webb|author6=[[Elanor Huntington]]|author7=Akira Furusawa|date=April 2011|title=Teleportation of Nonclassical Wave Packets of Light|journal=Science|volume=332|issue=6027|pages=330–333|arxiv=1205.6253|bibcode=2011Sci...332..330L|citeseerx=10.1.1.759.1059|doi=10.1126/science.1201034|pmid=21493853}}</ref><ref name=NewQuantTelep>{{cite web|last=Trute|first=Peter|title=Quantum teleporter breakthrough|url=http://www.unsw.edu.au/news/pad/articles/2011/apr/Quantum_teleport_paper.html|publisher=The University Of New South Wales|accessdate=17 April 2011}}</ref>  In August 2013, the achievement of "fully deterministic" quantum teleportation, using a hybrid technique, was reported.<ref>Takeda et al., [http://www.nature.com/nature/journal/v500/n7462/abs/nature12366.html "Deterministic quantum teleportation of photonic quantum bits by a hybrid technique"], ''Nature'', August 2013.</ref> On 29 May 2014, scientists announced a reliable way of transferring data by quantum teleportation. Quantum teleportation of data had been done before but with highly unreliable methods.<ref name="NYT-20140529">{{cite news |last=Markoff |first=John |title=Scientists Report Finding Reliable Way to Teleport Data |url=https://www.nytimes.com/2014/05/30/science/scientists-report-finding-reliable-way-to-teleport-data.html |date=29 May 2014 |work=[[The New York Times]] |accessdate=29 May 2014 }}</ref><ref name="SCI-20140529">{{cite journal |author=Pfaff, W. |title=Unconditional quantum teleportation between distant solid-state quantum bits |date=29 May 2014 |journal=[[Science (journal)|Science]] |doi=10.1126/science.1253512 |arxiv = 1404.4369 |bibcode = 2014Sci...345..532P |display-authors=etal |volume=345 |issue=6196 |pages=532–535 |pmid=25082696}}</ref> On 26 February 2015, scientists at the [[University of Science and Technology of China]] in Hefei, led by [[Chao-yang Lu]] and [[Jian-Wei Pan]] carried out the first experiment teleporting multiple degrees of freedom of a quantum particle. They managed to teleport the quantum information from ensemble of rubidium atoms to another ensemble of rubidium atoms over a distance of {{convert|150|m}} using entangled photons.<ref>{{cite web|title=Two quantum properties teleported together for first time|url=http://physicsworld.com/cws/article/news/2015/feb/27/two-quantum-properties-teleported-together-for-first-time|publisher=PhysicsWorld.com|date=27 February 2015}}</ref><ref name=nature-20150226>{{cite journal |last=Wang |first=Xi-Lin |author2=Xin-Dong Cai |author3=Zu-En Su |author4=Ming-Cheng Chen |author5=Dian Wu |author6=Li Li |author7=Nai-Le Liu | author8=Chao-Yang Lu | author9=Jian-Wei Pan |date=26 February 2015 |title=Quantum teleportation of multiple degrees of freedom of a single photon |journal=Nature |volume=518 |issue=7540 |pages=516–519 |doi=10.1038/nature14246 |pmid=25719668 |bibcode=2015Natur.518..516W }}</ref><ref name="Quantum Science and Technology">{{cite journal |last=Xia |first=Xiu-Xiu |author2=Qi-Chao Sun |author3=Qiang Zhang |author4=Jian-Wei Pan |date=2018 |title=Long distance quantum teleportation |journal=Quantum Science and Technology |volume=3 |issue= 1|pages=014012 |doi=10.1088/2058-9565/aa9baf |bibcode=2018QS&T....3a4012X }}</ref> In 2016, researchers demonstrated quantum teleportation with two independent sources which are separated by {{cvt|6.5|km}} in Hefei optical fiber network.<ref>{{Cite journal|last=Sun|first=Qi-Chao|last2=Mao|first2=Ya-Li|last3=Chen|first3=Sijing|last4=Zhang|first4=Wei|last5=Jiang|first5=Yang-Fan|last6=Zhang|first6=Yanbao|last7=Zhang|first7=Weijun|last8=Miki|first8=Shigehito|last9=Yamashita|first9=Taro|last10=Terai|first10=Hirotaka|last11=Jiang|first11=Xiao|last12=Chen|first12=Teng-Yun|last13=You|first13=Lixing|last14=Chen|first14=Xianfeng|last15=Wang|first15=Zhen|last16=Fan|first16=Jingyun|last17=Zhang|first17=Qiang|last18=Pan|first18=Jian-Wei|date=2016-09-19|title=Quantum teleportation with independent sources and prior entanglement distribution over a network|journal=Nature Photonics|language=En|volume=10|issue=10|pages=671–675|doi=10.1038/nphoton.2016.179|issn=1749-4893|arxiv=1602.07081}}</ref> In September 2016, researchers at the University of Calgary demonstrated quantum teleportation over the Calgary metropolitan fiber network over a distance of {{cvt|6.2|km}}.<ref>{{Cite journal|last=Valivarthi|first=Raju|last2=Puigibert|first2=Marcel.li Grimau|last3=Zhou|first3=Qiang|last4=Aguilar|first4=Gabriel H.|last5=Verma|first5=Varun B.|last6=Marsili|first6=Francesco|last7=Shaw|first7=Matthew D.|last8=Nam|first8=Sae Woo|last9=Oblak|first9=Daniel|date=2016-09-19|title=Quantum teleportation across a metropolitan fibre network|journal=Nature Photonics|volume=10|issue=10|pages=676–680|doi=10.1038/nphoton.2016.180|issn=1749-4885|arxiv=1605.08814|bibcode=2016NaPho..10..676V}}</ref>

