Editing Quantum teleportation (section)

== Experimental results and records ==
Work in 1998 verified the initial predictions,<ref name="Rome1998">{{cite journal
|last1=Boschi |first1=D. |last2=Branca |first2=S. |last3=De Martini |first3=F. |last4=Hardy |first4=L. |last5=Popescu |first5=S.
|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
|date=1998-02-09
|arxiv = quant-ph/9710013 |bibcode = 1998PhRvL..80.1121B |s2cid=15020942
}}</ref> and the distance of teleportation was increased in August 2004 to 600 meters, using [[optical fiber]].<ref name="Danube2004">{{cite journal
|title=Quantum teleportation across the Danube
|last1=Ursin |first1=Rupert |last2=Jennewein |first2=Thomas |last3=Aspelmeyer |first3=Markus |last4=Kaltenbaek |first4=Rainer |last5=Lindenthal |first5=Michael |last6=Walther |first6=Philip |last7=Zeilinger |first7=Anton
|date=18 August 2004
|journal=Nature
|volume=430
|issue=7002
|doi=10.1038/430849a
|pmid=15318210
|page=849
|bibcode=2004Natur.430..849U
|s2cid=4426035
|doi-access=free }}</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 name="Ma-2012">{{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=269–273 |doi=10.1038/nature11472 |pmid=22951967 |bibcode=2012Natur.489..269M |arxiv=1205.3909 |s2cid=209109}}</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="Ma-2012"/> 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 |last2=Dyer |first2=Shellee D. |last3=Stevens |first3=Martin J. |last4=Verma |first4=Varun |last5=Mirin |first5=Richard P. |author6=Sae Woo Nam |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 |arxiv=1510.00476 |bibcode=2015Optic...2..832T |s2cid=55109707}}</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 |s2cid=6597459}}</ref>

