Quantum Entanglement and Teleportation

Quantum Entanglement and Teleportation (1900s)

At first glance, the collapse approach to quantum mechanics appears to contradict Einstein's theory of special relativity, which states that nothing can travel faster than the speed of light. This is because of an effect called entanglement, a term coined by Schrodinger in 1935. Schrodinger stated that if two quanta "come into a situation in which they influence one another and then again separate themselves, then there regularly arises that which I just called entanglement of our knowledge of the two bodies" (Schrodinger, pp.555).

Entanglement can be illustrated with examples of any observable property, including spin. Two entangled electrons must possess opposite spins. Spin can be measured at any angle and is usually described as being 'up' or 'down' or 'left' or 'right' when measured in horizontal or vertical planes. It was soon discovered that measuring the spin of one member of an entangled pair of electrons instantaneously determines the spin of the other, even if it is very far away. Schrodinger showed that there is no equation that describes the state of a single entangled electron and the overall spin-state cannot be equated with any combination of the individual states. Entangled electrons cannot really be said to be individuals.

Einstein did not like the collapse approach because it suggests that instantaneous action at a distance occurs when the wavefunction collapses. Einstein, along with American physicist Boris Podolsky and American-Israeli physicist Nathan Rosen, presented what has become known as the EPR paper in 1935, as part of an on-going debate with Bohr, (Einstein et al., pp.777). The EPR paper states that quantum mechanics is incomplete. There must be hidden variables which explain why there is no need for instantaneous travel, something Einstein famously referred to as "spooky actions at a distance" (Einstein, 1971).

Einstein tried to think of a way to ascribe observable properties to a system without measuring it directly. He realised that if the position of one electron was measured then he could also determine its momentum by measuring that of the second electron. This would contradict Heisenberg's statement that two non-commuting variables cannot be known simultaneously. Einstein hoped that the effects of entanglement could be explained if the motion of the photons were somehow guided by the electromagnetic field (Wigner, pp.262).

In 1964, Northern Irish physicist John Stewart Bell devised a way to theoretically test for a hidden variable theory such as Einstein's (Bell, 1964, pp.195-200). Belgium mathematician Simon Kochen and Swiss mathematician Ernst Specker showed that Einstein's hidden variable theory could not be correct in 1967 (Kochen and Specker, pp.59-87) and in 1972, the first experimental test was performed by American physicists Stuart Freedman and John Clauser (Freedman and Clauser, pp.938-941). They showed that Einstein was wrong, quantum mechanics does appear to exhibit instantaneous action at a distance. This was verified by French physicist Alain Aspect in 1982 (Aspect et al., 1982). Aspect showed that if information is sent though spacetime, then it must travel faster than the speed of light. An experiment in 2008 showed that it must travel at least ten thousand times this speed (Salart et al., pp.864).

Quantum 'action at a distance' is similar to Newtonian instantaneous action at a distance but it differs in two respects. Firstly, quantum action at a distance does not have the symmetry that gravitational force has because in quantum mechanics the first measurement always determines the outcome of the second, they are not of mutual influence. Secondly, in quantum mechanics the effects are irrespective of distance, whereas in the Newtonian model gravitational force decreases proportionally to the square of the distance between objects. A better interpretation may be quantum holism. Holism refers to the idea that aspects of a state are not determined by its constituent parts but by the state as a whole.

Quantum entanglement will one day allow us to devise unbreakable encryptions but it does not allow for any meaningful information to be sent faster than the speed of light. This is because we cannot control what information is sent.

In 1952, American physicist David Bohm suggested that there is no need for instantaneous action at a distance if the collapse approach is incorrect and there is no collapse of the wavefunction (Bohm, pp.166). Bohm devised a hidden variable theory known as Bohmian mechanics. This suggests that quantum objects follow paths which are determined by a guiding equation, an idea which was first devised by French physicist Louis de Broglie in 1927 and was supported by Bell (Bell, 2004, pp.160).

In 1993, American physicist Charles Bennett and a team of researchers at IBM showed that the effects of quantum entanglement allow for teleportation as long as the object travels at the speed of light and the original copy is destroyed (Bennett et al., pp.1895-1899). This was first demonstrated in 1998 by physicists in Europe and America who teleported a photon about one metre across a room (Furusawa et al., pp.706-709). A laser beam was successfully teleported in 2002 (Treps et al., 2002).

References

Aspect, A., Grangier, P. and Roger, G., 1982, 'Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities', Physical Review Letters, Vol.49, pp.91-94 and Aspect, A., Dalibard J. and Roger G., 1982, 'Experimental Test of Bell's Inequalities Using Time-Varying Analyzers', Physical Review Letters, Vol. 49, pp.1804-1807

Bell, J.S., 1964, 'On the Einstein-Poldolsky-Rosen paradox', Physics, Vol.1

Bell, J. S., 2004, 'Speakable and unspeakable in quantum mechanics: collected papers on quantum philosophy', Cambridge University Press, Cambridge

Bennett, C.H. et al., 1993, 'Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels', Physical Review Letters, Vol.70

Bohm, D., 1952, 'A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables, I and II', Physical Review, Vol.85

Einstein, A., 1971, 'Letter to Max Born written in 1947', The Born-Einstein Letters; Correspondence between Albert Einstein and Max and Hedwig Born from 1916 to 1955, Walker, New York

Einstein, A., Podolsky, B. and Rosen, N., 1935, 'Can quantum-mechanical description of physical reality be considered complete?', Physical Review, Vol.47

Freedman, S.J. and Clauser, J.F., 1972, 'Experimental test of local hidden-variable theories', Physical Review Letters, Vol.28

Furusawa, A., et al., 1998, 'Unconditional Quantum Teleportation', Science, Vol.282

Kochen, S. and Specker, E.P., 1967, 'The problem of hidden variables in quantum mechanics', Journal of Mathematics and Mechanics, Vol.17

Salart, D., Baas, A., Branciard, C., Nicolas Gisin, N. and Zbinden, H., 2008, 'Testing the speed of "spooky action at a distance"', Nature, Vol.454, pp.861-864

Schrodinger, E., 1935, 'Discussion of Probability Relations Between Separated Systems', Proceedings of the Cambridge Philosophical Society, Vol.31, pp.555-563

Treps, N., et al., 2002, 'Surpassing the Standard Quantum Limit for Optical Imaging Using Nonclassical Multimode Light', Physical Review Letters, Vol.88

Wigner, E. P., 1983, 'Interpretation of Quantum Mechanics', Quantum Theory and Measurement, Wheeler, J. A. and Zurek, W. H. (eds.), Princeton University Press, Princeton