**Quantum teleportation**

is a process by 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. It also cannot be used to make copies of a system, as this violates the no-cloning theorem. While it has proven possible to teleport one or more qubits of information between two (entangled) atoms,

this has not yet been achieved between molecules or anything larger.

Although the name is inspired by the teleportation commonly used in fiction, there is no relationship outside the name, because quantum teleportation concerns only the transfer of information. Quantum teleportation is not a form of transportation, but of communication; it provides a way of transporting a qubit from one location to another, without having to move a physical particle along with it.

The seminal paper

^{[4]}
first expounding the idea was published by C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters in 1993.

^{[}
Since then, quantum teleportation was first realized with single photons

^{[}and later demonstrated with various material systems such as atoms, ions, electrons and superconducting circuits. The record distance for quantum teleportation is 143 km (89 mi).^{}

In October 2015, scientists from the Kavli Institute of Nanoscience reported that the Quantum nonlocality phenomenon is supported at the 96% confidence level based on a "loophole-free Bell test" study.

^{[8]}^{[9]}These results were confirmed by two studies with statistical significance over 5 standard deviations which were published in December 2015.## Non-technical summary

In matters relating to quantum or classical 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 that a qubit is normally attached to. 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. However, as of 2013

^{[update]}, only photons and single atoms have been employed as information bearers.
The movement of qubits does require the movement of "things"; in particular, 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 link to be established, as two classical bits must be transmitted to accompany each qubit. The need for such links may, at first, seem disappointing; however, this is not unlike ordinary communications, which requires wires, radios or lasers. What's more, Bell states are most easily shared using photons from lasers, and so teleportation could be done, in principle, through open space.

The quantum states of single atoms have been teleported.

^{[1]}^{[2]}^{[3]}An atom consists of several parts: the qubits in the electronic state or electron shells surrounding the atomic nucleus, the qubits in the nucleus itself, and, finally, the electrons, protons and neutrons making up the atom. Physicists have teleported the qubits encoded in the electronic state of atoms; they have not teleported the nuclear state, nor the nucleus itself. It is therefore false to say "an atom has been teleported". It has not. The quantum state of an atom has. 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 nuclear state is unclear: nuclear state does affect the atom, e.g. in hyperfine splitting, but whether such state would need to be teleported in some futuristic "practical" application is debatable.
An important aspect of quantum information theory is entanglement, which imposes statistical correlations between otherwise distinct physical systems. 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.

The proper description of quantum teleportation requires a basic mathematical toolset, which, although complex, is not out of reach of advanced high-school students, and indeed becomes accessible to college students with a good grounding in finite-dimensional linear algebra. In particular, the theory of Hilbert spaces and projection matrixes is heavily used. A qubit is described using a two-dimensional complex number-valued vector space (a Hilbert space); the formal manipulations given below do not make use of anything much more than that. Strictly speaking, a working knowledge of quantum mechanics is not required to understand the mathematics of quantum teleportation, although without such acquaintance, the deeper meaning of the equations may remain quite mysterious.

Protocol

The prerequisites for quantum teleportation are a qubit that is to be teleported, a conventional communication channel capable of transmitting two classical bits (i.e., one of four states), and means of generating an entangled EPR pair of qubits, transporting each of these to two different locations, A and B, performing a Bell measurement on one of the EPR pair qubits, and manipulating the quantum state of the other of the pair. The protocol is then as follows:

- An EPR pair is generated, one qubit sent to location A, the other to B.
- At location A, a Bell measurement of the EPR pair qubit and the qubit to be teleported (the quantum state ) is performed, yielding 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, due to speed-of-light considerations.)
- As a result of the measurement performed at location A, the EPR pair qubit at location B is in one of four possible states. Of these four possible states, one is identical to the original quantum state , and the other three are closely related. Which of these four possibilities actually obtains is encoded in the two classical bits. Knowing this, the qubit at location B is modified in one of three ways, or not at all, to result in a qubit identical to , the qubit that was chosen for teleportation.

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