Researchers have also successfully used quantum teleportation to transmit information between clouds of gas atoms, notable because the clouds of gas are macroscopic atomic ensembles.<ref>{{cite web|title=Quantum teleportation between atomic systems over long distances|url=http://phys.org/news/2013-06-quantum-teleportation-atomic-distances.html|publisher=Phys.Org}}</ref><ref>{{cite journal|title=Deterministic quantum teleportation between distant atomic objects|first1=H.|last1=Krauter|first2=D.|last2=Salart|first3=C. A.|last3=Muschik|first4=J. M.|last4=Petersen|first5=Heng|last5=Shen|first6=T.|last6=Fernholz|first7=E. S.|last7=Polzik|date=2 June 2013|journal=Nature Physics|volume=9|issue=7|pages=400|doi=10.1038/nphys2631|arxiv=1212.6746|bibcode=2013NatPh...9..400K}}</ref>

In 2018, physicists at Yale demonstrated a deterministic teleported [[Controlled NOT gate|CNOT]] operation between [[Quantum error correction#Bosonic codes|logically encoded]] qubits.<ref>K.S. Chou et al., ''Deterministic teleportation of a quantum gate between two logical qubits.'' https://arxiv.org/abs/1801.05283</ref>

==Formal presentation==
There are a variety of ways in which the teleportation protocol can be written mathematically. Some are very compact but abstract, and some are verbose but straightforward and concrete. The presentation below is of the latter form: verbose, but has the benefit of showing each quantum state simply and directly. Later sections review more compact notations.

The teleportation protocol begins with a quantum state or qubit <math>|\psi\rangle</math>, in Alice's possession, that she wants to convey to Bob. This qubit can be written generally, in [[bra–ket notation]], as:

:<math>|\psi\rangle_C = \alpha |0\rangle_C + \beta|1\rangle_C.</math>

The subscript ''C'' above is used only to distinguish this state from ''A'' and ''B'', below.

Next, the protocol requires that Alice and Bob share a maximally entangled state. This state is fixed in advance, by mutual agreement between Alice and Bob, and can be any one of the four Bell states shown. It does not matter which one.

:<math>|\Phi^+\rangle_{AB} = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_{B} + |1\rangle_A \otimes |1\rangle_{B})</math>,
:<math>|\Phi^-\rangle_{AB} = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_{B} - |1\rangle_A \otimes |1\rangle_{B})</math>,
:<math>|\Psi^+\rangle_{AB} = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |1\rangle_{B} + |1\rangle_A \otimes |0\rangle_{B})</math>,
:<math>|\Psi^-\rangle_{AB} = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |1\rangle_{B} - |1\rangle_A \otimes |0\rangle_{B})</math>.