A variant of teleportation called "open-destination" teleportation, with receivers located at multiple locations, was demonstrated in 2004 using five-photon entanglement.<ref>{{Cite journal | doi=10.1038/nature02643| pmid=15229594| title=Experimental demonstration of five-photon entanglement and open-destination teleportation| journal=Nature| volume=430| issue=6995| pages=54–58| year=2004| last1=Zhao| first1=Zhi| last2=Chen| first2=Yu-Ao| last3=Zhang| first3=An-Ning| last4=Yang| first4=Tao| last5=Briegel| first5=Hans J.| last6=Pan| first6=Jian-Wei| bibcode=2004Natur.430...54Z| arxiv=quant-ph/0402096| s2cid=4336020}}</ref> Teleportation of a composite state of two single qubits has also been realized.<ref>{{Cite journal |arxiv = quant-ph/0609129|doi = 10.1038/nphys417|title = Experimental quantum teleportation of a two-qubit composite system|journal = Nature Physics|volume = 2|issue = 10|pages = 678–682|year = 2006|last1 = Zhang|first1 = Qiang|last2 = Goebel|first2 = Alexander|last3 = Wagenknecht|first3 = Claudia|last4 = Chen|first4 = Yu-Ao|last5 = Zhao|first5 = Bo|last6 = Yang|first6 = Tao|last7 = Mair|first7 = Alois|last8 = Schmiedmayer|first8 = Jörg|last9 = Pan|first9 = Jian-Wei|bibcode = 2006NatPh...2..678Z|s2cid = 18201599}}</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-link=Elanor Huntington |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 |s2cid=206531447}}</ref><ref>{{cite web |last=Trute |first=Peter |title=Quantum teleporter breakthrough |publisher=The University Of New South Wales |url=http://www.unsw.edu.au/news/pad/articles/2011/apr/Quantum_teleport_paper.html |access-date=17 April 2011|archive-url=https://web.archive.org/web/20110418200747/http://www.unsw.edu.au/news/pad/articles/2011/apr/Quantum_teleport_paper.html |archive-date=18 April 2011 |url-status=dead}}</ref> In August 2013, the achievement of "fully deterministic" quantum teleportation, using a hybrid technique, was reported.<ref>{{cite journal |last1=Takeda |first1=Shuntaro |last2=Mizuta |first2=Takahiro |last3=Fuwa |first3=Maria |last4=van Loock |first4=Peter |last5=Furusawa |first5=Akira |title=Deterministic quantum teleportation of photonic quantum bits by a hybrid technique |journal=Nature |date=14 August 2013 |volume=500 |issue=7462|pages=315–318 |doi=10.1038/nature12366|pmid=23955230 |arxiv=1402.4895 |bibcode=2013Natur.500..315T |s2cid=4344887 }}</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>{{cite news |last=Markoff |first=John |title=Scientists Report Finding Reliable Way to Teleport Data |work=[[The New York Times]] |url=https://www.nytimes.com/2014/05/30/science/scientists-report-finding-reliable-way-to-teleport-data.html |date=29 May 2014 |access-date=29 May 2014}}</ref><ref>{{cite journal |vauthors=Pfaff W, Hensen BJ, Bernien H, van Dam SB, Blok MS, Taminiau TH, Tiggelman MJ, Schouten RN, Markham M, Twitchen DJ, Hanson R |title=Unconditional quantum teleportation between distant solid-state quantum bits |date=29 May 2014 |journal=Science |volume=345 |issue=6196 |pages=532–535 |doi=10.1126/science.1253512 |bibcode=2014Sci...345..532P |pmid=25082696 |s2cid=2190249 |arxiv=1404.4369}}</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 |website=PhysicsWorld.com |date=27 February 2015 |url=http://physicsworld.com/cws/article/news/2015/feb/27/two-quantum-properties-teleported-together-for-first-time |last=Commissariat |first=Tushna}}</ref><ref name=nature-20150226>{{cite journal |author1=Xi-Lin Wang |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 |s2cid=4448594 |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|at=014012 |doi=10.1088/2058-9565/aa9baf |bibcode=2018QS&T....3a4012X |s2cid=125240574}}</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|last1=Sun|first1=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 |bibcode=2016NaPho..10..671S |s2cid=126228648}}</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 |last1=Valivarthi |first1=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 |s2cid=119163338}}</ref> In December 2020, as part of the INQNET collaboration, researchers achieved quantum teleportation over a total distance of 44&nbsp;km (27.3&nbsp;mi) with fidelities exceeding 90%.<ref>{{Cite journal |last1=Valivarthi |first1=Raju |last2=Davis |first2=Samantha I. |last3=Peña |first3=Cristián |last4=Xie |first4=Si |last5=Lauk |first5=Nikolai |last6=Narváez |first6=Lautaro |last7=Allmaras |first7=Jason P. |last8=Beyer |first8=Andrew D. |last9=Gim |first9=Yewon |last10=Hussein |first10=Meraj |last11=Iskander |first11=George |date=2020-12-04 |title=Teleportation Systems Toward a Quantum Internet |journal=PRX Quantum |language=en |volume=1 |issue=2 |pages=020317 |doi=10.1103/PRXQuantum.1.020317 |arxiv=2007.11157 |bibcode=2020PRXQ....1b0317V |s2cid=220686903 |issn=2691-3399}}</ref><ref>{{Cite web |last=Tangermann |first=Victor |date=2020-12-18 |title=Researchers Achieve First "Sustained" Long Distance Quantum Teleportation |website=Futurism |url=https://futurism.com/researchers-achieve-first-sustained-long-distance-quantum-teleportation |access-date=2021-06-06}}</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 |author=University of Copenhagen |date=2013-06-13 |title=Quantum teleportation between atomic systems over long distances |url=http://phys.org/news/2013-06-quantum-teleportation-atomic-distances.html |website=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 |s2cid=118724313}}</ref>

It is also possible to teleport ''logical operations'', see [[quantum gate teleportation]]. In 2018, physicists at Yale demonstrated a deterministic teleported [[Controlled NOT gate|CNOT]] operation between [[Quantum error correction#Bosonic codes|logically encoded]] qubits.<ref>{{Cite journal |arxiv = 1801.05283|doi = 10.1038/s41586-018-0470-y|pmid = 30185908|title = Deterministic teleportation of a quantum gate between two logical qubits|journal = Nature|volume = 561|issue = 7723|pages = 368–373|year = 2018|last1 = Chou|first1 = Kevin S.|last2 = Blumoff|first2 = Jacob Z.|last3 = Wang|first3 = Christopher S.|last4 = Reinhold|first4 = Philip C.|last5 = Axline|first5 = Christopher J.|last6 = Gao|first6 = Yvonne Y.|last7 = Frunzio|first7 = L.|last8 = Devoret|first8 = M. H.|last9 = Jiang|first9 = Liang|last10 = Schoelkopf|first10 = R. J.|bibcode = 2018Natur.561..368C|s2cid = 3820071}}</ref>

[[File:Conditional quantum teleportation of photon polarization.png|thumb|Schematic of the quantum teleportation experiment performed by Zeilinger's group in 1997. For details, see the text.]]

