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Quantum Teleportation
 Section 1 : General Introduction 

Old Version:

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 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 qubits of information between two (entangled) quanta, this has not yet been achieved between anything larger than molecules.

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 transferring a qubit from one location to another.

The term was coined by physicist Charles Bennett. The seminal paper first expounding the idea of quantum teleportation was published by C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters in 1993. Quantum teleportation was first realized in single photons, later being demonstrated in various material systems such as atoms, ions, electrons and superconducting circuits. The latest reported record distance for quantum teleportation is 1,400 km (870 mi) by the group of Jian-Wei Pan using the Micius satellite for space-based quantum teleportation.

New Version:

Quantum teleportation is a technique that is used to transfer quantum information from a sender to a receiver that is some arbitrary distance away from each other. While teleportation is commonly mentioned in science fiction works as a means to transfer physical objects from one location to the next, quantum teleportation is a means to communicate quantum information in a efficient and precise manner between a sender and receiver. One of the first scientific articles that specifically investigates quantum teleportation is " Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels" published by C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters in 1993 as they used dual communication methods to send/receive quantum information; an important note is that the sender of the information does not know the location of the recipient not the quantum state that will be transferred.

Experimental determinations of quantum teleportation have been made in information content- including photons, atoms, electrons, and superconducting circuits - as well as distance with 1,400 km (870 mi) being the longest distance of successful teleportation by the group of Jian-Wei Pan using the Micius satellite for space-based quantum teleportation.

Challenges faced in quantum teleportation include the no-cloning theorem which sets the limitation that creating an exact copy of a quantum state is impossible, the no-deleting theorem that states that quantum information cannot be destroyed,the size of the information teleported, the amount of quantum information the sender or receiver has before teleportation, and noise that the teleportation system has within its circuitry.

OLD VERSION

Non-technical summary[edit]
In matters relating to quantum 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. As of 2015, 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.

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 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 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 between the source and destination so as to reconstruct the qubit, or else the state of the destination qubit would not be known to the source, and any attempt to reconstruct the state would be random; this must be done over ordinary classical communication channels. The need for such classical channels may, at first, seem disappointing, and this explains why teleportation is limited to the speed of transfer of information, i.e., the speed of light. The main advantages is that Bell states can be shared using photons from lasers, and so teleportation is achievable through open space, i.e., without the need to send information through cables or optical fibers.

The quantum states of single atoms have been teleported. 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. The importance of teleporting the nuclear state is unclear:[citation needed] the nuclear state does affect[how?] 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?]

An important aspect of quantum information theory is entanglement, which imposes statistical correlations between otherwise distinct physical systems by creating or placing two or more separate particles into a single, shared quantum 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 (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 spaces and projection matrixes. 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.[original research?]

NEW VERSION

Non-technical summary
In matters relating to 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. (A traditional bit can only be measured as a 0 or 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 need for teleportation include: a sender, the information (a qubit), a traditional channel, a quantum channel, and a receiver. An interesting fact is that the sender does not need to know the exact contents of the information that is being sent. Keeping in mind the measurement postulate of quantum mechanics-when a measurement is made upon a quantum state, any subsequent measurements will "collapse" or that the observed state will be lost- creates an imposition within teleportation: If a sender makes a measurement on their information, the state could collapse when the receiver obtains the information since the state has changed from when the sender made the initial measurement.

For actual teleportation, it is required that an entangled quantum state or Bell 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 dependent on each other as they form a connection: if one particle is moved, the other particle will move along with it. Any changes that one particle of the entanglement undergoes, the other particle will also undergo that change, causing the entangled particles to act as one quantum state.

The sender will then prepare the particle (or information) in the qubit and combine with one of the entangled particles of the intermediate state, causing a change of the entangled quantum state. The changed state of the entangled particle is then sent to an analyzer that will measure this 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 entanglement 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 because of the no-communication theorem. The main advantage with this is that Bell states can be shared using photons from lasers making teleportation achievable through open space having no need to send information through physical cables or optical fibers.

Developments in Quantum Teleportation
While Quantum Teleportation is in an infantry stage, there are many aspects pertaining to teleportation that scientists are working to better understand or improve the process that include:

Higher Dimensions

Quantum Teleportation can improve the errors associated with fault tolerant quantum computation via an arrangement of logic gates. Experiments by D. Gottesman and I. L. Chuang have determined that a "Clifford hierarchy" gate arrangement which acts to enhance protection against environmental errors. Overall, a higher threshold of error is allowed with the Clifford hierarchy as the sequence of gates requires less resources that are needed for computation. While the more gates that are used in a quantum computer create more noise, the gates arrangement and use of teleportation in logic transfer can reduce this noise as it calls for less "traffic" that is compiled in these quantum networks. The more qubits used for a quantum computer, the more levels are added to a gate arrangement, with the diagonalization of gate arrangement varying in degree. Higher dimension analysis involves the higher level gate arrangement of the Clifford hierarchy.

Information Size/Variations

Considering the previously mentioned requirement of an intermediate entangled state for quantum teleportation, there needs to be consideration placed on to the purity of this state for information quality. A protection that has been developed involves the use of continuous variable information (rather than a typical discrete variable) creating a superimposed coherent intermediate state. This involves making a phase shift in the received information and then adding a mixing step upon reception using a preferred state, which could be an odd or even coherent state, that will be "conditioned to the classical information of the sender" creating a two mode state that contains the originally sent information.

There have also been developments with teleporting information between systems that already have quantum information in them. Experiments done by Feng, Xu, Zhou et. al have demonstrated that teleportation of a qubit to a photon that already has a qubit worth of information is possible due to using a optical qubit-ququart entangling gate. This quality can increase computation possibilities as calculations can be done based on previously stored information allowing for improvements on past calculations.