In the following, assume that Alice and Bob share the state <math>|\Phi^+\rangle_{AB}.</math>
Alice obtains one of the particles in the pair, with the other going to Bob. (This is implemented by preparing the particles together and shooting them to Alice and Bob from a common source.) The subscripts ''A'' and ''B'' in the entangled state refer to Alice's or Bob's particle.

At this point, Alice has two particles (''C'', the one she wants to teleport, and ''A'', one of the entangled pair), and Bob has one particle, ''B''. In the total system, the state of these three particles is given by

:<math> |\psi\rangle_C\otimes|\Phi^+\rangle_{AB}   = (\alpha |0\rangle_C + \beta|1\rangle_C)\otimes\frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_B + |1\rangle_A \otimes |1\rangle_B) . </math>

Alice will then make a local measurement in the Bell basis (i.e. the four Bell states) on the two particles in her possession. To make the result of her measurement clear, it is best to write the state of Alice's two qubits as superpositions of the Bell basis. This is done by using the following general identities, which are easily verified:

:<math>|0\rangle \otimes |0\rangle = \frac{1}{\sqrt{2}} (|\Phi^+\rangle + |\Phi^-\rangle),</math>

:<math>|0\rangle \otimes |1\rangle = \frac{1}{\sqrt{2}} (|\Psi^+\rangle + |\Psi^-\rangle),</math>

:<math>|1\rangle \otimes |0\rangle = \frac{1}{\sqrt{2}} (|\Psi^+\rangle - |\Psi^-\rangle),</math>

and

:<math>|1\rangle \otimes |1\rangle = \frac{1}{\sqrt{2}} (|\Phi^+\rangle - |\Phi^-\rangle).</math>

One applies these identities with ''A'' and ''C'' subscripts. The total three particle state, of ''A'', ''B'' and ''C'' together, thus becomes the following four-term superposition:

:<math>
\begin{align}
| & \psi\rangle_C \otimes\ |\Phi^+\rangle_{AB} \   = \\
\frac{1}{2} \Big \lbrack
\ & |\Phi^+\rangle_{AC} \otimes (\alpha |0\rangle_B + \beta|1\rangle_B)
\ + \ |\Phi^-\rangle_{AC} \otimes (\alpha |0\rangle_B - \beta|1\rangle_B) \\
\ + \ & |\Psi^+\rangle_{AC} \otimes (\beta |0\rangle_B + \alpha|1\rangle_B)
\ + \ |\Psi^-\rangle_{AC} \otimes (\alpha |1\rangle_B - \beta|0\rangle_B) \Big \rbrack . \\
\end{align}
</math><ref>{{Cite book|title=Quantum Computation and Quantum Information|last=Chuang|first=Nielsen|year=|isbn=|location=|pages=26–27}}</ref>

The above is just a change of basis on Alice's part of the system. No operation has been performed and the three particles are still in the same total state. The actual teleportation occurs when Alice measures her two qubits A,C, in the Bell basis

:<math>|\Phi^+\rangle_{AC}, |\Phi^-\rangle_{AC}, |\Psi^+\rangle_{AC}, |\Psi^-\rangle_{AC}</math>.

Experimentally, this measurement may be achieved via a series of laser pulses directed at the two particles{{citation needed|date=June 2018}}. Given the above expression, evidently the result of Alice's (local) measurement is that the three-particle state would [[Wave function collapse|collapse]] to one of the following four states (with equal probability of obtaining each):

*<math>|\Phi^+\rangle_{AC} \otimes (\alpha |0\rangle_B + \beta|1\rangle_B)</math>
*<math>|\Phi^-\rangle_{AC} \otimes (\alpha |0\rangle_B - \beta|1\rangle_B)</math>
*<math>|\Psi^+\rangle_{AC} \otimes (\alpha |1\rangle_B + \beta |0\rangle_B)</math>
*<math>|\Psi^-\rangle_{AC} \otimes (\alpha |1\rangle_B - \beta |0\rangle_B)</math>

Alice's two particles are now entangled to each other, in one of the four [[Bell states]], and the entanglement originally shared between Alice's and Bob's particles is now broken. Bob's particle takes on one of the four superposition states shown above. Note how Bob's qubit is now in a state that resembles the state to be teleported. The four possible states for Bob's qubit are unitary images of the state to be teleported.