First proposed theoretically in 1993, quantum teleportation has since been demonstrated in many different guises. It has been carried out using two-level states of a single photon, a single atom and a trapped ion – among other quantum objects – and also using two photons. In 1997, two groups experimentally achieved quantum teleportation. The first group, led by [[Sandu Popescu]], was based in Italy. An experimental group led by [[Anton Zeilinger]] followed a few months later.

The results obtained from experiments done by Popescu's group concluded that classical channels alone could not replicate the teleportation of linearly polarized state and an elliptically polarized state. The Bell state measurement distinguished between the four Bell states, which can allow for a 100% success rate of teleportation, in an ideal representation.<ref name="Rome1998"/>

Zeilinger's group produced a pair of entangled photons by implementing the process of parametric down-conversion. In order to ensure that the two photons cannot be distinguished by their arrival times, the photons were generated using a pulsed pump beam. The photons were then sent through narrow-bandwidth filters to produce a coherence time that is much longer than the length of the pump pulse. They then used a two-photon interferometry for analyzing the entanglement so that the quantum property could be recognized when it is transferred from one photon to the other.<ref name="Bouwmeester-1997">{{Cite journal |last1=Bouwmeester |first1=Dik |author-link1=Dirk Bouwmeester |last2=Pan |first2=Jian-Wei |last3=Mattle |first3=Klaus |last4=Eibl |first4=Manfred |last5=Weinfurter |first5=Harald |last6=Zeilinger |first6=Anton |date=1997-12-01 |title=Experimental quantum teleportation |journal=Nature |volume=390 |issue=6660 |pages=575–579 |doi=10.1038/37539 |arxiv=1901.11004 |bibcode=1997Natur.390..575B |s2cid=4422887}}</ref>

Photon 1 was polarized at 45° in the first experiment conducted by Zeilinger's group. Quantum teleportation is verified when both photons are detected in the <math>|\Psi^-\rangle_{12}</math> state, which has a probability of 25%. Two detectors, f1 and f2, are placed behind the beam splitter, and recording the coincidence will identify the <math>|\Psi^-\rangle_{12}</math> state. If there is a coincidence between detectors f1 and f2, then photon 3 is predicted to be polarized at a 45° angle. Photon 3 is passed through a polarizing beam splitter that selects +45° and −45° polarization. If quantum teleportation has happened, only detector d2, which is at the +45° output, will register a detection. Detector d1, located at the −45° output, will not detect a photon. If there is a coincidence between d2f1f2, with the 45° analysis, and a lack of a d1f1f2 coincidence, with −45° analysis, it is proof that the information from the polarized photon 1 has been teleported to photon 3 using quantum teleportation.<ref name="Bouwmeester-1997" />

=== Quantum teleportation over 143 km ===

Zeilinger's group developed an experiment using active feed-forward in real time and two free-space optical links, quantum and classical, between the Canary Islands of La Palma and Tenerife, a distance of over 143 kilometers. The results were published in 2012. In order to achieve teleportation, a frequency-uncorrelated polarization-entangled photon pair source, ultra-low-noise single-photon detectors and entanglement assisted clock synchronization were implemented. The two locations were entangled to share the auxiliary state:<ref name="Ma-2012" />

:<math>|\Psi^-\rangle_{23}=\frac{1}{\surd2}((|H\rangle_2|V\rangle_3)-(|V\rangle_2|H\rangle_3))</math>

La Palma and Tenerife can be compared to the quantum characters Alice and Bob. Alice and Bob share the entangled state above, with photon 2 being with Alice and photon 3 being with Bob. A third party, Charlie, provides photon 1 (the input photon) which will be teleported to Alice in the generalized polarization state:

:<math>|\phi\rangle_1=\alpha|H\rangle_1+\beta|V\rangle_1</math>

where the complex numbers <math>\alpha</math> and <math>\beta</math> are unknown to Alice or Bob.

