Editing Quantum teleportation (section)

== 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 |s2cid=9684671}}</ref>
 
The generalization to infinite-dimensional so-called [[Continuous-variable quantum information|continuous-variable systems]] was proposed by Braunstein and Kimble<ref name="BrKi98">{{cite journal |last1=Braunstein |first1=Samuel L. |last2=Kimble |first2=H. J. |title=Teleportation of Continuous Quantum Variables |journal=Physical Review Letters |date=26 January 1998 |volume=80 |issue=4 |pages=869–872 |doi=10.1103/PhysRevLett.80.869 |bibcode=1998PhRvL..80..869B |url=https://resolver.caltech.edu/CaltechAUTHORS:BRAprl98 }}</ref> and led 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 |pmid=9784123 |s2cid=14269209 }}</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 |author=Dür |first1=W. |last2=Cirac |first2=J. I. |name-list-style=and |date=2000 |title=Multiparty teleportation |journal=J. Mod. Opt. |volume=47 |issue=2–3 |pages=247–255 |bibcode=2000JMOp...47..247D |doi=10.1080/09500340008244039 |s2cid=216116503}}</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 |s2cid=5170837}}</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.