The result of Alice's Bell measurement tells her which of the above four states the system is in. She can now send her result to Bob through a classical channel. Two classical bits can communicate which of the four results she obtained.

After Bob receives the message from Alice, he will know which of the four states his particle is in. Using this information, he performs a unitary operation on his particle to transform it to the desired state <math>\alpha |0\rangle_B + \beta|1\rangle_B</math>:

*If Alice indicates her result is <math>|\Phi^+\rangle_{AC}</math>, Bob knows his qubit is already in the desired state and does nothing. This amounts to the trivial unitary operation, the identity operator.
*If the message indicates <math>|\Phi^-\rangle_{AC}</math>, Bob would send his qubit through the unitary [[quantum gate]] given by the [[Pauli matrix]]

:<math>\sigma_3 = \begin{bmatrix} 1 & 0 \\ 0 & -1\end{bmatrix}</math>

to recover the state.

*If Alice's message corresponds to <math>|\Psi^+\rangle_{AC}</math>, Bob applies the gate

:<math>\sigma_1 = \begin{bmatrix} 0 & 1 \\ 1 & 0\end{bmatrix}</math>

to his qubit.

*Finally, for the remaining case, the appropriate gate is given by

:<math>  \sigma_1 \sigma_3  =  - \sigma_3 \sigma_1 =  -i \sigma_2 = \begin{bmatrix} 0 & -1 \\ 1 & 0\end{bmatrix}.</math>

Teleportation is thus achieved. The above-mentioned three gates correspond to rotations of π radians (180°) about appropriate axes (X, Y and Z) in the [[Bloch sphere]] picture of a qubit.

Some remarks:

* After this operation, Bob's qubit will take on the state <math>|\psi\rangle_B= \alpha |0\rangle_B + \beta|1\rangle_B</math>, and Alice's qubit becomes an (undefined) part of an entangled state. Teleportation does not result in the copying of qubits, and hence is consistent with the [[no cloning theorem]].
* There is no transfer of matter or energy involved. Alice's particle has not been physically moved to Bob; only its state has been transferred. The term "teleportation", coined by Bennett, Brassard, Crépeau, Jozsa, Peres and Wootters, reflects the indistinguishability of quantum mechanical particles.
* For every qubit teleported, Alice needs to send Bob two classical bits of information. These two classical bits do not carry complete information about the qubit being teleported. If an eavesdropper intercepts the two bits, she may know exactly what Bob needs to do in order to recover the desired state. However, this information is useless if she cannot interact with the entangled particle in Bob's possession.
Alice's state in qubit 2 is transferred to Bob's qubit 0 using a priorly entangled pair of qubits between Alice and Bob, qubits 1 and 0.

== Alternative notations ==
{{wide image|Teleport.png|780px| Quantum teleportation in its diagrammatic form.,<ref name=coecke>{{Cite journal|arxiv=0908.1787|last1=Coecke|first1=Bob|title=Quantum Picturalism|journal=Contemporary Physics|volume=51|issue=2010|pages=59–83|year=2009|doi=10.1080/00107510903257624|bibcode=2010ConPh..51...59C}}</ref> employing [[Penrose graphical notation]].<ref name=Penrose>R. Penrose, Applications of negative dimensional tensors, In: Combinatorial Mathematics and its Applications, D.~Welsh (Ed), pages 221–244. Academic Press (1971).</ref> Formally, such a computation takes place in a [[dagger compact category]].  This results in the abstract description of quantum teleportation as employed in [[categorical quantum mechanics]].}}

[[File:Quantum teleportation circuit.svg|300px|thumb|right| [[Quantum circuit]] representation of quantum teleportation]]

There are a variety of different notations in use that describe the teleportation protocol. One common one is by using the notation of [[quantum gate]]s. In the above derivation, the unitary transformation that is the change of basis (from the standard product basis into the Bell basis) can be written using quantum gates. Direct calculation shows that this gate is given by

:<math>G = (H \otimes I) \; C_N</math>

where ''H'' is the one qubit [[Hadamard gate|Walsh-Hadamard gate]] and <math>C_N</math> is the [[Controlled NOT gate]].

