Quantum entanglement From Wikipedia, the free encyclopedia Spontaneous parametric down-conversion process can split photons into type II photon pairs with mutually perpendicular polarization. Quantum mechanics \Delta x\cdot\Delta p_x \geqslant \frac{\hbar}{2} Uncertainty principle Introduction Glossary History Background[show] Fundamentals[show] Experiments[show] Formulations[show] Equations[show] Interpretations[show] Advanced topics[show] Scientists[show] v t e Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently – instead, a quantum state may be given for the system as a whole. Measurements of physical properties such as position, momentum, spin, polarization, etc. performed on entangled particles are found to be appropriately correlated. For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise. Because of the nature of quantum measurement, however, this behavior gives rise to effects that can appear paradoxical: any measurement of a property of a particle can be seen as acting on that particle (e.g. by collapsing a number of superimposed states); and in the case of entangled particles, such action must be on the entangled system as a whole. It thus appears that one particle of an entangled pair "knows" what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances. Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky and Nathan Rosen,[1] describing what came to be known as the EPR paradox, and several papers by Erwin Schrödinger shortly thereafter.[2][3] Einstein and others considered such behavior to be impossible, as it violated the local realist view of causality (Einstein referred to it as "spooky action at a distance"),[4] and argued that the accepted formulation of quantum mechanics must therefore be incomplete. Later, however, the counterintuitive predictions of quantum mechanics were verified experimentally.[5] Experiments have been performed involving measuring the polarization or spin of entangled particles in different directions, which – by producing violations of Bell's inequality – demonstrate statistically that the local realist view cannot be correct. This has been shown to occur even when the measurements are performed more quickly than light could travel between the sites of measurement: there is no lightspeed or slower influence that can pass between the entangled particles.[6] Recent experiments have measured entangled particles within less than one part in 10,000 of the light travel time between them.[7] According to the formalism of quantum theory, the effect of measurement happens instantly.[8][9] It is not possible, however, to use this effect to transmit classical information at faster-than-light speeds[10] (see Faster-than-light → Quantum mechanics). Quantum entanglement is an area of extremely active research by the physics community, and its effects have been demonstrated experimentally with photons, electrons, molecules the size of buckyballs,[11][12] and even small diamonds.[13][14] Research is also focused on the utilization of entanglement effects in communication and computation. Contents [hide] 1 History 2 Concept 2.1 Meaning of entanglement 2.2 Apparent paradox 2.3 The hidden variables theory 2.4 Violations of Bell's inequality 2.5 Other types of experiment 2.6 Special Theory of Relativity 3 Non-locality and hidden variables 4 Quantum mechanical framework 4.1 Pure states 4.2 Ensembles 4.3 Reduced density matrices 4.4 Entropy 4.5 Quantum field theory 5 Applications 5.1 Entangled states 5.2 Methods of creating entanglement 5.3 Testing a system for entanglement 6 See also 7 References 8 Further reading 9 External links History[edit] May 4, 1935 New York Times article headline regarding the imminent EPR paper. The counterintuitive predictions of quantum mechanics about strongly correlated systems were first discussed by Albert Einstein in 1935, in a joint paper with Boris Podolsky and Nathan Rosen.[1] In this study, they formulated the EPR paradox (Einstein, Podolsky, Rosen paradox), a thought experiment that attempted to show that quantum mechanical theory was incomplete. They wrote: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete."[1] However, they did not coin the word entanglement, nor did they generalize the special properties of the state they considered. Following the EPR paper, Erwin Schrödinger wrote a letter (in German) to Einstein in which he used the word Verschränkung (translated by himself as entanglement) "to describe the correlations between two particles that interact and then separate, as in the EPR experiment."[15] He shortly thereafter published a seminal paper defining and discussing the notion, and terming it "entanglement." In the paper he recognized the importance of the concept, and stated:[2] "I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought." Like Einstein, Schrödinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the theory of relativity.[16] Einstein later famously derided entanglement as "spukhafte Fernwirkung"[17] or "spooky action at a distance." The EPR paper generated significant interest among physicists and inspired much discussion about the foundations of quantum mechanics (perhaps most famously Bohm's interpretation of quantum mechanics), but relatively little other published work. So, despite the interest, the flaw in EPR's argument was not discovered until 1964, when John Stewart Bell proved that one of their key assumptions, the principle of locality, was not consistent with the hidden variables interpretation of quantum theory that EPR purported to establish. Specifically, he demonstrated an upper limit, seen in Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and he showed that quantum theory predicts violations of this limit for certain entangled systems.[18] His inequality is experimentally testable, and there have been numerous relevant experiments, starting with the pioneering work of Freedman and Clauser in 1972[19] and Aspect's experiments in 1982.[20] They have all shown agreement with quantum mechanics rather than the principle of local realism. However, the issue is not finally settled, for each of these experimental tests has left open at least one loophole by which it is possible to question the validity of the results. The work of Bell raised the possibility of using these super strong correlations as a resource for communication. It led to the discovery of quantum key distribution protocols, most famously BB84 by Bennet and Brassard and E91 by Artur Ekert. Although BB84 does not use entanglement, Ekert's protocol uses the violation of a Bell's inequality as a proof of security. David Kaiser of MIT mentioned in his book, How the Hippies Saved Physics, that the possibilities of instantaneous long-range communication derived from Bell's theorem stirred interest among hippies, psychics, and even the CIA, with the counter-culture playing a critical role in its development toward practical use.[21]