Alice will perform a Bell-state measurement (BSM) that randomly projects the two photons onto one of the four Bell states with each one having a probability of 25%. Photon 3 will be projected onto <math>|\phi\rangle</math>, the input state. Alice transmits the outcome of the BSM to Bob, via the classical channel, where Bob is able to apply the corresponding unitary operation to obtain photon 3 in the initial state of photon 1. Bob will not have to do anything if he detects the <math>|\psi^-\rangle_{12}</math> state. Bob will need to apply a <math>\pi</math> phase shift to photon 3 between the horizontal and vertical component if the <math>|\psi^+\rangle_{12}</math> state is detected.<ref name="Ma-2012" />

The results of Zeilinger's group concluded that the average fidelity (overlap of the ideal teleported state with the measured density matrix) was 0.863 with a standard deviation of 0.038. The link attenuation during their experiments varied between 28.1&nbsp;dB and 39.0&nbsp;dB, which was a result of strong winds and rapid temperature changes. Despite the high loss in the quantum free-space channel, the average fidelity surpassed the classical limit of 2/3. Therefore, Zeilinger's group successfully demonstrated quantum teleportation over a distance of 143&nbsp;km.<ref name="Ma-2012" />

=== Quantum teleportation across the Danube River ===
In 2004, a quantum teleportation experiment was conducted across the Danube River in Vienna, a total of 600 meters. An 800-meter-long optical fiber wire was installed in a public sewer system underneath the Danube River, and it was exposed to temperature changes and other environmental influences. Alice must perform a joint Bell state measurement (BSM) on photon b, the input photon, and photon c, her part of the entangled photon pair (photons c and d). Photon d, Bob's receiver photon, will contain all of the information on the input photon b, except for a phase rotation that depends on the state that Alice observed. This experiment implemented an active feed-forward system that sends Alice's measurement results via a classical microwave channel with a fast electro-optical modulator in order to exactly replicate Alice's input photon. The teleportation fidelity obtained from the linear polarization state at 45° varied between 0.84 and 0.90, which is well above the classical fidelity limit of 0.66.<ref name="Danube2004" />

=== Deterministic quantum teleportation with atoms ===
Three qubits are required for this process: the source qubit from the sender, the ancillary qubit, and the receiver's target qubit, which is maximally entangled with the ancillary qubit. For this experiment, <chem>^{40}Ca+</chem> ions were used as the qubits. Ions 2 and 3 are prepared in the Bell state <math>|\psi^+\rangle_{23}=\frac{1}{\sqrt{2}}(|0\rangle_2|1\rangle_3+|1\rangle_2|0\rangle_3)</math>. The state of ion 1 is prepared arbitrarily. The quantum states of ions 1 and 2 are measured by illuminating them with light at a specific wavelength. The obtained fidelities for this experiment ranged between 73% and 76%. This is larger than the maximum possible average fidelity of 66.7% that can be obtained using completely classical resources.<ref>{{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. |title=Deterministic quantum teleportation with atoms |journal=Nature |date=June 2004 |volume=429 |issue=6993 |pages=734–737 |doi=10.1038/nature02570 |pmid=15201903 |bibcode=2004Natur.429..734R |s2cid=4397716 }}</ref>