== Entanglement swapping ==
Teleportation can be applied not just to pure states, but also [[density matrix|mixed states]], that can be regarded as the state of a single subsystem of an entangled pair. The so-called entanglement swapping is a simple and illustrative example.

If Alice has a particle which is entangled with a particle owned by Bob, and Bob teleports it to Carol, then afterwards, Alice's particle is entangled with Carol's.

A more symmetric way to describe the situation is the following: Alice has one particle, Bob two, and Carol one. Alice's particle and Bob's first particle are entangled, and so are Bob's second and Carol's particle:
                       ___
                      /   \
  Alice-:-:-:-:-:-Bob1 -:- Bob2-:-:-:-:-:-Carol
                      \___/

Now, if Bob does a projective measurement on his two particles in the Bell state basis and communicates the results to Carol, as per the teleportation scheme described above, the state of Bob's first particle can be teleported to Carol's. Although Alice and Carol never interacted with each other, their particles are now entangled.

A detailed diagrammatic derivation of entanglement swapping has been given by [[Bob Coecke]],<ref>Bob Coecke, "The logic of entanglement". ''Research Report PRG-RR-03-12'', 2003. [https://arxiv.org/abs/quant-ph/0402014 arXiv:quant-ph/0402014] (8 page shortversion) [http://web.comlab.ox.ac.uk/oucl/publications/tr/rr-03-12.html (full 160 page version)]</ref> presented in terms of [[categorical quantum mechanics]].

== Generalizations of the Teleportation Protocol ==
The basic teleportation protocol for a qubit described above has been generalized in several directions, in particular regarding the dimension of the system teleported and the number of parties involved (either as sender, controller, or receiver).

==== ''d''-dimensional systems ====
A generalization to <math>d</math>-level systems (so-called [[qudit]]s) is straight forward and was already discussed in the original paper by Bennett ''et al.'':<ref name="BBCJPW93"/> the maximally entangled state of two qubits has to be replaced by a maximally entangled state of two qudits and the Bell measurement by a measurement defined by a maximally entangled orthonormal basis. All possible such generalizations were discussed by Werner in 2001.<ref name="Werner2001">{{cite journal |title=All teleportation and dense coding schemes |last1=Werner |first1=Reinhard F. |date=2001 |journal=J. Phys. A: Math. Gen. |volume=34 |number=35 |pages=7081–7094 |doi=10.1088/0305-4470/34/35/332 |arxiv=quant-ph/0003070|bibcode=2001JPhA...34.7081W }}</ref> 
The generalization to infinite-dimensional so-called [[Continuous-variable quantum information|continuous-variable systems]] was proposed in <ref name="BrKi98">{{cite journal |first1=S. L. |last1=Braunstein |first2=H. J. |last2=Kimble |title=Teleportation of Continuous Quantum Variables |journal=Phys. Rev. Lett. |volume=80 |issue=4 |pages=869–872 |year=1998 |doi=10.1103/PhysRevLett.80.869|url=https://authors.library.caltech.edu/3827/1/BRAprl98.pdf |bibcode=1998PhRvL..80..869B }}</ref> and lead to the first teleportation experiment that worked unconditionally.<ref name="Furu98">{{cite journal |first1=A. |last1=Furusawa |first2=J. L. |last2=Sørensen |first3=S. L. |last3=Braunstein |first4=C. A. |last4=Fuchs |first5=H. J. |last5=Kimble |first6=E. S. |last6=Polzik |title=Unconditional Quantum Teleportation |journal=Science |volume=282 |issue=5389 |pages=706–709 |year=1998 |doi=10.1126/science.282.5389.706|bibcode=1998Sci...282..706F }}</ref>

