Quantum teleportation From Wikipedia, the free encyclopedia 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 superluminal transport or communication of classical bits. It also cannot be used to make copies of a system, as this violates the no-cloning theorem. Although the name is inspired by the teleportation commonly used in fiction, current technology provides no possibility of anything resembling the fictional form of teleportation. While it is possible to teleport one or more qubits of information between two (entangled) atoms,[1][2][3] this has not yet been achieved between molecules or anything larger. One may think of teleportation either as a kind of transportation, or as a kind 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.[5] Since then, quantum teleportation has been realized in various physical systems. Presently, the record distance for quantum teleportation is 143 km (89 mi) with photons,[6] and 21 m with material systems.[7] In August 2013, the achievement of "fully deterministic" quantum teleportation, using a hybrid technique, was reported.[8] On 29 May 2014, scientists announced a reliable way of transferring data by quantum teleportation. Quantum teleportation of data had been done before but with highly unreliable methods.[9][10] Contents [hide] 1 Non-technical summary 2 Protocol 3 Experimental results and records 4 Formal presentation 5 Alternative notations 6 Entanglement swapping 7 N-state particles 8 Logic gate teleportation 8.1 General description 8.2 Further details 9 Local explanation of the phenomenon 10 See also 11 References 12 External links Non-technical summary[edit] It is known, from axiomatizations of quantum mechanics (such as categorical quantum mechanics), that the universe is fundamentally composed of two things: bits and qubits.[11][12] Bits are units of information, and are commonly represented using zero or one, true or false. These bits are sometimes called "classical" bits, to distinguish them from quantum bits, or qubits. Qubits also encode a type of information, called quantum information, which differs sharply from "classical" information. For example, a qubit cannot be used to encode a classical bit (this is the content of the no-communication theorem). Conversely, classical bits cannot be used to encode qubits: the two are quite distinct, and not inter-convertible. Qubits differ from classical bits in dramatic ways: they cannot be copied (the no-cloning theorem) and they cannot be 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, only photons and single atoms have been teleported; molecules have not, nor does this even seem likely in the upcoming years, as the technology remains daunting. Specific distance and quantity records are stated below. 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. Single atoms have been teleported,[1][2][3] although not in the science-fiction sense. 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. 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. The quantum world is strange and unusual; so, aside from no-cloning and no-deleting, there are other oddities. For example, quantum correlations arising from Bell states seem to be instantaneous (the Alain Aspect experiments), whereas classical bits can only be transmitted slower than the speed of light (quantum correlations cannot be used to transmit classical bits; again, this is the no-communication theorem). Thus, teleportation, as a whole, can never be superluminal, as a qubit cannot be reconstructed until the accompanying classical bits arrive. 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.