=== Ground-to-satellite quantum teleportation ===
The quantum state being teleported in this experiment is <math>|\chi\rangle_1=\alpha|H\rangle_1+\beta|V\rangle_1</math>, where <math>\alpha</math> and <math>\beta</math> are unknown complex numbers, <math>|H\rangle</math> represents the horizontal polarization state, and <math>|V\rangle</math> represents the vertical polarization state. The qubit prepared in this state is generated in a laboratory in Ngari, Tibet. The goal was to teleport the quantum information of the qubit to the Micius satellite that was launched on August 16, 2016, at an altitude of around 500&nbsp;km. When a Bell state measurement is conducted on photons 1 and 2 and the resulting state is <math>|\phi^+\rangle_{12}=\frac{1}{\sqrt{2}}(|H\rangle_1|H\rangle_2+|V\rangle_1|V\rangle_2))</math>, photon 3 carries this desired state. If the Bell state detected is <math>|\phi^-\rangle_{12}=\frac{1}{\sqrt{2}}(|H\rangle_1|H\rangle_2-|V\rangle_1|V\rangle_2)</math>, then a phase shift of <math>\pi</math> is applied to the state to get the desired quantum state. The distance between the ground station and the satellite changes from as little as 500&nbsp;km to as large as 1,400&nbsp;km. Because of the changing distance, the channel loss of the uplink varies between 41&nbsp;dB and 52&nbsp;dB. The average fidelity obtained from this experiment was 0.80 with a standard deviation of 0.01. Therefore, this experiment successfully established a ground-to-satellite uplink over a distance of 500–1,400&nbsp;km using quantum teleportation. This is an essential step towards creating a global-scale quantum internet.<ref name="sat1400">{{cite journal |last1=Ren |first1=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 |last10=Li |first10=Li |last11=Yang |first11=Kui-Xing |last12=Han |first12=Xuan |last13=Yao |first13=Yong-Qiang |last14=Li |first14=Ji |last15=Wu |first15=Hai-Yan |last16=Wan |first16=Song |last17=Liu |first17=Lei |last18=Liu |first18=Ding-Quan |last19=Kuang |first19=Yao-Wu |last20=He |first20=Zhi-Ping |last21=Shang |first21=Peng |last22=Guo |first22=Cheng |last23=Zheng |first23=Ru-Hua |last24=Tian |first24=Kai |last25=Zhu |first25=Zhen-Cai |last26=Liu |first26=Nai-Le |last27=Lu |first27=Chao-Yang |last28=Shu |first28=Rong |last29=Chen |first29=Yu-Ao |last30=Peng |first30=Cheng-Zhi |last31=Wang |first31=Jian-Yu |last32=Pan |first32=Jian-Wei |title=Ground-to-satellite quantum teleportation |journal=Nature |date=7 September 2017 |volume=549 |issue=7670 |pages=70–73 |doi=10.1038/nature23675 |pmid=28825708 |arxiv=1707.00934 |bibcode=2017Natur.549...70R |s2cid=4468803 }}</ref>

=== Quantum teleportation over internet cables ===
Quantum teleportation has been demonstrated over fiber optic cables simultaneously carrying regular telecommunications traffic. This eliminates the need for separate, dedicated infrastructure for quantum networking and shows that quantum teleportation and classical communications can coexist on the same fiber optic cables.  A less crowded wavelength of light was used for the quantum signal and  special filters were required to reduce noise from other traffic.<ref>{{Cite journal |last1=Thomas |first1=Jordan M. |last2=Yeh |first2=Fei I. |last3=Chen |first3=Jim Hao |last4=Mambretti |first4=Joe J. |last5=Kohlert |first5=Scott J. |last6=Kanter |first6=Gregory S. |last7=Kumar |first7=Prem |date=2024-12-20 |title=Quantum teleportation coexisting with classical communications in optical fiber |url=https://opg.optica.org/optica/viewmedia.cfm?uri=optica-11-12-1700&html=true |journal=Optica |language=en |volume=11 |issue=12 |pages=1700 |doi=10.1364/OPTICA.540362 |issn=2334-2536|arxiv=2404.10738 }}</ref><ref>{{Cite web |title=First demonstration of quantum teleportation over busy Internet cables |url=https://news.northwestern.edu/stories/2024/12/first-demonstration-of-quantum-teleportation-over-busy-internet-cables/ |access-date=2024-12-23 |website=news.northwestern.edu |language=en}}</ref>{{Unreliable source?|date=December 2024|reason=primary source has no citations}}

=== Quantum teleportation with nonlinear sum frequency generation ===
In April 2025, researchers at the [[University of Illinois Urbana-Champaign]] achieved quantum teleportation with 94% [[Fidelity of quantum states|fidelity]] using a nanophotonic [[indium]]-[[gallium]]-[[phosphide]] platform to perform nonlinear sum frequency generation (SFG). This method mitigated multiphoton noise and boosted teleportation efficiency by a factor of 10,000 compared to prior SFG-based systems.<ref>{{cite journal |last1=Akin |first1=Joshua |last2=Zhao |first2=Yunlei |last3=Kwiat |first3=Paul G. |last4=Goldschmidt |first4=Elizabeth A. |last5=Fang |first5=Kejie |year=2025 |title=Faithful Quantum Teleportation via a Nanophotonic Nonlinear Bell State Analyzer |journal=Physical Review Letters |volume=134 |issue=16 |pages=160802 |doi=10.1103/PhysRevLett.134.160802 }}</ref>