Editing Quantum teleportation (section)

==Non-technical summary==

In matters relating to [[Quantum information|quantum]] [[information theory]], it is convenient to work with the simplest possible unit of information: the two-state system of the [[qubit]]. The qubit functions as the quantum analog of the classic computational part, the [[bit]], as it can have a measurement value of ''both'' a 0 ''and'' a 1, whereas the classical bit can only be measured as a 0 ''or'' a 1. The quantum two-state system seeks to transfer quantum information from one location to another location without losing the information and preserving the quality of this information. This process involves moving the information ''between carriers'' and not movement of the ''actual carriers'', similar to the traditional process of communications, as two parties remain stationary while the information (digital media, voice, text, etc.) is being transferred, contrary to the implications of the word "teleport". The main components needed for teleportation include a sender, the information (a qubit), a traditional channel, a quantum channel, and a receiver. The sender does not need to know the exact contents of the information being sent. The measurement postulate of quantum mechanics{{snd}}when a measurement is made upon a quantum state, any subsequent measurements will "collapse" or that the observed state will be lost{{snd}}creates an imposition within teleportation: if a sender measures their information, the state could collapse when the receiver obtains the data since the state had changed from when the sender made the initial measurement and in so making it different.

[[File:Quantum teleportation - interactive simulation in Virtual Lab by Quantum Flytrap.png|thumb|upright=2|An interactive simulation of quantum teleportation in the Virtual Lab by Quantum Flytrap,<ref>{{cite journal |last1=Migdał |first1=Piotr |last2=Jankiewicz |first2=Klementyna |last3=Grabarz |first3=Paweł |last4=Decaroli |first4=Chiara |last5=Cochin |first5=Philippe |year=2022 |title=Visualizing quantum mechanics in an interactive simulation – Virtual Lab by Quantum Flytrap |journal=Optical Engineering |volume=61 |issue=8 |pages=081808 |arxiv=2203.13300 |bibcode=2022OptEn..61h1808M |doi=10.1117/1.OE.61.8.081808}}</ref> [https://lab.quantumflytrap.com/lab/quantum-teleportation available online]. In this optical setup, qubits are encoded using the [[Polarization_(waves)|polarization of light]]. Teleportation occurs between the source photon (set to an arbitrary state) and one photon from an entangled pair. A Bell pair measurement is performed on the source photon and one entangled photon using a [[Controlled_NOT_gate|quantum CNOT gate]], yielding two bits of classical information. The target photon is then rotated with two controllable [[Waveplate|waveplates]] based on this information.]]

For actual teleportation, it is required that an [[Entangled state|entangled quantum state]] be created for the qubit to be transferred. Entanglement imposes statistical correlations between otherwise distinct physical systems by creating or placing two or more separate particles into a single, shared quantum state. This intermediate state contains two particles whose quantum states are related to each other: measuring one particle's state provides information about the measurement of the other particle's state. 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]]. This is known as the [[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.

The sender will combine the particle, whose information is teleported, with one of the entangled particles, causing a change of the overall entangled quantum state. Of this changed state, the particles in the receiver's possession are then sent to an analyzer that will measure the change of the entangled state. The "change" measurement will allow the receiver to recreate the original information that the sender had, resulting in the information being teleported or carried between two people that have different locations. Since the initial quantum information is "destroyed" as it becomes part of the entangled state, the no-cloning theorem is maintained as the information is recreated from the entangled state and not copied during teleportation.

The [[quantum channel]] is the communication mechanism that is used for all quantum information transmission and is the channel used for teleportation (relationship of quantum channel to traditional communication channel is akin to the qubit being the quantum analog of the classical bit). However, in addition to the quantum channel, a traditional channel must also be used to accompany a qubit to "preserve" the quantum information. When the change measurement between the original qubit and the entangled particle is made, the measurement result must be carried by a traditional channel so that the quantum information can be reconstructed and the receiver can get the original information. Because of this need for the traditional channel, the speed of teleportation can be no faster than the speed of light (hence the [[no-communication theorem]] is not violated). The main advantage with this is that Bell states can be shared using [[photon]]s from [[laser]]s, making teleportation achievable through open space, as there is no need to send information through physical cables or optical fibers.

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. 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 |bibcode=2004Natur.429..737B |doi=10.1038/nature02608 |pmid=15201904 |s2cid=1608775}}</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 name="Pirandola-2015">{{cite journal |last1=Pirandola |first1=S. |last2=Eisert |first2=J. |last3=Weedbrook |first3=C. |last4=Furusawa |first4=A. |last5=Braunstein |first5=S. L. |year=2015 |title=Advances in quantum teleportation |journal=Nature Photonics |volume=9 |issue=10 |pages=641–652 |arxiv=1505.07831 |bibcode=2015NaPho...9..641P |doi=10.1038/nphoton.2015.154 |s2cid=15074330}}</ref>

Understanding quantum teleportation requires a good grounding in finite-dimensional [[linear algebra]], [[Hilbert space]]s and [[projection matrix|projection matrices]]. 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.