Editing Quantum teleportation (section)

==Protocol==
[[File:Quantum teleportation diagram.PNG|upright=1.35|thumb |right| Diagram for quantum teleportation of a photon]]

The resources required for quantum teleportation are a [[communication channel]] capable of transmitting two classical bits, a means of generating an entangled [[Bell state]] of qubits and distributing to two different locations, performing a [[Bell measurement]] on one of the Bell state qubits, and manipulating the quantum state of the other qubit from the pair. Of course, there must also be some input qubit (in the quantum state <math>|\phi \rangle</math>) to be teleported. The [[protocol (computing)|protocol]] is then as follows:

# A Bell state is generated with one qubit sent to location A and the other sent to location B.
# A Bell measurement of the Bell state qubit and the qubit to be teleported (<math>|\phi \rangle</math> ) is performed at location A. This yields 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 since information transfer is limited by the speed of light.)
# As a result of the measurement performed at location A, the Bell state 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. The identity of the state actually obtained is encoded in two classical bits and sent to location B. The Bell state qubit at location B is then modified in one of three ways, or not at all, which results in a qubit identical to <math>|\phi \rangle</math>, the state of the qubit that was chosen for teleportation.

It is worth noticing that the above protocol assumes that the qubits are individually addressable, meaning that 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 Bell state. This can be made by addressing the internal degrees of freedom of the qubits (e.g., spins or polarisations) by spatially localized measurements performed in separated regions A and B where the two spatially overlapping, indistinguishable qubits can be found.<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| bibcode=2018PhRvL.120x0403L| s2cid=49562954}}</ref> This theoretical prediction has been then verified experimentally via polarized photons in a quantum optical setup.<ref name="Sunetal_Teleportation">{{cite journal |last1=Sun |first1=K. |last2=Wang |first2=Y. |last3=Liu |first3=Z.-H. |last4=Xu |first4=X.-Y. |last5=Xu |first5=J.-S. |last6=Li |first6=C.-F. |last7=Guo |first7=G.-C. |last8=Castellini |first8=A. |last9=Nosrati |first9=F. |last10=Compagno |first10=G. |last11=Lo Franco |first11=R. |title=Experimental quantum entanglement and teleportation by tuning remote spatial indistinguishability of independent photons |journal=Optics Letters |date=2020 |volume=45 |issue=23 |pages=6410–6413 |doi=10.1364/OL.401735 |pmid=33258824 |arxiv=2003.10659 |bibcode=2020OptL...45.6410S |hdl=10447/449875 |s2cid=227245593 }}</ref>