==== Multipartite versions ====
The use of [[Multipartite entanglement|multipartite entangled states]] instead of a bipartite maximally entangled state allows for several new features: either the sender can teleport information to several receivers either sending the same state to all of them (which allows to reduce the amount of entanglement needed for the process) <ref name="DuCi00">{{cite journal |title=Multiparty teleportation |author=W. Dür and J. I. Cirac |journal=J. Mod. Opt. |volume=47 |date=2000 |issue=2–3 |pages=247–255 |doi=10.1080/09500340008244039|bibcode=2000JMOp...47..247D }}</ref> or teleporting multipartite states <ref name="YeCh06">{{cite journal |title=Teleportation and Dense Coding with Genuine Multipartite Entanglement |first1=Ye |last1=Yeo |first2=Wee Kang |last2=Chua |journal=Phys. Rev. Lett. |volume=96 |issue=6 |pages=060502 |year=2006 |doi=10.1103/PhysRevLett.96.060502|pmid=16605974 |arxiv=quant-ph/0510029 |bibcode=2006PhRvL..96f0502Y }}</ref> or sending a single state in such a way that the receiving parties need to cooperate to extract the information.<ref name="KaBo98">{{cite journal |title=Quantum teleportation using three-particle entanglement |first1=Anders |last1=Karlsson |first2=Mohamed |last2=Bourennane |journal=Phys. Rev. A |volume=58 |issue=6 |pages=4394–4400 |date=1998 |doi=10.1103/PhysRevA.58.4394|bibcode=1998PhRvA..58.4394K }}</ref> A different way of viewing the latter setting is that some of the parties can control whether the others can teleport.

== Logic gate teleportation ==
In general, [[mixed state (physics)|mixed states]] ρ may be transported, and a linear transformation ω applied during teleportation, thus allowing data processing of [[quantum information]]. This is one of the foundational building blocks of quantum information processing. This is demonstrated below.

=== General description ===

A general teleportation scheme can be described as follows. Three quantum systems are involved. System 1 is the (unknown) state ''ρ'' to be teleported by Alice. Systems 2 and 3 are in a maximally entangled state ''ω'' that are distributed to Alice and Bob, respectively. The total system is then in the state

:<math>\rho \otimes \omega.</math>

A successful teleportation process is a [[LOCC]] [[quantum channel]] Φ that satisfies

:<math>(\operatorname{Tr}_{12} \circ \Phi ) (\rho \otimes \omega) = \rho\,,</math>

where Tr<sub>12</sub> is the [[partial trace]] operation with respect systems 1 and 2, and <math>\circ</math> denotes the composition of maps. This describes the channel in the Schrödinger picture.

Taking adjoint maps in the Heisenberg picture, the success condition becomes

:<math>\langle \Phi(\rho \otimes \omega)| I \otimes O \rangle = \langle \rho | O \rangle</math>

for all observable ''O'' on Bob's system. The tensor factor in <math>I \otimes O</math> is <math>12 \otimes 3</math> while that of <math>\rho \otimes \omega</math> is <math>1 \otimes 23</math>.

=== Further details ===

The proposed channel Φ can be described more explicitly. To begin teleportation, Alice performs a local measurement on the two subsystems (1 and 2) in her possession. Assume the local measurement have ''effects''

:<math>{F_i} = {M_i ^2}.</math>

If the measurement registers the ''i''-th outcome, the overall state collapses to

:<math>(M_i \otimes I)(\rho \otimes \omega)(M_i \otimes I).</math>

The tensor factor in <math>(M_i \otimes I)</math> is <math>12 \otimes 3</math> while that of <math>\rho \otimes \omega</math> is <math>1 \otimes 23</math>. Bob then applies a corresponding local operation Ψ''<sub>i</sub>'' on system 3. On the combined system, this is described by

:<math>(Id \otimes \Psi_i)(M_i \otimes I)(\rho \otimes \omega)(M_i \otimes I).</math>

where ''Id'' is the identity map on the composite system <math>1 \otimes 2</math>.

Therefore, the channel Φ is defined by

:<math>\Phi (\rho \otimes \omega) = \sum_i (Id \otimes \Psi_i)(M_i \otimes I)(\rho \otimes \omega)(M_i \otimes I)</math>

Notice Φ satisfies the definition of [[LOCC]]. As stated above, the teleportation is said to be successful if, for all observable ''O'' on Bob's system, the equality

:<math>\langle \Phi(\rho \otimes \omega), I \otimes O \rangle = \langle \rho, O \rangle</math>

holds. The left hand side of the equation is:

:<math>
\sum_i \langle (Id \otimes \Psi_i)(M_i \otimes I)(\rho \otimes \omega)(M_i \otimes I), \; I \otimes O \rangle
</math>

:<math>
= \sum_i \langle (M_i \otimes I)(\rho \otimes \omega)(M_i \otimes I), \; I \otimes \Psi_i ^*(O)\rangle 
</math>

where Ψ''<sub>i</sub>*'' is the adjoint of Ψ''<sub>i</sub>'' in the Heisenberg picture. Assuming all objects are finite dimensional, this becomes

:<math>\sum_i \operatorname{Tr} \; (\rho \otimes \omega)(F_i \otimes \Psi_i^*(O)).</math>

The success criterion for teleportation has the expression

:<math>\sum_i \operatorname{Tr} \; (\rho \otimes \omega)(F_i \otimes \Psi_i ^*(O)) = \operatorname{Tr} \; \rho \cdot O.</math>

==Local explanation of the phenomenon==

A [[Principle of locality#Quantum mechanics|local]] explanation of quantum teleportation is put forward by [[David Deutsch]] and [[Patrick Hayden (scientist)|Patrick Hayden]], with respect to the [[many-worlds interpretation]] of quantum mechanics. Their paper asserts that the two bits that Alice sends Bob contain "locally inaccessible information" resulting in the teleportation of the quantum state. "The ability of quantum information to flow through a classical channel ''[…]'', surviving decoherence, is ''[…]'' the basis of quantum teleportation."<ref>{{Cite journal| arxiv=quant-ph/9906007| last1=Deutsch| first1=David| title=Information Flow in Entangled Quantum Systems| journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences| volume=456| issue=1999| pages=1759–1774| last2=Hayden| first2=Patrick| date=1999| doi=10.1098/rspa.2000.0585|bibcode = 2000RSPSA.456.1759H }}</ref>

==See also==
*[[Quantum complex network]]
* [[Quantum mechanics]]
** [[Introduction to quantum mechanics]]
** [[Quantum computer]]
** [[Quantum cryptography]]
** [[Quantum energy teleportation]]
** [[Quantum nonlocality]]
** [[Uncertainty principle|Heisenberg uncertainty principle]]
* [[Wheeler–Feynman absorber theory]]

==References==

===Specific===
{{Reflist|30em}}

===General===
{{refbegin}}
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*Theoretical proposal:
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** {{cite journal | last1 = Kim | first1 = Y.-H. | last2 = Kulik | first2 = S.P. | last3 = Shih | first3 = Y. | title = Quantum teleportation of a polarization state with a complete bell state measurement | journal = Phys. Rev. Lett. | volume = 86 | issue = 7 | pages = 1370–1373 | date = 2001 | doi=10.1103/PhysRevLett.86.1370 | pmid = 11178086 | bibcode=2001PhRvL..86.1370K |arxiv = quant-ph/0010046 }}
**{{cite journal | last1 = Marcikic | first1 = I. | last2 = Tittel | first2 = W. | last3 = Zbinden | first3 = H. | last4 = Gisin | first4 = N. | date = 2003 | title = Long-Distance Teleportation of Qubits at Telecommunication Wavelengths | journal = Nature | volume = 421 | issue = 6922 | pages = 509–513 | doi=10.1038/nature01376 | pmid = 12556886 | bibcode=2003Natur.421..509M |arxiv = quant-ph/0301178 }}
**{{cite journal | last1 = Ursin | first1 = R. | display-authors = etal   | title = Communications: Quantum Teleportation Link across the Danube | journal = Nature | volume = 430 | issue = 7002 | page = 849 | date = August 2004 | doi=10.1038/430849a | pmid = 15318210 | bibcode=2004Natur.430..849U }}
*First experiments with atoms:
**{{cite journal | last1 = Riebe | first1 = M. | last2 = Häffner | first2 = H. | last3 = Roos | first3 = C. F. | last4 = Hänsel | first4 = W. | last5 = Ruth | first5 = M. | last6 = Benhelm | first6 = J. | last7 = Lancaster | first7 = G. P. T. | last8 = Körber | first8 = T. W. | last9 = Becher | first9 = C. | last10 = Schmidt-Kaler | first10 = F. | last11 = James | first11 = D. F. V. | last12 = Blatt | first12 = R. | date = 2004 | title = Deterministic Quantum Teleportation with Atoms | journal = Nature | volume = 429 | issue = 6993 | pages = 734–737 | doi=10.1038/nature02570 | pmid = 15201903 | bibcode=2004Natur.429..734R }}
**{{cite journal | last1 = Barrett | first1 = M. D. | last2 = Chiaverini | first2 = J. | last3 = Schaetz | first3 = T. | last4 = Britton | first4 = J. | last5 = Itano | first5 = W. M. | last6 = Jost | first6 = J. D. | last7 = Knill | first7 = E. | last8 = Langer | first8 = C. | last9 = Leibfried | first9 = D. | last10 = Ozeri | first10 = R. | last11 = Wineland | first11 = D. J. | date = 2004| title = Deterministic Quantum Teleportation of Atomic Qubits | journal = Nature | volume = 429 | issue = 6993 | pages = 737–739 | doi=10.1038/nature02608 | pmid = 15201904 | bibcode=2004Natur.429..737B }}
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{{refend}}

==External links==
*[http://hansonlab.tudelft.nl/loophole-free-bell-test/ Loophole-free Bell test] - [[Kavli Institute of Nanoscience]]
*[http://www.signandsight.com/features/614.html "Spooky action and beyond"] – Interview with Prof. Dr. Anton Zeilinger about quantum teleportation. Date: 2006-02-16
*[http://www.research.ibm.com/quantuminfo/teleportation/ Quantum Teleportation at IBM]
*[http://www.spacedaily.com/news/physics-04zi.html Physicists Succeed In Transferring Information Between Matter And Light]
*[http://www.physorg.com/news10924.html Quantum telecloning: Captain Kirk's clone and the eavesdropper]
*[https://web.archive.org/web/20081218105859/http://www.math.uwaterloo.ca/~amchilds/talks/pi03.ppt Teleportation-based approaches to universal quantum computation]
*[http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TVK-3TXC7TP-4-1&_cdi=5537&_user=4799849&_orig=search&_coverDate=09%2F01%2F1998&_sk=998799998&view=c&wchp=dGLbVtz-zSkWb&md5=4f615b57a53a67a4268535a9ba311407&ie=/sdarticle.pdf Teleportation as a quantum computation]
*[http://www.iop.org/EJ/article/1367-2630/9/7/211/njp7_7_211.html#nj248372s4 Quantum teleportation with atoms: quantum process tomography]
*[https://web.archive.org/web/20081218105900/http://www.imit.kth.se/QEO/qucomm/DelD19QuComm.pdf Entangled State Teleportation]
*[http://koasas.kaist.ac.kr/bitstream/10203/1029/1/e022316.pdf Fidelity of quantum teleportation through noisy channels by]
*[https://www.cs.technion.ac.il/~talmo/CV/my-new-papers/BHM04-IBM.pdf TelePOVM— A generalized quantum teleportation scheme]
*[https://web.archive.org/web/20081218105859/http://web.am.qub.ac.uk/users/m.s.kim/PRL04236.pdf Entanglement Teleportation via Werner States]
*[http://www.physics.ohio-state.edu/~wilkins/writing/Assign/topics/Q-trans-prl.pdf Quantum Teleportation of a Polarization State]
*[https://books.google.com/books?id=zENRkvFO0SEC&pg=PA224 The Time Travel Handbook: A Manual of Practical Teleportation & Time Travel]
*[https://web.archive.org/web/20081218105859/http://heart-c704.uibk.ac.at/publications/papers/nature04_riebe.pdf letters to nature: Deterministic quantum teleportation with atoms]
*[http://qi.phys.msu.ru/kulik/Papers/p221.pdf Quantum teleportation with a complete Bell state measurement]
*[http://sciencenews.org/view/feature/id/34762/title/Welcome_to_the_Quantum_Internet Welcome to the quantum Internet.] ''Science News'', Aug. 16 2008.
*[http://www.QuantumLab.de Quantum experiments – interactive.]
*[http://lightlike.com/teleport/ A (mostly serious) introduction to quantum teleportation for non-physicists]

{{Quantum computing}}
{{Emerging technologies}}

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[[Category:Quantum information science]]
[[Category:Quantum computing]]
[[Category:Emerging technologies]]
[[Category:Teleportation]]